Embedded Actuators, Sensors, and Structure in Adaptive and ...btrease/share/trease-prelim-proposal.pdf · Embedded Actuators, Sensors, and Structure in Adaptive and Distributed Compliant

Dissertation Proposal

Embedded Actuators, Sensors, and Structure in Adaptive and Distributed Compliant Systems

- An Engineering Analogue to the Musculo-Skeletal-Nervous System -

Brian Patrick Trease

May 23, 2005

The University of Michigan Dept. of Mechanical Engineering

Ann Arbor, MI 48109

Thesis Committee Sridhar Kota, Chair

Brent Gillespie Kazu Saitou

Paul Webb

ABSTRACT Electromechanical systems are generally comprised of separate, nearly rigid components, with relative motion occurring at discrete locations, e.g. joints. In contrast, many designs in nature develop as one connected whole, with flexure distributed throughout the material. In particular, 90% of all living creatures, the invertebrates, rely on compliance for motion and force transmission. Compliant mechanisms are a relatively new class of mechanisms that use engineered elasticity of the constituent elements to transmit motion and/or force. Since flexure is permitted in these mechanisms, they lend themselves to integration with unconventional actuation schemes including thermal, electrostatic, piezo-electric, artificial muscle, and shape-memory-alloy actuators. Here I propose automated synthesis of compliant systems, defined as joint-less monolithic mechanisms embedded with actuators and sensors. I will develop methods for optimal topology, size, and shape of monolithic elastic mechanisms with integrated synthesis of sensors and actuators, for maximum energy efficiency and adaptive performance. The proposed research lays a scientific foundation and a mathematical framework for systematic synthesis of biomimetic designs by addressing issues fundamental to a new paradigm of distributed sensing within a compliant active structure. The design methods and the applications of compliant mechanisms apply to many domains in micro, meso, and macro scales. Engineers and nature both prefer robustness, adaptability, and autonomy in their ‘designs’, yet no paradigm exists for the structured practice of biomimicry. I recognize that the goal of biomimetics is still an open research question to be explored. The motivation for this proposal is to address fundamental research issues in compliant mechatronics towards development of a systematic synthesis methodology and a practical demonstration. Through this proposed research, I will investigate basic research issues including (i) optimal layout of the structure, actuators and sensors and (ii) the groundwork for embedded controls in adaptive compliant systems. I propose a generalized synthesis scheme in which the design requirements are captured in a mathematical form to transform an initial grid of elements into an optimal layout of elastic beams, sensors, and actuators. I will employ genetic algorithms for their ability to find global optima for discrete, nonlinear problems. In addition, the actuators will be mathematically characterized by their operational load-deflection curves and active stiffness, in contrast to the practice of simple point-load representation. The broader impact of the proposed research is: (i) high performance designs of several products ranging from autonomous robots, surgical instruments, adaptive wings, structural health monitoring systems, and adaptive orthoses, (ii) a deeper insight and appreciation of biological systems, and (iii) advancement of the state of the art to the next level of sophistication through creation of monolithic systems with embedded-and-distributed sensing and actuation, in contrast to individually designed structures, actuators, and sensors.

Brian Trease, University of Michigan Page 2 of 63 6/9/2005

TABLE OF CONTENTS

ABSTRACT .................................................................................................................................................................2 1. INTRODUCTION..............................................................................................................................................5

1.1. MOTIVATION...............................................................................................................................................5 1.2. PERSONAL MOTIVATION .............................................................................................................................6 1.3. APPLICATIONS.............................................................................................................................................7 1.4. BENEFITS.....................................................................................................................................................7

2. PROBLEM STATEMENT / HYPOTHESIS...................................................................................................8 2.1. VISION OF AN ADAPTIVE COMPLIANT SYSTEM............................................................................................8

2.1.1. Embedded Actuation ............................................................................................................................10 2.1.2. Embedded Sensing ...............................................................................................................................11

2.2. THEORETICAL FRAMEWORK FOR THE PROPOSED STUDY............................................................................11 3. SCOPE ..............................................................................................................................................................12 4. BACKGROUND / LITERATURE REVIEW ...............................................................................................12

4.1. COMPLIANT MECHANISMS ........................................................................................................................12 4.1.1. Distributed Compliance.......................................................................................................................13 4.1.2. Synthesis Methodology ........................................................................................................................14 4.1.3. Current Research Directions and Labs ...............................................................................................14

4.2. LOAD PATH METHOD ................................................................................................................................15 4.3. RELATED WORK (ACTUATOR ARCHITECTURE).........................................................................................17

5. BASIC RESEARCH ISSUES..........................................................................................................................19 6. RESEARCH PLAN OVERVIEW ..................................................................................................................19

6.1. SPECIFIC RESEARCH ACTIVITIES ...............................................................................................................22 7. PRELIMINARY WORK AND RESULTS....................................................................................................22

7.1. STUDIES WITH GROUND STRUCTURE APPROACH AND GENETIC ALGORITHMS..........................................22 7.2. TEST STUDY PARAMETERS........................................................................................................................26 7.3. TEST STUDY RESULTS ...............................................................................................................................30 7.4. CURRENT CHALLENGES: DENSE STRUCTURES ..........................................................................................33 7.5. MODIFIED GENETIC REPRODUCTION.........................................................................................................35 7.6. THE QUESTION OF CONVERGENCE ............................................................................................................38

8. DETAILED RESEARCH PLAN....................................................................................................................39 8.1. DESIGN ALGORITHMS ...............................................................................................................................39

8.1.1. Task Definition.....................................................................................................................................39 8.1.2. Problem Discretization ........................................................................................................................40 8.1.3. Nonlinear Topology Optimization and Synthesis.................................................................................43 8.1.4. Objective Functions .............................................................................................................................44 8.1.5. Constraints...........................................................................................................................................44 8.1.6. Cross-over strategies ...........................................................................................................................45 8.1.7. Genetic Engineering ............................................................................................................................45 8.1.8. Size / Shape Optimization ....................................................................................................................45 8.1.9. Finite Element Confirmation ...............................................................................................................46 8.1.10. Physical Prototype ..........................................................................................................................46 8.1.11. Integration of Supplementary Concepts..........................................................................................46

8.2. ACTUATION...............................................................................................................................................50 8.2.1. Actuation Selection and Evaluation.....................................................................................................51 8.2.2. Characterization ..................................................................................................................................51


8.2.3. Commercial Artificial Muscle Actuators .............................................................................................52 8.3. BIO-DISCUSSION – “BIOMIMETICS”...........................................................................................................52

8.3.1. Observations & Comparisons..............................................................................................................52 8.3.2. Inspiration via Direct Borrowing ........................................................................................................53 8.3.3. Inspiration via Objective / Task...........................................................................................................54 8.3.4. Genetic Algorithms ..............................................................................................................................55 8.3.5. Idea of an integrated Musculo-Skeletal-Ligament-(Nervous) System..................................................55 8.3.6. Biological Evidence of Distributed Actuation .....................................................................................55

9. CONFIRMATION OF RESULTS .................................................................................................................56 10. CASE STUDIES ..........................................................................................................................................56

10.1. VARIABLE STIFFNESS ................................................................................................................................56 10.2. ADAPTIVE ORTHOTIC AND PROSTHETIC DEVICES .....................................................................................58 10.3. SHAPE-CHANGING WINGS AND FINS...........................................................................................................58

11. RESEARCH TIMELINE ...........................................................................................................................58 12. POTENTIAL CONTRIBUTIONS.............................................................................................................59 13. SUMMARY .................................................................................................................................................60 14. REFERENCES............................................................................................................................................61

14.1. GENERAL...................................................................................................................................................61 14.2. COMPLIANT MECHANISMS ........................................................................................................................61 14.3. RELATED WORK........................................................................................................................................62 14.4. LOAD PATH METHOD ................................................................................................................................62 14.5. BIOLOGY ...................................................................................................................................................63


1. Introduction

1.1. Motivation The research topic I propose is a new methodology for the synthesis of distibuted

compliant systems with embedded actuation. The basic premise of a compliant system is the

integration of motion/force transmission via elastic deformation with embedded actuation and

sensing. The motion and force transmission problem has been researched for more than a decade

at the University of Michigan. A new field of jointless monolithic devices called Compliant

Mechanisms (CM’s) has been established, with Michigan’s Compliant Systems Design

Laboratory (CSDL) authoring numerous papers and software on the topic. These devices use

flexure and deformation to transmit motion and force, rather than rigid bodies with conventional

mechanical joints. This design paradigm is inspired by nature, where strength and compliance

are observed in structures, as opposed to the goal of strength and stiffness employed in traditional

engineering. The proposed research extends this biological inspiration to create truly monolithic

systems – autonomous, adaptive, efficient, self-contained devices.

I propose to further explore the potential and logical ends of compliant mechanism

technology. There is an interest and a need to synthesize compliant mechanisms with elements

of other fields including controls and adaptive structures. By combining these fields, a new

paradigm emerges for complete and embedded systems that offer a basis for autonomy. In doing

so, we continue to be inspired by nature, and become more intimate with the question of the

relationship between nature and engineering design. If indeed we feel compelled to take

inspiration from biology, then we need to better understand why and how we can appropriately

use biomimetics.

The objective of the proposed research is restated as the further advancement along the

path from traditional mechanical design forward to biomimetic design, as graphically depicted in

Figure 1. The steps made will include systematic design tools and algorithms. From these it is

also desired to gain the specific insights that can lead to general engineering design guidelines

for embedded systems.


Figure 1: Transition from Traditional Mechanical Design to Biomimetic Design with Distributed and

Embedded Compliant Systems. Current State-of-the-Art is Compliant Design.

1.2. Personal Motivation The development of a new methodology poses completely new challenges in formulating

the synthesis equations and objective functions to yield compliant systems. While the topic is an

interest of my advisor, my previous research experience both prompted the question of

embedded actuation in my own mind and provided a path and tools for investigation. I have

been studying compliant mechanisms for five years, first considering their implementation as

macro-scale adaptive structures. Several times I have addressed the problem of forming a

mathematical basis for motion synthesis via such mechanisms. I have also explored this at the

micro-scale for internally-actuated electro-thermal MEMS devices. I have worked on CM

synthesis projects using both continuous and discrete optimization strategies. I have also led a

project on the design of a biomimetic aquatic vessel with compliant-fin stroke propulsion,

provoking my thought in the usefulness of biomimicry. Most recently, I am part of an effort to

integrate compliant mechanisms with haptic control devices.

Further, I have several years experience with a variety of smart-material actuators. I have

observed that actuation type, placement, and magnitude are always design parameters defined in

the project statement for CM synthesis. Having now worked on many projects based on the

synthesis of motion from elastic mechanisms, I propose to move the technology one step forward

in my Ph.D. research. By including both actuators and sensors within the synthesis algorithms

for new devices, an already promising technology will be made relevant to a broader range of

applications.


1.3. Applications The use of multifunctional elements as both structural members and actuators, the

integration of multiple materials, and the freedom from dependency on external drives comprise

a biomimetic nature specifically attractive to several exciting fields. Many biomedical

applications require these qualities. Examples include surgical tools and grippers, active-assist

joints, and active valves, all at the millimeter scale. Another area where compliant mechanisms

have already proven to perform well is in MEMS. Often, the only practical solutions for MEMS

design problems have been delivered via compliant mechanisms. As research of smart-material

implementation at the MEMS level increases, this proposed research will advance the creation of

autonomous devices at the micron scale, unfettered by external actuation sources.

Assuming perfect success of the methodology, a mathematical framework for design of

smart/adaptive systems will be enabled. The embedding of sensing, actuation, and control will

aide in the design of autonomous vehicles. Smart structure applications include adaptive

orthoses and prosthetics and conformal interfaces.

1.4. Benefits The primary benefits of this research are at the product and design levels. Embedded and

distributed compliant systems will provide many advantages in applications requiring robustness

and autonomy. Energy efficiency can be increased, reducing requirements of external energy

sources. Additionally, internalization of the actuator and sensor components offers protection

from the external environment.

At the design tool level, our research will benefit those seeking methods for tailored

design of synergistic, monolithic systems. Increased actuator efficiency can be attained by

seeking global optima at the system level. These new methods will be systematic and applicable

to a general case of adaptive structure problems.

Secondary benefits of this research occur at the learning level – the study of biomimetics.

Again, one of the benefits of this research is in exploring the potential to learn from nature.

Delimiting the potential role of biomimetics results in understanding how biological insights are

useful to engineering. Indeed, many comparisons can be made, but which of these provides

benefit and useful knowledge? Arguments can be made for direct mimicry or for the indirect

borrowing of apparent principles and objectives in biological design. To add credibility to the


idea of biomimicry, we should identify the cases in which nature should and should not serve as

engineering inspiration.

2. Problem Statement / Hypothesis

The proposed activities of this research are part of a much larger vision. The paradigm of

distributed systems poses many new challenges in the function and architecture of structures,

actuator, and sensors. The grand research vision, described in this section, is to investigate and

gain fundamental understanding of the basic research issues underlying those challenges. The

focus is then narrowed in the Scope and Research Plan Overview sections.

I hypothesize that modified versions of the existing algorithms for compliant mechanism

optimization can be implemented to design efficient and controllable systems of integrated

structures, sensors, and actuators (see Figure 3). The physical layout of these components will

be optimized for energy efficiency, controllability, and responsiveness, while satisfying various

weight and performance constraints (e.g. for autonomous robots). Figure 4 shows an example of

the problem definition and a conceptual solution. Allowing for multiple inputs in compliant

mechanism design leads to the question of control. A method for including knowledge of the

controller during the design synthesis may results in more controllable and sensitive structures.

It is also intended to increase the accuracy and functionality of previous compliant

mechanism design schemes by including the actuator and its stiffness in the optimization for the

first time. This provides a more realistic view of actuators, which provide neither a fixed force

nor a fixed displacement, but rather a load-curve relationship for a given power input. Whether

stiffness-matched systems will naturally result from the simultaneous optimization of structure

and actuator is a pertinent research question. Further, I seek to develop a general, parameterized

embedded actuation system methodology, for which any particular actuator's characteristics only

need be specified. The final outcome will be the transformation of computer-generated designs

with optimized geometry, materials, and properties directly into the physical realization of

distributed compliant systems.

2.1. Vision of an Adaptive Compliant System Engineers generally mold electromechanical systems in the rigid-and-discrete paradigm:

a rigid structure with mechanical joints is first designed and then actuators and sensors are


integrated with a final afterthought of designing controls. In spite of the “mechatronic”

revolution of the early 90s, this paradigm is still prevalent today. I propose a compliant-and-

distributed paradigm with embedded (not integrated) actuation and an embedded sensing

continuum. In this research, “embedded” refers to systems simultaneously designed for optimal

performance. “Integrated” refers to components that are “slapped on” to an already completed

design. Exploiting compliance or elasticity of the underlying structure has several benefits

including elimination of mechanical joints, joint-wear, and joint-clearance. The proposed

paradigm also embodies the notion of “continuous”. Rather than placing discrete sensors

throughout a rigid and discrete structure, distributed sensing can be achieved by embedding

compliant sensors (simple wires coupled by mutual inductance) within a compliant structure (see

Figure 4). Such an arrangement may be practical for many applications ranging from haptic

feedback on surgical manipulators to sense-and-control adaptive aircraft wings.

The vision of an adaptive, embedded compliant system is a synthesis of compliance,

actuators, sensors, and controls. It is a system that both senses and responds to the external

environment via internal structures; a black box converting inputs to outputs. This trade from

external to internal components offers several benefits. First is efficiency by part reduction. A

few well-placed actuators inside a structure may be capable of many complex deformations of

the external structure. Likewise for sensing: rather than numerous, costly pressure sensors along

the external boundaries of the system, a small number of internal sensors can determine the

internal state of stress and map it to the external environment (see Figure 3 and Figure 4). Such

elements are safe from potentially harsh environments; they are even protected from the

conditions they are sensing or imposing.

Insulator(Electrical

and/or Thermal)

Structuraland

EmbeddedActuators

andSensors

Biocompatible

Ext

erna

l Sen

sing

DesiredOutput

Figure 2. Sample design domain for an Adaptive Compliant Systems Problem


Flexible Structure

Ext. SensingActuators

Biomaterial

Insu

late

d Ba

se

Internal Sensing

Figure 3. Artistic Vision of a fully Embedded and Distributed Compliant System

The idea of internal, remote, and local components performing external and global

sensing and actuation is biologically inspired. In human and animal biology/psychology, distal

attribution is the experience of thinking we are actually sensing phenomena directly where they

occur, whereas we usually sense them in structures internal to the body (Loomis, 1992). While

we speak informally of "the five senses" that connect us with the external world, most of our

senses are in fact monitoring internal conditions (email corr. with Peshkin, 2005). When enabled

with biomimetic “internal state sensors,” will machines benefit by being so introspective as well?

external pressure sensing

actuators

internal stress state sensors

Figure 4: Artistic Vision of an Internalized and Adaptive Compliant System

2.1.1. Embedded Actuation By “embedding actuators” within a compliant mechanism, I refer to a topology design

process that simultaneously determines the configuration of the actuators and the compliant


structure. That is, certain beams in the initial set will transform into actuators during topology

synthesis. The result is not simply an optimized mechanism, but an optimized system with the

number, size, location, and orientation of all actuators matched to the synthesized structure of the

mechanism. Such a system will have better performance compared to one in which the actuator

is “integrated” after the fact. The proposed work lays a scientific foundation for designing

monolithic mechanical transmissions embedded with unconventional actuators such as artificial

muscle actuators.

2.1.2. Embedded Sensing Aspects of the dynamics that are unmodeled or unsensed often limit the performance of

traditional (lumped-parameter) machines under closed loop control. For instance, in a robot arm,

one may have a rotational encoder at a joint, but no way to monitor the flexing of a link. Robot

links are built to be relatively stiff, so that modeling them as perfectly stiff is a good

approximation, at least up to some frequency. Stiffness adds weight of course.

Compliant machines with distributed compliance, inertia, and sometimes damping or

frictional elements, are more challenging to model or sense than lumped-parameter machines.

Whereas traditional mechanisms use point-like sensors (e.g., the joint rotation sensor in a robot),

compliant mechanisms do not concentrate their motion at a single point (c.f. a revolute joint).

The motion that must be sensed is distributed spatially across the entire extent of a compliant

member. This "distributed" character of motion in a compliant mechanism is well matched to

the "distributed sensing” which is characteristic of mutual inductance sensors. By proper design

of the mutual inductance sensors (email corr. with Peshkin, 2005), we can effectively integrate

the motions of the compliant member being sensed over its spatial extent.

2.2. Theoretical framework for the proposed study While many methods may be suggested to explore the design of adaptive, biomimetic

structures, I propose to primarily work within the framework of structural design optimization. It

is an area well-suited and proven in structural and mechanism problems, as described in the

Background section. It promises to fare well for the inclusion of actuation, sensing, and control

in the design objectives. Several objectives will be formulated to explore the problem. These

fitness functions that drive our problems will be formulated from energy principles, observations

of nature, and aspects of control theory.


3. Scope Specifically, the scope is to formulate a topology synthesis optimization algorithm for

compliant structures that includes structures, actuators, and sensors. In this research, I will focus

on the pseudo-static cases. Because dynamic, time-dependent phenomena are very important for

some tasks, for now I take care to correctly lay the groundwork so that such items can be

considered in the future. In setting the framework for sensing and control, I will define for

structures the ideas of observability and controllability. These definitions will be used to

evaluate these quantities within the design algorithm.

Concurrent with the development of a design methodology, several specific areas of

biology will continue to be studied. These include variable stiffness in structures and its various

uses, shape-change for locomotion and/or attenuation, and closed-loop control in force or

displacement feedback systems.

The creation of new optimization algorithms will mark completion of the research. I will

show several examples to evaluate these algorithms, including some variable-stiffness designs

and several case studies for load-adaptive airfoils and fit-adaptive orthoses. Further, while it is

difficult to predict the results of exploratory research, I aim to describe at least one new aspect

about the relationship between nature and engineering.

4. Background / Literature Review

4.1. Compliant Mechanisms Compliant mechanisms are of immediate appeal in addressing the problem of complex,

biomimetic deformation because of their inherent flexibility and distributed compliance. The

synthesis of these mechanisms has been well studied, and their advantages have been well

documented, including: absence of wear, backlash, and friction and ease of manufacture. The

pioneering concept of distributed compliance led to development of design algorithms for the

creation of compliant systems. The design methods and the applications of compliant

mechanisms apply to many domains in micro, meso, and macro scales.


(a) (b) (c)

Figure 5: (a) Comparison of a multi-part conventional office-stapler with a no-assembly compliant stapler, (b) Adaptive Compliant Wing – embedded compliant mechanism provides leading edge camber change on demand (c) A MEMS electrostatic actuator integrated with a compliant motion amplifier running at 27KHz.

4.1.1. Distributed Compliance Figure 6 illustrates the idea of distributed compliance, showing a MEMS actuator with

integrated compliant motion amplifier.

Figure 6: A MEMS actuator integrated with a 20X motion amplification compliant mechanism is being mechanically probed. Figures illustrate distributed compliance where beams and the mechanism deform as a whole without any stress-prone flexural joints. The device was fabricated at Sandia National Labs using Sandia’s SUMMiT-5 process.

It is important to note a significant difference between the compliant mechanisms

discussed in this proposal and conventional flexures. Conventional flexures have relatively rigid

sections connected by very thin flexural joints. These flexures localize the deformation and are

prone to high stresses and reduced fatigue life. Such flexures have been known for a long time

(Paros & Weisbord, 1965) and have been successfully employed in less-demanding applications

(ex. shampoo bottle lid). The mechanisms discussed here have distributed compliance. That is,

the mechanism deforms as a whole and does not have any flexural joints. In fact, the links or

beams deform without any connecting joints.

The challenge in designing distributed compliant mechanisms is to determine the optimal

distribution of the material to fit within a given space such that the resulting design not only

performs the desired kinematic function but also satisfies various constraints such as permissible

stresses, fatigue, stiffness (natural frequency), manufacturing (minimum widths and thicknesses),

weight, and power.


4.1.2. Synthesis Methodology Synthesis involves two steps: (I) generation of the mechanism topology and (II)

determination of optimum size, geometry, and shape of various constituent elements of the

mechanism. A pictorial summary of one such design method is shown in Figure 7, illustrating

how a compliant gripper is created algorithmically. Starting with functional requirements of

desired forces and displacement, a conceptual design is automatically created in Stage I topology

synthesis. Based on material constraints (i.e. permissible stress, strain), fabrication constraints

(minimum feature size, etc.), external loads, and desired mechanical advantage, the exact size,

shape, and geometry of each of the beam elements is optimized in Stage II.

Figure 7: An illustration of the typical two-stage approach for compliant mechanism synthesis:

(a) Stage I: topology synthesis, and (b) Stage II: dimensional synthesis.

4.1.3. Current Research Directions and Labs A brief history of compliant mechanism design begins with the work of Ananthasuresh in

1994, who first proposed using a structural optimization approach for mechanism design. Many

followed, implementing the ground structure approach, energy efficiency formulation, refined

size/shape optimization, and inclusion of nonlinear deformation effects. Refer to Lu’s

dissertation (2004) for a detailed history.


Current research in the field has spread to a small number of universities. At The

University of Michigan we continue to focus on medical applications, biomimetics, new

synthesis formulations, and easy-to-use design software. Research at Brigham Young University

under Larry Howell centers on the Pseudo-Rigid-Body-Approach to compliant mechanisms,

which uses empirical data to employ a traditional kinematics-based approach to mechanism

design. (http://research.et.byu.edu/llhwww/) Mary Frecker at Penn State continues research into

many areas including medical devices and reconfigurable structures.

(http://www.me.psu.edu/ODACSL/) Current research at the University of Illinois in Chicago is

focused on the development of novel MEMS-based miniaturized devices, led by Laxman

Saggere. (http://www.uic.edu/labs/microsystems/index.html) Kerr-Jia Lu is continuing her

research into Shape-Morphing Compliant Mechanism at Geroge Washington University.

(http://www.seas.gwu.edu/~kjlu/) Just Herder at the Delft University of Technology works in

the area of statically-balanced compliant mechanisms, with a focus on medical tools and human-

assist devices. (http://mms.tudelft.nl/staff/herder/index.htm) Finally, Martin Culpepper heads

the Precision Compliant Systems Lab at MIT, where research focuses on MEMS devices,

machine tools, layered and formed actuator technology, and design tools for capture of designer

intent. (http://psdam.mit.edu/) The potential contributions that the research described in this

proposal will make to the literature are listed at the end of this proposal.

4.2. Load Path Method The Load Path Method was developed by Lu to address the issue of structural

connectivity in compliant mechanism synthesis problems. In her dissertation, she observes:

“Since the binary topology variables are defined in the element level, they do not explicitly contain any information about the overall connectivity, which is in the structural level. When certain elements are eliminated at the same time, the GA can produce invalid designs such as those shown in Figure 8 that include disconnected substructures or are disconnected from the input or ground. In general, the structural connectivity is unknown when simply looking at the design variables.”


http://research.et.byu.edu/llhwww/

http://www.me.psu.edu/ODACSL/

http://www.uic.edu/labs/microsystems/index.html

http://www.seas.gwu.edu/~kjlu/

http://mms.tudelft.nl/staff/herder/index.htm

http://psdam.mit.edu/

Figure 8: (a) The binary ground structure used to discretize the design domain; (b) an invalid

design with disconnected substructure; (c) an invalid design that is disconnected from the ground; (d) an invalid design where the input is disconnected. (Lu, 2004)

To resolve this problem, a graph-based discretization is formulated as an alternative to

the Grounded Structure Approach. This method may be very relevant to this research because of

the discrete nature of the actuator variables. The Load Path Approach begins with numerous

subgraphs (paths) that already connect all of the relevant points of interest in the design space

(see Figure 9). Thus, the resulting structure is guaranteed to be properly connected. In addition,

the method treats the sub-graphs as variables (not the individual elements), leading to a large

reduction in the total number of design variables and reducing computation time. This process is

further described in the Problem Discretization section.

(a) (b)Figure 9: (a) A fully connected graph of a shape-morphing compliant mechanism.

(b) Different port locations render different geometries in the compliant mechanisms.


4.3. Related Work (Actuator Architecture) There are a few literature references to the optimization of actuator architecture, which is

similar in appearance to the proposed research. However, these methods are of different scope

and employ different methods. Actuator architecture problems aim to lay out the material

makeup of an actuator, but do not address how that actuator relates to the rest of a physical

system. Most of these studies focus on the distribution of only the actuator material, without any

supporting structural elements. First, consider the problem shown in Figure 10, which seeks to

find the optimal layout of actuator material in a flexible airfoil (Anusonti-Inthra and Frecker,

2003). The only non-actuator elements are the skin elements, which are not included as design

variables. The result (Figure 11) shows a network of only actuators. Such a structure may be

suitable when considering the entire device as a single bender actuator, but is highly impractical

in describing implementation of actuators within a mechanical system. E. Silva seeks a similar

goal of distributing piezo-electric actuator material in his dissertation work (1998).

Figure 10: Design Domain Used for Actuation Distribution in a Flexible Airfoil (Anusonti-Inthra, 2003)

Figure 11: Actuator Distribution Optimization Results with a Volume Constraint of 50%

Only one relevant paper has been discovered that takes on the task of embedded actuator

with structure during synthesis. Bharti and Frecker (2003) provide a two-stage method for

topology synthesis of piezo-electric actuators. Their work differs from others in that the

discretized elements can become either “active” (actuator) or “passive” (structural) elements. In

the first design process, they treat all elements as actuators and proceed to optimize the layout.


Actuators that are understressed and appear not to be contributing to the objective are converted

to structural elements and the structure is optimized a second time. In an example, they redesign

the flextensional actuator shown in Figure 12. But rather than specify the red area as the

actuator, their method distributes the actuator and structure as depicted in Figure 13.

Figure 12: PZT Flextensional Actuator Problem, shown with internal, fixed actuator

Figure 13: Topology Optimization with all elements shown in different shades according to their relative

importance in providing a maximized output deflection. (Bharti and Frecker, 2003)

The results in Figure 13 are undesirable for the same reasons as those in Figure 11. This

is only a “material distribution” problem and not a mean for integrating actuators within a

structure. Bharti does conjecture further, however, that the structure in Figure 13 could be

interpreted to a form like that shown Figure 14. While this interpretation comes closer to our

concept of actuators distributed within a compliant system, no method or rationality is provided

for how such an interpretation is to be made. The final structure shown is in fact only a concept

for what an interpretation might look like; a quick look at it indicates that the actuator locations

are nonsensical and that the structure would not have the same functionality as that shown in

Figure 13.


Figure 14: Possible Interpretation of Figure 13. (Bharti and Frecker, 2003)

5. Basic Research Issues The basic research issues are in identifying and implementing the appropriate objective

functions for synthesis of embedded compliant systems. The choice of objective function may

depend on whether actuator power, actuator number, and/or actuator effectiveness is to be

minimized. In addition, potential actuators for use in such systems should be researched. A

practical choice must be made while considering how an actuator’s limitations constrain the

design goals. Once chosen, the next task is to mathematically characterize actuators for

inclusion in the optimization. Successful results will require guaranteed structural connectivity,

an important issue that will be ensured using graph-based methods.

Another issue is setting the framework for “design for control” of embedded compliant

systems. This will be established by developing specific definitions for the input and output

functions of the structure, followed by their mathematical implementation in the algorithms.

Finally, in terms of biomimetics, the issues are identifying what exactly from nature is

worthy of use as an objective function. Another matter is interpretation of synthesized designs in

terms of what is seen in nature, in search of useful correlations or potential opportunities for

continued research.

6. Research Plan Overview The proposed research consists of three concurrent areas of focus. Primary attention is

given to the development of the optimization algorithms. At the same time, I will continue

research into appropriate actuators for embedded compliant systems and their mathematical

characterization. Also ongoing will be the question of biomimicry. What additional objectives

can we find from nature, and how can we gain additional insight from our results via biological

comparison?


Figure 15 provides a pictorial overview of the proposed method of synthesis. It is from

this description that I identify the specific research activities to be undertaken. We begin with

the given problem specifications and design space, depicted in (a). The workspace constrains the

maximum allowed size of the system. Portions of the workspace deemed to be rigid (connected

to either ground or another structure) are indicated. The specific output points (blue circle) and

desired output direction (blue arrow) are shown. Many synthesis problems also include reaction

forces at the output point; either a reaction load or an external spring. Here, the external load is

applied along a loading region depicted in pink. The external load in the case is an uneven

pressure along a line, shown by the black arrows. Note that no input ports are specified; it is

only required that the actuators fall within the physical workspace.

Step (b) shows the workspace discretized using the Ground Structure Approach.

Resolution depends on the number of nodes used and the adjacency of connected nodes. In this

case, no elements span more than two square units. Each element is represented by a discrete

variable that will determine its presence in the optimal structure. The structural and actuator

materials are specified, allowing each element to contribute to the overall structural stiffness.

Step (c) is the result of the topology synthesis optimization achieved with a genetic

algorithm. The result reflects the specified objective function subject to any constraints.

Actuators are indicated in red and elements with embedded sensing in blue. Here, the objective

function is the energy efficiency of the structure, calculated as the work at the output nodes

divided by the sum of the work at all the input (actuator) nodes. The work terms are found by

analyzing the structure with the finite element method. Actuators are represented by more than

point force or displacements; they are designated as structural elements with load-deflection

output curves. The structure is required to meet a minimum displacement at the output node

while bearing the depicted external pressure load.

After the topology is determined and fixed in step (c) the individual elements are resized

and reshaped in step (d), the Size and Shape Optimization. All of the external loading conditions

are still applied, but the objective function may be changed to fine tune the structure’s function,

such as optimal geometric advantage. Stress and buckling constraints are also included at this

stage to check and prevent element failure. Note how the elements adjust in length and

thickness, yet the original topology is maintained.


Step (e) shows the synthesized structure in its deformed state. The figure shows two

kinds of sensing: external and internal. The distributed internal sensors are preferred to the

external sensors because they can determine external loads with fewer elements, while not

exposed to the environment. It is intended that the internal and embedded nature of the sensors

provides for simplified control of the embedded actuators. Finally, step (f) shows a physical

interpretation of the synthesized structure. The figure conveys the vision of a monolithic

skeleton with embedded sensors and actuators acting as a cohesive whole.

(a) (b) (c)

(d) (e) (f)

Figure 15: Various steps in the proposed synthesis scheme. (a) design specifications (b) initial array of beam elements as a ground structure (c) optimized topology of beams, actuators, and sensors (d) size optimization (e) deformed position (f) physical interpretation.


6.1. Specific Research Activities My specific research intentions are summarized in the following list and further

elaborated in the Detailed Research Plan section.

• I intend to include the orientation, location, and number of actuators as variables in the topology synthesis problem for designing compliant mechanisms.

• I intend to use genetic algorithms as the means of optimization, and will pursue two methods of problem discretization: the Grounded Structure Approach and the Load Path Approach.

• I intend to include the structural and operational loading-curve properties of the actuators in the mechanical analysis used to calculate the fitness function.

• I intend to lay the groundwork for optimal sensor layout and embedded controls in adaptive compliant systems. This requires mechanical definitions for “observability” and “controllability”, which will serve as metrics in the design for optimal control.

• I intend to explore and articulate aspects of the relationship between engineering and nature for potential exploitation in design. This relationship includes comparative design, discovery and sharing of objective functions for optimization, and the particular study of variable stiffness.

7. Preliminary Work and Results

7.1. Studies with Ground Structure Approach and Genetic Algorithms To demonstrate the feasibility of this research, I have created some optimization code and

completed a number of initial studies. Thus far, I have used the Grounded Structure Approach

(GSA) with a genetic algorithm, although a number of connectivity problems can occur when

combining the GSA with genetic algorithms. I have added a number of graph-checking

constraints to resolve the issue, but it is still believed that the Load Path method will further

alleviate these problems. The current implementation of the GSA thus serves as a benchmark to

rate the quality of the Load Path method.

In all of the studies performed thus far, the objective function is to maximize the energy,

expressed in term of a spring-based efficiency, η. That is, while the actuators act against the

structure at the input ports, springs are placed at the output ports to simulate the reaction loads

(See Figure 16).


koutdout Fin1, din1

actuator Fin2, din2

ground Figure 16: Basis for calculation of Energy Efficiency

This enables the easy calculation of work output divided by work input in Eq. (1), where

all forces and displacements are measured parallel to the intended direction of motion. Thus, this

formulation does not include output work that does not contribute to the mechanism’s function.

Hetrick (1999) provides a derivation for this formulation, shown in Figure 17.

%100

η

2

≤===∑∑ inin

outout

in

out

in

out

dFdk

WW

WW

(1)

Figure 17: The Input and Output Work History (Spring Formulation) (Hetrick, 1999)

In addition to the energy efficiency, two constraint penalties are added to the objective

function. The first is a constraint that requires the output deflection in the desired direction to be

greater than a minimum value, d0. The second requires the output deflection perpendicular to the

desired direction be less than a maximum value, dtan. The final form of the objective function is


shown in Eq. (2), where η is from Eq. (1) and w1 and w2 are relative weighting constants. From

the formulation, the penalties are applied when dout < d0 or dtan > . ⊥outd

[ ])d - (d w )d - (d w η maximize outtan20out1⊥×+×+ (2)

In the code, the workspace is broken down into a grid of nodes which are interconnected

by elements (Figure 18). A design variable exists for every element shorter than a specified

length, and determines whether or not the element exists. In practice, each variable is allowed

one of four discrete values (0, t1, t2, t3). A value of 0 deactivates the element, removing it from

the structure. A value of ti indicates one of three thickness values for the thickness of the beam,

e.g. 1mm, 2mm, or 3mm. In addition, there is a variable for every actuator to be used in the

structure. This variable has a value between 1 and the total number of elements. Its value marks

the element selected to be the actuator in a given structure. This approach guarantees a specified

number of actuators for each problem and will prevent results like those seen in related literature

(See the Related Work section).

Amplifier Problem, 6x6 grid, 250 elements Gripper Problem, 5x5 grid, 168 elements

dout kout

dtan

dout

koutline of symmetry

Figure 18: Design Domains and Discretization for the Test Problems


Graph searches are implemented to ensure connectivity of the actuators, output port, and

at least one ground point all within the same graph. Disconnected structures that do not meet

minimal requirements for analysis, such at that pictured in Figure 19, will be rejected

(infanticide) and replaced with a new member. A brief overview of this process is shown in

Figure 20 and described in further detail in the Modified Genetic Reproduction section.

0 50 100

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Figure 19: Example of a Disconnected Structure that would be rejected from

the population before the assessment of the fitness function. (white circles are ground, green arrow is output node, red lines are actuators)

Also of major importance has been the implementation of genetic modification. This is

referred to as Lamarckian evolution or genetic engineering. Before the structures are even

analyzed, all excess subgraphs are removed (genetic engineering). This often results in

unanalyzable structures becoming analyzable. Further, elements that are discovered not to be

contributing to the objective function after analysis are removed and not passed on

(Lamarckian).


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Figure 20: Brief Overview of Reproduction. (a) initial random design;

(b) trimming of disconnected elements (genetic engineering); (c) analysis for fitness function; (d) elimination of non-participating elements (Lamarck)

7.2. Test Study Parameters The operational parameters of the genetic algorithm have depended on the size of the

chosen grounded structure. For a workspace grid of 5x5 nodes, there are 168 elements; for a 6x6

grid, there are 250 elements; every element is a design variable. As a general rule, the size of the

population should be greater than the number of design variables. Populations of sizes from 150

to 250 members have been tried for both grid sizes. In all cases, the algorithms have been

allowed to run for 1000 generations. The zero-bias for initial populations has been set to values

from 1/30 to 1/60 (i.e. a 1/N chance of existing). There are three types of mutation that occur,

and their likelihoods are as follows: normal element mutation (16%), mutation toward

elimination (mutilation) (30-40%), and mutation of actuator element choice (15-25%).

Two problems have been studied with the algorithms: a displacement amplifier and a

gripper mechanism. These problems are chosen as they are considered benchmark problems for

compliant mechanism design (refer to Lu, 2004). This proposal describes three results for each


problem type (A1, A2, A3, G1, G2, G3). The specifications for each of these are shown in

Figure 18. Lu’s results for these problems with a single-output and a single-input are shown in

Figure 21.

Figure 21: Design Domains and Results from Lu (2004) for Benchmark Problems top = amplifier problem, bottom = gripper problem

Many different amplifier designs have been created in previous research (Joo, Kota, and

Kikuchi, 2001; Kota, Rodgers, and Hetrick, 2001 (patent); Hetrick, Joel and Kota, 2003

(patent)). This compliant mechanism serves as a transmission so that the input displacement is

amplified at the output port. The overall design domain is 240mm by 100mm (9.45inch by

3.94inch). To ensure linear motion at the output port, the design is chosen to be symmetric about

the y-axis. Thus, only the right half of the design domain is considered in the synthesis process.


Table 1: Design summary of the benchmark studies by Lu (2004) Amplifier Gripper External Load: 1N 8N Input Displacement: 1mm 2mm Geometric Advantage: 27.6 8.35 CPU time: 194sec (3.23min) 51.48sec (0.86min) Maximum stress: 30.17MPa (4.38kpsi) 34.45MPa (5kpsi) Required input force: -98.7N (-22.19lbf) -85.18N (-19.15lbf)

Estimation of design inputs for the new research problems Input forces chosen for new problems: 90N 80N

Output stiffness chose for new problems: (Fout/dout)

1/~20 = 0.05 N/mm 8/(2*~8) = 0.5 N/mm

The compliant gripper design is also one of the most commonly seen benchmark

problems and has been investigated in many previous literatures (Frecker et al., 1997; Hetrick, J.

and Kota, 2000; Joo, Kota, and Kikuchi, 2000; Saxena, A. and Ananthasuresh, 2001). The goal

is to design a compliant mechanism that deforms to grip an object and has appropriate stiffness

to withstand the reaction force upon gripping the object. The overall design domain is 100mm

by 80mm (3.94inch by 3.15inch). The gripper is designed to be symmetric about the x-axis, so

that the output ends will close by input actuation and grip the hypothetical object placed at

(100,0). Due to symmetry, only the upper half of the design domain is modeled with a single

output point located at (100,20).

Table 1 summarizes the results Lu obtained using the Load Path method and a genetic

algorithm. While she used displacement as an input, the new formulation requires force as input,

which is chosen by picking a value near Lu’s calculated input forces. Similarly, output

stiffnesses for my new problems is estimated from Lu’s output loads and output displacements.

These calculated values are listed at the bottom of Table 1. Table 2 lists the remaining

parameters for the preliminary problems studied for my research.


Table 2: Parameters for Test Studies depicted in Figure 22 through Figure 27 Amplifier Gripper A1 A2 A3 G1 G2 G3 units Grid Size 5x5 5x5 6x6 6x6 6x6 6x6 nodes Symmetry Y Y N Y Y Y # of Actuators 1 1 2 2 1 2 Initial Zero Bias 1/55 1/55 1/51 1/50 1/50 1/55 Input Force 90 90 90 80 80 80 N Element Stiffness 2480 2480 2480 2480 2480 2480 MPa Actuator Stiffness 2000 2000 2000 2000 2000 2000 MPa Output Stiffness 0.05 0.05 0.05 0.5 0.5 0.5 N/mm Population Size 130 150 230 200 200 230 Generations 200 1000 1000 1000 1000 1000 Min Output d 20 20 20 16 16 16 mm

Penalty Weight 0.1 0.1 0.1 0.2 0.2 0.1 Max Tangential d symm. symm. 5 4 4 4 mm

Penalty Weight symm. symm. 0.6 0.3 0.3 0.3 Element Mutation 0.16 0.16 0.16 0.16 0.16 0.16 Zero Mutilation 0.3 0.33 0.4 0.4 0.4 0.4 Actuator Mutation 0.2 0.2 0.2 0.23 0.23 0.2 Optimization Results Energy Efficiency 21.4 51.4 12.3 23.3 33.2 25.8 % Output Disp. 21.5 29.1 23.4 5.5 11.1 11.1 mm

The test studies included in this paper and summarized in Table 2 are only a subset of all

the studies completed. Table 3 lists the complete set of studies. The number of test studies for

each case is indicated in parentheses. The key parameters that differentiate these studies are:

• Symmetric / Asymmetric • One / Two Actuators • Remote / Free Actuator Location • Push / Pull Actuator • GA Parameters (Population Size, Generations, Mutation Rates) • Grid Size


Table 3: Full Set of Test Studies performed in Preliminary Research

1. Amplifier Problem a. Asymmetric Amplifier

i. Single Actuator (6 push, 1 pull) ii. Two Actuator (3)

b. Symmetric Amplifier i. Single Actuator (2)

2. Gripper Problem a. Symmetric Gripper

i. Full Actuator Domain (4) ii. Remote Actuator

1. Single Actuator (2) 2. Two Actuator (1)

7.3. Test Study Results The figures in this section show the optimization results for each of the test studies

alongside their convergence histories. Each figure shows the complete symmetric structure, but

with the deformed shape shown in only one half. Study A1 shows the first attempt at a

displacement multiplier; the optimization was terminated prematurely at only 200 generations.

Study A2 is nearly the same, but with a 15% larger population size and a full 1,000 generations

of design propagation.

-120 -80 -40 0 40 80 1200

50

100

0 20 40 60 80 100 120 1400

10

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30Objective Function

0 20 40 60 80 100 120 1400

10

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30Efficiency, in Percent

→200

Figure 22: Study A1 - Single Actuator Symmetric Amplifier. Efficiency = 21.4%, dout = 21.5mm

The result for Study A2 is topologically identical to that from Lu in Figure 21 (top). The

only difference is the layout of the actuator, which was not optimized in Lu’s study. The two

symmetric actuators in Figure 23 act to create a vertical force as specified for the benchmark

case.


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Figure 23: Study A2 - Single Actuator Symmetric Amplifier. Efficiency = 51.4%, dout = 29.1mm

Study A3 departed from the symmetric design space to explore the synthesis of an

amplifier without a guaranteed vertical output displacement. A penalty is imposed when the

output displacement is more than 5mm in the horizontal direction. The jagged history of the

efficiency indicates the conflict between energy efficiency and this penalty constraint.

0 20 40 60 80 100 1200

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Figure 24 : Study A3 - Double Actuator Asymmetric Amplifier. Efficiency = 12.3%, dout = 23.4mm

The next three cases show the results for the compliant gripper problem. The results for

all of these are topologically the same. An underlying four-bar mechanism can be identified in

each figure, with a rigid extension of the coupler link connecting to the output point (see bottom

half of Figure 25). In all of the cases, the actuator pushes on one of the corners of the coupler

link. In Study G3, the coupler is stiffened with some truss elements.


0 20 40 60 80 100-30

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→1000

Figure 25: Study G1 - Double Actuator Gripper. Efficiency = 23.3%, dout = 5.5mm Underlying four-bar mechanism shown in black.

Note that actuator location was restricted in all the gripper studies to ensure that the

actuators are remote from the output point. Only elements on the left-hand half of the design

space could serve as actuators. The unintended result of this restriction is that most of the

element bending occurs on the left side of the structures. The beams connecting to the output

point are mostly stiff and unbending. This is contradictive to our goal of fully distributed

compliance and signals a need to re-evaluate the implementation of the fitness function.

0 20 40 60 80 100-40

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Figure 26: Study G2 - Single Actuator Gripper. Efficiency = 33.2%, dout = 11.1mm


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Figure 27: Study G3 - Double Actuator Gripper. Efficiency = 25.8%, dout = 11.1mm Note the formation of trusses to stiffen the output link.

7.4. Current Challenges: Dense Structures A major challenge thus far has been controlling the results of initial random population

generation and of genetic reproduction. Given purely random chance, most initial structures will

be highly dense and highly connected, with almost every node connected to the structure,

resulting in a nearly rigid-body structure, as depicted in the first frame of Figure 28. To control

this problem in the initial population, the likelihood of an element existing is given an uneven

bias toward zero. The greater the bias, the sparser, and usually the more desirable, are the initial

structures (Figure 28). Zero Bias is represented as a fraction, 1/N (used in Table 2), or as a

percent, 100/N% (used in Figure 28). A value of 1/5 (20%), means that any given element only

has a 20% chance of being used, meaning a structural density of approximately 20%. This

comes at a cost, however: many of the sparse initial structures are not valid because they do not

have enough elements to provide connectivity. This conflict is handled by simply rejecting these

initial members and trying again with another random structure (infanticide). The best initial

structures tend to result when choosing a bias that rejects about 95% of the initial attempts. For

example, when attempting to populate the first generation with 200 members, between 4,000 and

7,000 members are checked before 200 good ones are attained. While this may seem

overabundant and computationally costly, it far outweighs the inefficiency of running an

algorithm where 90% of the members cannot even participate in the objective function.


20%

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Figure 28: Effect of Zero-Bias on Structural Density of Initial Population Members In each structure, every element has an X% chance of being included.

The problem appears to worsen during reproduction. While two given structures may be

sparse as they stand alone, their cross-over and mutation more often results in an addition of the

structures, akin to 1 + 1 = 100 (See Figure 29(e,f)). One reason for this problem is that there is

no easy way to relate the individual genetic variables to the structures they create. In biologists’

terms, the genotype does not map to the phenotype in any meaningful way.

The density problem is handled by random “hole-punching” (mutilation) in the offspring

before they are ever assessed for connectivity and fitness. This is achieved by randomly turning

off elements within the child structure. This works well because a few breaks in the structure

can eliminate large sections during the subsequent graph connectivity search and trimming. In

practice, this has been accomplished by giving all the elements in a structure a 20% to 40%

chance of being mutilated. In the future, this problem can be handled by better genetic

engineering of the parents before cross-over. Currently, only those elements in parent members

that contribute nothing to the fitness are eliminated. Often, however, many elements provide

next to no effect on the fitness. That is, if these extra elements are removed, the objective


function remains nearly the same. By setting a tolerance for how much “value” each element

has in the fitness function, a filter can be created to eliminate those of little value (Lamarckian).

In a sense, the structure that is left behind is truly sought in the first place, for it provides the

basic functional topology.

7.5. Modified Genetic Reproduction Figure 29, Figure 30, and Figure 31 show two examples of the modifications I have made

to the genetic reproduction process. Figure 29 and Figure 30 each follow two parent structures

through cross-over and mutation. First, the original parent members are shown (a,b), followed

by the children that result from cross-over (c,d). Next is shown the result of mutation and

mutilation (e,f). Finally, the graph checks are performed. An invalid structure (g) is rejected

(infanticide) and a valid structure (h) is trimmed to its essential elements (genetic engineering).

Figure 31 demonstrates the fitness function and post-processing of the surviving structure from

Figure 30. The complete process for genetic reproduction is listed here:

1. Cross-over & Mutation

• Standard method of reproduction in GA.

2. Mutilation

• Random removal of elements in a structure to reduce density.

3. Infanticide

• Rejection of any structures incapable of even performing the fitness function.

• Rejected members are replaced with new members by starting over again at step one until an acceptable member is found.

4. Genetic Engineering

• Trimming of structures to remove elements that will prevent or not contribute to the analysis.

• Helps keep structure clean and sparse for improved reproduction of next generation.

5. Fitness and Survival

• Standard method of analysis and selection in GA.

6. Lamarckian Engineering

• Evaluation of structural members to see which are not contributing to the objective function.

7. Repeat Process for Next Generation


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Genetic Engineering

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Figure 29. First Demonstration of Reproduction Process


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Figure 30: Second Demonstration of the Reproduction Process


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LAMARCK FILTERING Figure 31: Final Processing of Surviving Design from Figure 30(h).

Non-contributing structural members are deleted.

Ideally, I seek to simplify the reproduction process by improving the genetic engineering

performed by fitness assessment. I hope to analyze the effects of the Lamarckian filtering so that

we can tell what elements are likely to be trivial, and then create a general filtering rule so that

we can delete them during genetic engineering, before the fitness function. In addition, the latest

results have provided some explanation for high-density structures resulting from reproduction.

An initial theory was that the cross-over operation was combining what had been insignificant

elements into significant structures, resulting in a dense overall structure. However, it now

appears that the dense structures result from the basic element mutation. At a high mutation rate,

many elements are added to the structure that were previously inactivated, thus cluttering the

design. By limiting mutation to below 5%, it is hoped to dramatically reduce the need for

mutilation and infanticide. An improved process for genetic reproduction would only use the

following four steps:

1. Cross-over & Mutation

2. Genetic Engineering

3. Fitness and Survival

4. Repeat Process for Next Generation

7.6. The Question of Convergence Finally, there is a question of the nature of convergence of the optimization employed

thus far. It is not clearly evident that the GA’s are actually working by passing down useful

genetic information. The theologian’s argument that our evolutionary algorithms are relying


only on random chance may be the current case. 250 population members multiplied by 1,000

generations offer 250,000 possible chances for a good structure, especially when combined with

the genetic engineering that acts to improve these structures “with a divine hand.” Further

observance of the inner workings of the algorithms, and not just the results, is required to

evaluate the efficiency of the proposed synthesis strategy.

8. Detailed Research Plan

8.1. Design Algorithms

8.1.1. Task Definition The first step is development of the optimization algorithms. Hypothetical actuators will

be chosen as the inputs to one of the following problems: Single-Input/Single-Output (SISO),

Multiple-Input/Single-Output (MISO), or Multiple-Input/Multiple-Output (MIMO) mechanism

design. These problems are traditional categories of mechanism design that can be applied to

many situations. Work has already been done on the single-output problem with both single-

actuator and multiple-actuator inputs (SISO and MISO). The next task would be the MIMO

problem, which often takes the form of the shape-change problem. Beyond those tasks, I also

propose to study the multiple-load-case problem, which is the generalization of the adaptive-

output problem. That is, with more than one actuator, more than one output can be achieved, and

it is desirable to achieve as many unique outputs as possible with a small number of actuators.

The development of the adaptive-output problem also leads to the variable stiffness problem.

When the functionality of the design algorithms is established, other objectives observed from

nature may be applied.

Once the type of problem is chosen, all relevant quantities are parameterized for use in

mechanical analysis and optimization. An output node is selected, for which a desired

displacement or output force is prescribed. Multiple output nodes are chosen for shape control

applications. Whether single or multi-node output, we also specify an external-load sensing

region. The structure ‘communicates’ with its environment through this interface. The system

must fit within a specified 2-D design space.


8.1.2. Problem Discretization With the actuator chosen and the problem defined, the next step is to discretize the

problem so that it may be optimized. Let us consider the two-dimensional design space,

discretized by one of two different methods. The first method to employ is the grounded

structure approach (GSA). GSA divides a workspace up into nodes and all of the elements that

connect those nodes, as in Figure 18. The design space is the interconnected network of beams,

from which the structure and actuators of the final system will be selected. GSA has been widely

implemented in compliant mechanism and structural optimization and is chosen for this research

because the structural form of actuators tends to be beam-like in shape and connectivity. One of

the drawbacks of using GSA is that structural connectivity of the inputs, outputs, and ground is

not guaranteed. Solutions to this issue include graph-based constraints that check for valid

structures.

As mentioned in the Background section, another method of discretization has been

developed: the Load Path Method (Lu, 2004). The load path method begins with connected

graph components, ensuring connectivity of all design configurations. In the load path method,

key parts of the design domain are identified, such as the input port, the output port, and the

fixed ports. Variable “load paths” are established between these ports, which will eventually

form the final structure, guaranteed to be connected.

Originally developed to synthesize shape-morphing compliant mechanisms, the load-path

representation (Lu, 2004) is a design domain parameterization that represents the structural

topology in terms of the physical connections between the input and the output points. These

physical connections are the load-paths through which the energy from the input actuator can be

delivered to output points. The structural topology is determined by the presence/absence of

each path as well as the connectivity between different paths. A binary topology variable is

assigned to each load-path to represent the presence of the path, while a set of intermediate

connection ports controls the connectivity between different paths. This representation is

incorporated into a genetic algorithm to synthesize shape-morphing compliant mechanisms.

Figure 32 shows an example topology using the load-path representation. The design

domain is reduced to only the upper half of the triangular area to achieve symmetry. Five

connection ports are used in this design to control the intermediate connections between different

paths. The locations of the connection ports may also wander within the design domain to create


various topologies. Figure 33 shows how the topology changes according to the binary topology

variables. The connection port locations are the same in Figure 32 and Figure 33, but the binary

topology variables listed in Table 4 have different values (e.g. paths 1, 4, and 13). Furthermore,

the locations of the intermediate connection ports (e.g. node 11) can also wander within the

design domain, leading to yet another different topology, shown in Figure 34.

Figure 32: Example topology for Load-Path method

Figure 33: Effect of changing binary topology variables


Table 4: Topology Variables used in Figure 32 and Figure 33 Path type

Path No.

Path sequence Figure 18 Figure 19

1 {1,9,4} 1 0 2 {1,5} 1 1 3 {1,10,6} 0 0

in ∞

out 4 {1,11,9,7} 1 0 5 {1,11,2} 1 1 in

∞ sym 6 {1,8,3} 0 0

7 {2,9,4} 0 0 8 {2,5} 0 0 9 {2,8,6} 0 0 10 {2,7} 0 0 11 {3,4} 0 0 12 {3,9,5} 0 0 13 {3,11,6} 0 1

sym ∞

out

14 {3,8,7} 0 0

Figure 34: Effect of wandering connection port

It may also be of interest to investigate other graph-based methods for mapping the

design space. These include permutating a basic graph that already has the minimal connectivity

requirements. Another option is to conduct graph searches over an entire Grounded Structure

network. In the latter, individual elements would no longer be the variables, but rather their

connected graphs.

Actuator models serve as both force generators and structural elements. Actuators must

be properly parameterized to include their various force-deflection responses in both the

activated and inactivated states. These constraints can all be implemented numerically within the

optimization software. In both single and multiple output scenarios, every element has the


discrete potential to be one of the following: an actuator, a structural elastic member to support

loads and undergo controlled deformation, or absent from the design.

8.1.3. Nonlinear Topology Optimization and Synthesis Given a model of the design space, all the variables can be optimized via a genetic

algorithm (GA) to yield a mechanism topology. GA’s are a form of nonlinear optimization that

find global optima as opposed to local optima. Genetic algorithms convert all the design

variables into a long sequence of genes that can be propagated from generation to generation

with the effects of cross-over and mutation. The best-fit individuals survive by scoring high

against an objective (fitness) function. The GA starts with a population of randomly generated

designs. The selection scheme in GA is based on the ‘survival of the fittest.’ The performance

of each design is evaluated using the objective function. Once the global part of the algorithm

finds the basin of convergence of the optimum, the local part of the algorithm (size/shape

optimization) quickly and automatically exploits it.

While the optimizer is nonlinear, the structural analysis within the optimizer may be

linear or nonlinear. For more information refer to the Objective Functions section (8.1.4).

Genetic algorithms are chosen for several reasons. GA’s are well suited to handle the

discrete nature of the problem of actuator and element distribution. Elements either must exist or

be removed; there is no choice in between. Further, previous genetic based algorithms for

compliant mechanism synthesis have outperformed the continuous optimization methods (Lu,

2004).

To aide in convergence of the algorithm, both Darwinian and Lamarckian evolution are

employed. Lamarckian evolution refers to the actual modification of the genome (genetic

engineering) before it is passed on to offspring. The motivation and details of this are described

in the Preliminary Work and Results section (7.5). When modifications occur before fitness

function assessment, the term genetic engineering applies. Modifications after assessment are

based on performance and referred to as Lamarckian engineering.

While GA’s are very powerful for finding global optimums in difficult, nonlinear

problems, they suffer from high computational cost. I will also examine other nonlinear

optimization methods, such as stochastic local search (Hoos, 2004).


8.1.4. Objective Functions A key aspect of the research is implementing the proper objective function to achieve

meaningful results. The choice of objective function depends on the type of problem being

solved, which has already been described (SISO, MISO, MIMO, shape-change, etc.) The

objectives include energy efficiency with regards to input work and output work. The

maximization of energy efficiency may lead to distributed compliance in our structures. Other

objective functions may be applied to minimize actuator power consumption, minimize the total

number of actuators used, or to maximize the combined effect of multiple actuators. Shape

change objectives have been implemented via least squares formulations, by calculating the

deviations of points on a deflected structure from corresponding points on a target curve.

The quantities used in the various objective functions will be calculated using beam

elements within a linear finite element analysis. The analysis will be written in Matlab. Should

synthesis results indicate a need for nonlinear analysis within the optimizer, FEMlab, a

commercial Matlab toolbox, will be used to reduce run-times.

The design objective functions will be developed with increasing levels of complexity in

design goals, working our way to the fully embodied problem, as follows:

(i) maximize energy efficiency of the embedded actuator compliant mechanisms, plus

(ii) ⊕ optimal layout of sensors, plus

(iii) ⊕ controllability including ‘orthogonality’ of ‘deformation modes’, plus

(iv) ⊕ optimal layout for distributed sensing ‘internal stress state’, plus

(v) ⊕ multiple load-case objectives for dynamic/adaptive performance

8.1.5. Constraints In seeking various objectives that will bring us toward an optimal system, several

practical constraints will also be placed on the models such as weight, energy efficiency, peak-

power consumption (especially important for autonomous robots), materials (permissible stresses

and strains), and manufacturing (minimum width and thickness), dynamic performance

(responsiveness, adaptability, variable stiffness, natural frequency), and the type of actuators

(force-displacement curves). Of particular importance are constraints that guarantee the ground,

input, and output are all connected to the same structure, and that there are no other floating

structures. Additional research is required to identify the best means of ensuring structure

connectivity. Constraints are needed to guarantee specified output displacement, while keeping


deflection in undesired directions below a specified limit. Stress constraints are also important,

and will be applied later in Size/Shape Optimization.

8.1.6. Cross-over strategies It is desirable to have a meaningful cross-over strategy that corresponds to the actual

problem when devising genetic algorithms. That is, the exchange of genes should correspond to

the exchange of subsystems in the phenotype. (i.e. genotype sequencing does not map to

phenotype expression.) While the Grounded Structure Approach makes this difficult, either an

appropriate strategy will be sought, or another discretization will be employed (i.e. Load Path

Method.)

8.1.7. Genetic Engineering I propose to apply “genetic engineering” to our design population members during the

GA. This means trimming away substructures that are not affecting the operation of the

mechanism. Graph search is used to find elements that branch off the main structure and do not

connect to anything else. Elements that simply undergo rigid body motion do not contribute to

the structural function and are also eliminated. The designs are effectively “cleaned up” and

only the core elements are passed on to future generations. For further details please refer back

to the Preliminary Work and Results: Modified Genetic Reproduction section (7.5).

8.1.8. Size / Shape Optimization It is typical to separate the topology optimization from the size and shape optimization in

the synthesis of compliant mechanisms. Topology optimization for the current problem has

already been described; it is the discrete choice of the elements that create the unique physical

layout of the structure to satisfy kinematic motion or shape-morphing function. This establishes

a functional design. However, many other practical constraints and performance requirements

must be met before the design is deemed useful. These include materials (permissible stresses

and strains), desired fatigue life, prevention of localized buckling, natural frequency, making

sure that the dimensions and shapes can be physically realized (manufacturing constraints), etc.

All these constraints are accounted for during size/shape and geometry optimization. Fine tuning

of the mechanical function can be achieved (such as mechanical or geometric advantage) along

with the monitoring and control of stress constraints.


During this size optimization, the nodes or interconnection points are allowed to wander

within a certain window thereby modifying the geometry without altering the topology. Size and

shape optimization is performed on an already fixed topology, only changing the node locations

and beam width and thickness. The objective function might be stated as maximizing energy

efficiency of the system, maximizing the energy storage, or reduction of the peak force or peak

power consumption, depending on the nature of the task. Figure 7 shows a schematic of how

various dimensions, geometry, and shapes are optimized during size optimization. The results of

Stage I and Stage II have the same topology but different size and shape.

8.1.9. Finite Element Confirmation To confirm that the genetic algorithms generate feasible structures that actually display

the desired attributes, the resulting structures will be modeled and analyzed with a commercial

finite element code such as ANSYS. Rather than beam elements, solid elements will be used,

allowing for the inclusion of stress concentration effects.

8.1.10. Physical Prototype In addition to the finite element analysis, a physical prototype will be constructed to

demonstrate proof of concept.

8.1.11. Integration of Supplementary Concepts While the synthesis of multiple actuator compliant systems is the main focus, there are

many other ideas I am interested in exploring and integrating within the design optimization as

extensions to the basic synthesis framework.

8.1.11.1. Optimal sensor layout Traditional mechanisms allow motion at a discrete set of sliding or rolling interfaces, e.g.

bearings. Appropriate motion sensors, such as potentiometers, LVDTs, and optical encoders, are

situated on the translational or rotational axes. They are discrete sensors, matched to the discrete

motions of traditional mechanisms.

Compliant mechanisms are dramatically different, allowing motion by distributed flexing

of continuous media. As an analogue to optimal actuator layout, I am also interested in optimal

sensor layout. As with actuators, we can also speak of embedded and distributed sensing. Work

from our peers and collaborators at NWU has resulted in the development of Mutual Inductance


Sensing. They developed a distributed sensing technology that is well matched to the distributed

motion of compliant mechanisms. The technology consists of embedded wires (or other

conductive traces) in the compliant members. A pair of such traces – one may be thought of as a

transmitter and one as a receiver – communicate electromagnetically, coupled by their mutual

inductance, which varies in response to deflection of the compliant member. Importantly, the

signal from a distributed sensor is an integrated signal, which accumulates the deflection of the

compliant member along its whole extent. Such sensors readily lend themselves to the compliant

mechanism framework, as has already been physically demonstrated by collaboration with UM

and NWU.

A key feature of the technology is that the transmitters and receivers may consist of

single traces (multi-turn coils are not necessary.) The resulting signals are small but easily

detected with modern electronics. Single traces can be fabricated inside or applied to the surface

of compliant members. On traditional mechanisms, signals from distributed sensors would need

wires to cross the gaps at other axes of motion, but on compliant mechanisms there need not be

such gaps. In some uses, there may be many receivers for a single transmitter. An example of

the use of distributed sensors on a compliant mechanism is measuring the deflection and shape of

a compliant wing or fin, in an autonomous aerial or underwater vehicle.

Further integration of these distributed sensors within a compliant systems environment

will require continued research into suitable fabrication methods for embedding them in

compliant mechanisms. Our collaborators continue efforts to miniaturize the sensor electronics

so that a significant density of sensors can be incorporated into a compliant mechanism

efficiently. In the meantime, I focus on a general theory and method for inclusion of sensors in

compliant systems.

8.1.11.2. Design for Control In what the literature indicates to be a first, I also seek to implement “design for control”

within our optimization strategies. The step from single-actuator to multiple-actuators in CM

design begets the question of how to properly control these multiple actuators. With the sensor

networks described above, I will explore the design of an embedded actuation system capable of

responding to varying and unpredictable environments. While it is possible to add sensors and a

controller to an already finished multi-actuator compliant device, I believe these designs can be

vastly improved by considering sensors and controls during the layout of the compliant structure.


8.1.11.2.1. Internal stress state sensing / correspondence to external loadings More specifically, I seek to implement effective control that uses internal stress state

sensing to correspond to external loads. To capture this intent within the optimizer, we borrow

the terms "controllability" and "observability" from the field of control theory. A task of this

research is to create specific, mathematical definitions of these terms as they apply to spatial

inputs and outputs of compliant structures. While it may result that our definitions are only

analogous to those from controls, it may turn out the specific parts of the controls definition

apply directly to our problem. From Ogata’s Modern Control Engineering textbook, these terms

are defined:

Controllability: A system is said to be controllable if it is possible by means of an unconstrained control vector to transfer the system from any initial state to any other state in a finite interval of time.

Observability: A system is said to be completely observable if every state can be determined from the observation of y(t) over a finite time interval. The system is, therefore, completely observable if every transition of the state eventually affects every element of the output vector. This is useful in reconstructing unmeasurable states from measurable ones.

I propose to explore the internal stress states as a means to map the external conditions.

This might be particularly useful, for instance, when the on-set of stagnation pressure on an

airfoil must be sensed slightly in advance to signal an appropriate actuator to deform the trailing

edge by a certain amount, thereby changing the angle of attack. Certain internal elements of the

compliant system will be designed to deform predictably to maximize the sensitivity of a sensor

embedded within these elements. Although force can be sensed directly at the point of interest

with pressure sensors, the external pressure forces could also be interpolated from internal stress

state of structure. Utilization of such internal sensors has the potential to measure “modes” of

pressure deflection. Summing various modes of deflection may be better than directly measuring

along the surface of interest. This will further protect the sensors from the environment and

fewer internal sensors may be needed. More importantly, the placement of internal sensors

avoids the tradeoff of needing the output to be stiff against external loads yet compliant enough

to create measurements.

The topology synthesis problem will have to be sophisticated enough to capture the

knowledge of the controller into the topology synthesis problem formulation. For instance,


additional constraints will be needed to ensure ‘orthogonal deformation modes’ for the actuators

and ‘orthogonal sensing modes’ for the sensors.

8.1.11.2.2. Implement knowledge of the controller in the initial actuator/structure/topology synthesis

With a method for calculating these terms for a given compliant device, one can include

these terms within the objective function or constraints of the optimization. I hypothesize that

linear independence (orthogonality) of the deformation shapes (modes) created by each actuator

will lead to a greater degree of freedom for controlling external aspects of the structure.

Likewise for sensors, they can be arranged for maximal sensitivity to a variety of external

loadings of the structure. The question remains as to whether these are better posed as objectives

or constraints.

8.1.11.2.3. Effective control methods As well as component layout for optimal control, one should also consider the most

effective control methods for actuators and their compliant transmissions, taking advantage of

feedback control. This is complicated by the fact that in compliant mechanisms essentially every

closed-loop control problem is distributed control; we do not have lumped-parameter systems.

Yet, it ought to be possible to design the embedded sensor such that its distributed sensitivity can

simplify the distributed actuation control problem.

8.1.11.3. Variable stiffness concept Variable stiffness of compliant mechanisms is an interesting open research question.

With regards to this proposal, I see variable stiffness as one of the biological imperatives to

explore, which is further motivated in the Biomimetics section. However, as my own and

outsider interest continues to grow, the appeal of mathematically studying this problem and

implementing it in our optimization becomes stronger.

In one sense, variable stiffness is another way to approach some of the problems that are

directly handled by the current objective formulations. Rather than desiring to resist an external

load directly, via an actuator and a leverage scheme, we can instead resist the external load by

changing the stiffness of the structure to meet it. This change is caused by actuators, which alter

the geometry to make the structure stiffer. A simple demonstration of this is changing the


orientation of beams to be in line with external forces, exploiting the axial stiffness of the beams,

which is much greater than their bending stiffness.

8.2. Actuation Concurrent with the development of the above design methodology, I will continue to

study the best actuator technology to integrate with our systems. Thus, one aspect of our design

methodology will be actuator parameterization, so that I can create a general embedded actuation

system methodology for which any particular actuator's characteristics only need be specified. I

have experience in taxonomy of actuator technologies; Figure 35 compares a wide variety of

actuator types (Trease, 2001).

Most actuators can be characterized by four key design specifications: force, size,

displacement, and frequency. Power consumption can be treated as a cost factor for further

comparison. Typically, actuators with high displacement provide low force and vice versa.

Even for a given actuator, the maximum force and maximum displacement are not achieved at

the same time. The maximum force is the “blocking force” measured when there is zero

displacement. The maximum displacement is the “free displacement” measured when there is no

load in resistance. Therefore, each actuator is not represented by a point on this graph, but by a

curve. It is therefore critical that actuator selection is based on the entire motion characteristics

(force displacement curves) rather than single-point designs. Ashby (1997) provides a

systematic method of selecting actuators.


Figure 35: A map of the actuator technology workspace, with respect to Force, Displacement, and Work.

B. Trease, 2001, A Survey and Comparison of Smart Material Linear Actuators

8.2.1. Actuation Selection and Evaluation Actuators best matched to our needs will be those that exhibit capability as structural

elements. Actuators of interest include Electrostrictive Polymer Artificial Muscles, Electrically-

activated PAN muscles, Ionic Metal Composite muscles, and Shape-Memory-Alloy (SMA)

actuators. Studies can evaluate which actuators are the most practical, and how their limitations

affect the research objective. For example, shape memory alloy wires on their own provide little

structural stiffness except in tension. Piezoelectric benders may serve well as long as not loaded

in tension. A possible solution is smart actuator composites: a composite embedded with shape

memory alloy wires would be able to support bending and compressive loads.

8.2.2. Characterization As stated before, I desire to implement any actuators in the code as more than mere point

forces or displacements. Our approach will focus on several increases in actuator model fidelity.


Since the simplest model is a mere point force, the next step is to add a structural element with

the stiffness of the actuator. However, this case still implies that an actuator can provide a

specified force or displacement, which in reality requires the use of closed-loop feedback

control. A powered actuator generates a force that corresponds to its unique load-displacement

actuation curve and the stiffness of the system on which upon it acts. Thus, we need to capture

this load-displacement curve within our finite element calculations. The FEA solution will

determine the actual actuator force and displacement.

In addition, I may take a solid continua approach to the mathematical modeling of these

actuators, developing 3-D stiffness matrices and coding the nonlinear force-deflection

relationships.

8.2.3. Commercial Artificial Muscle Actuators While I will consider all types of actuator technology, of particular interest are

Commercial Artificial Muscle Actuators. These are among the cutting edge of actuator

technology, often supplying the greatest displacements and strains compared to others. Their

biological-inspiration may indicate suitability for use in the proposed research. However,

research must be done to ensure that the match is genuine and not merely based on the word

“biomimetic.”

Figure 36: Commercial Artificial Muscle Actuators. Bending and linear types are shown.

http://www.artificialmuscle.com/

8.3. Bio-Discussion – “Biomimetics”

8.3.1. Observations & Comparisons “Biomimetic” can be an ambiguous term and this research considers its useful meaning it

at least three different ways. First, and most simple, is the observation that our synthesis results

from and compares to structures from biological systems. For example, proper implementation

of the methodology will allow the following question to be answered: are optimal


structure/actuator distributions similar to the musculo-skeletal systems found in nature? This is

not a guaranteed form of scientific inquiry, yet nature may provide some inspiration for one to

interpret what we have created. Existence of such evidence, or lack thereof, may support our

claims as to the strength of our methodology.

8.3.2. Inspiration via Direct Borrowing Next, as perhaps as most commonly done, we can think of biomimetics in terms of direct

borrowing from nature. This implies observation and study of specific structures in nature and

directly implementing them in engineered designs. While this is an exciting area of research,

nature is neither guaranteed to provide optimal designs nor designs appropriate for emulation

with technology. One can think of many man-made designs that surpass nature, from the

combustion engine to fixed-wing aircraft.

Figure 37: Spawlita, from the Center for Design Research at Stanford

Some examples of direct borrowing include various bio-robot and insectoid-robot

projects, such a Spawlita, the hexapedel biorobot shown in Figure 37. Compliant mechanisms

are of immediate appeal in addressing the problem of complex, biomimetic deformation. A

fully-compliant system also has great stealth potential for both aquatic and aeronautical craft.

Smooth, continuous deformations result in a much less distinguished sonar “signature”, but even

if spotted, biomimetic robots/vessels may be mistaken for their biological precedents. I have


worked on such projects, including a swimming fish project. This project sought to mimic the

kinematics of biological fish stroke data, while also using a compliant skeleton inspired by that

of a fish fin (Trease and Lu, 2003).

Yet in the end, the question remains: why force the issue? If specific structures are

indeed best, then they will also result from a properly design optimization, and we need not have

borrowed them directly.

8.3.3. Inspiration via Objective / Task Another form of biomimicry is inspiration via objective or task, which is an indirect

means of emulating nature. In other words, we should try to mimic the apparent goals and

purposes of nature, rather than nature directly. The question of what exactly from nature is

worthy of using as an objective function is interesting in itself. Some possibilities have already

been mentioned, such as variable stiffness and internalized sensing and actuation. Variable

stiffness is often employed in nature to alter passive dynamics, and is further discussed in the

Case Studies section. The concept of internal structures interacting with the external

environment was described in terms of distal attribution in the Vision section of this proposal.

Biology offers the additional case of embedded sensing for closed-loop muscle control. Pacinian

Corpuscles are elements of the haptic feedback system of human touch. They are structures

found within the skin that measure pressure and vibration so that forces may be estimated for

feedback in control (Thompson, 2001). Indeed, the idea of closed-loop force control is an area

from which to further seek biological objectives for implementation in our methods.

8.3.3.1. Homeostasis / Homeokinesis Along the lines of the internal actuation concept, the objective of embedded compliant

systems may be described as ‘homeostasis” or “homeokinesis”. These terms refer to internal

processes in biology that attempt to maintain internal balance. As the proposed structures can be

viewed as internally driven black boxes converting inputs into outputs, homeostasis refers to the

maintenance of a stable state and homeokinesis refers to such maintenance in spite of changing

environmental conditions.

8.3.3.2. Energetics Finally, the energetics of biological functions may also provide additional objectives. We

currently seek to define energy efficiency in a number of ways, such as work output divided by


work input, work throughput, and mutual strain energy. Nature may provide other formulations

of energy efficiency. For example, energy efficiency may be viewed in terms of the energy

potentially saved due to passive dynamics and the use of variable stiffness.

8.3.4. Genetic Algorithms Our choice of genetic algorithms to solve biologically-inspired problems may appear to

enable synergetic benefits, but this must studied and confirmed with stronger argument. As with

the use of artificial muscle actuators, for now it is only coincidence I am using biomimetic

algorithms to solve a biomimetic problem.

8.3.5. Idea of an integrated Musculo-Skeletal-Ligament-(Nervous) System Some background information about the idea of an integrated musculo-skeletal-ligament-

(nervous) system reveals the following views. Though it is distinctly a view with a lot of

potential, the idea of such integration at the system level is not a clearly articulated common

view of many in biology. Yet, it is a logical viewpoint from a design point-of-view. In fact, its

analogy in Mechanical Design is the defined goal of my proposed research. Not the mimicry of

specific structure, but the analogy of a combined structure-actuator-sensor system is the general

concept.

8.3.6. Biological Evidence of Distributed Actuation As an important note of the appropriateness of biomimicry, discussed here is biological

evidence of distributed actuation. This, again, refers to systems where the actuators/muscles are

embedded within the moving structures. There are questions among biologists whether such

actuators are used mainly in attenuation and shape-control situations. (e.g. camber control of

fish fins.) It is not as evident that embedded muscles are as useful for power generation or thrust.

Larger muscles are typically outside of the system due to their bulkiness, and attached to part of

the external skeleton. This debate, however, depends or how the system is defined; for some

muscles are clearly part of the system, such as those in the lower leg.

On the other hand, this may be the case where we look at nature and surpass it. Our

engineered designs have advantages that nature does not, such as high power density actuators,

which may enable force generation via embedded actuators.


9. Confirmation of Results The initial results of the genetic algorithms should be verified with commercial finite

element in ANSYS. Rapid-prototyping technology will be used to create initial physical models.

These models will serve not only as geometry checks, but can also be used for performance

testing. The next step in fabrication is investigation and sourcing of multi-material fabrication

for monolithic structures.

10. Case Studies Several case studies will be performed to evaluate the quality of the topology synthesis.

These include a variable stiffness problem, an adaptive orthosis/prosthesis problem, and an

adaptive shape-changing wing problem.

10.1. Variable Stiffness As already mentioned, there are many examples where nature uses variable stiffness in

structures. It is often used for adjusting the passive dynamics of a system. For example, many

animals will modify their stiffness so that their natural frequency matches their walking or

running speed. Variable stiffness is also used to prepare for impact absorption or sudden

movements.


equi

vale

nt s

tiffn

ess

com

plia

nt m

echa

nism

unactuated and compliant actuated and stiff

ground

output

Figure 38: Demonstration of Variable Stiffness achieved by Manipulation of Geometry

At least three means of achieving variable stiffness can be identified from nature and

possibly implemented as optimization fitness functions. First is the case of direct and active

force application to balance the external forces and result in an apparent change in stiffness. In

animals this is often achieved by co-contraction of opposing muscle groups. For example,

visualize a chef slicing through a stick of butter with an extended arm and then stiffening up the

arm to cut through an adjacent piece of thick steak.

Another way to change stiffness is to alter the structural geometry of the system (Figure

38). Using actuators or muscles to rearrange elements can change the effective load paths or

cause elements to use axial modes instead of bending modes and vice versa.

Finally, some muscles can change their very material stiffness to directly achieve this

effect. Similarly, there are now new smart materials that can change their stiffness under applied

electric or magnetic loads. While this is beyond the scope of the proposed work, the mechanism

behind changing muscle stiffness may be studied for further insight.


10.2. Adaptive Orthotic and Prosthetic Devices Another case study will be the design of an adaptive orthosis. Many current devices must

be custom fit to every individual and then cannot be changed during use. A self-adjusting device

would resolve both of these issues. A person’s limb will swell and change shape during use,

creating discomfort for the user. With a system capable of sensing the external pressure load and

changing the shape to minimize any stress concentrations, discomfort can be alleviated. Such

devices could also be used for functional changes in different scenarios. For example, an

orthosis could adjust to increase stiffness during running and before jumping.

10.3. Shape-changing wings and fins A third case study is a continuation of a standard compliant mechanism problem, the

shape-changing aircraft wing or aqua-craft fin. In this study, however, the goal would be to

create as system that could sense a variety of external pressure load profiles and respond with a

variety of shape changes. Such sense-and-control variable geometry wings could adjust to the

most appropriate and efficient configuration for both predicted and unpredicted flight conditions.

These benefits would also apply to loading-dependent shape-changing aqua-craft fins.

11. Research Timeline ● = deadline

X = conference Jun-Aug Sep-Nov Dec-Feb Mar-May Jun-Aug 2006

Embedded Actuator Synthesis

Load Path Approach Actuator Stiffness

Properties Controls Groundwork Biomimetic Studies

Biomimetic Implementations

Prototyping Diss. Writing

Res

earc

h P

rogr

ess

Journal of Mech. Design ●

SPIE Conf. ● X ASME Design Conf. ● >X

ASME IMECE Congress ● >XDea

dlin

es

ASME/IEEE Mechatronics ●


12. Potential Contributions The main potential contributions of the proposed research are as follows:

• A method for including actuators as variables in the optimization will be developed. The number, location, and orientation of the actuators will all be variables subject to change.

• This research will establish the benefit of including actuator stiffness and performance characteristics within the structural synthesis.

• Another contribution will be the consideration of “design for control” within compliant mechanisms.

• Finally, I aim to discover new aspects of the relationship between nature and design, addressing the appropriate use of biomimicry.

The key project deliverables will be mathematical characterizations, automatic design

synthesis software, and two journal papers tentatively on the following topics:

• Theory and Design Methodology for Synthesis of Compliant Mechanisms with Embedded Actuation

• Design for Embedded Actuation, Sensing, and Control in Distributed Compliant Systems

In addition, I propose a third journal article to write after September 2006 and completion

of the doctoral degree:

• Biologically-inspired Design and Interpretation of Adaptive, Distributed, and Embedded Compliant Systems

The proposed research advances the current state of the electromechanical systems design

in many fundamental ways. Traditionally, structures, mechanisms, actuators, and sensor design

is the focus of different people paying marginal attention to one another, resulting in suboptimal

systems. The proposed research paves way to a scientific approach to true mechatronic system

design rather than focus primarily on structures, sensors, or actuators.

The result of the proposed biologically-inspired research is a fundamental understanding

of what it takes to generate a globally-optimal solution for compliant systems with embedded

actuation and sensing. In sharp contrast to the current practice of “slapping on” actuators and

sensors to a finished design, the creative stage of design will simultaneously consider the

structural stiffness, power consumption, and actuator and sensor characteristics.


13. Summary In conclusion, I am leveraging my previous research experiences to develop a new design

paradigm for creating biologically-inspired devices for a variety of applications. I will introduce

many new aspects to the field of compliant mechanism design, including embedded actuators,

design for control, and genetic engineering within the synthesis algorithms. While pursuing this

goal, I while pay special attention to the methods and benefits of applying biomimicry to

mechanical system design. The culmination of my Ph.D. work will be transforming computer-

generated designs with optimized geometry, materials, and properties directly into the physical

realization of functional, embedded, and distributed compliant systems.


14. References

14.1. General Huber, JE, Fleck, NA and Ashby, MF. (1997). “The selection of mechanical actuators based on performance indices.” Proc R. Soc. 453: 2185-2205. Holger H. Hoos and Thomas Stützle: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (CA), USA, 2004 Ogata, Katsuhiko. Modern Control Engineering, Englewood Cliffs, NJ: Prentice Hall, 1990. Trease, B. P., 2001, “A Survey and Comparison of Smart Material Linear Actuators,” University of Michigan / WPAFB Internal Report, www-personal.engin.umich.edu/~btrease/share/Trease_Actuator_Report.doc

14.2. Compliant Mechanisms Anathasuresh, G.K., “A New Design Paradigm for Micro-Electro-Mechanical Systems & Investigations on the Compliant Mechanism Synthesis”, PhD Dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor. Frecker, M.I., Ananthasuresh, G.K., Nishiwaki, S., Kikuchi, N., and Kota, S., 1997, "Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization," ASME Journal of Mechanical Design, 119(2):238-245. Hetrick, J.A., 1999, "An Energy Efficiency Approach for Unified Topological and Dimensional Synthesis of Compliant Mechanisms," Ph.D. Dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor. Hetrick, J. and Kota, S., 1999, "An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms," ASME Journal of Mechanical Design, 121:229-234. Paros, J.M. and Weisbord, L., 1965, “How to Design Flexure Hinges”, Machine Design, pp. 151-156 Joo, J., 2001, "Nonlinear Synthesis of Compliant Mechanisms: Topology and Size and Shape Design," PhD Dissertation, Mechanical Engineering, University of Michigan, Ann Arbor. Joo, J., Kota, S., and Kikuchi, N., 2000, "Topological Synthesis of Compliant Mechanisms Using Linear Beam Elements," Mechanics Based Design of Structures and Machines, 28(4):245-280. Joo, J., Kota, S., and Kikuchi, N., 2001, "Large Deformation Behavior of Compliant Mechanisms," ASME 2001 Design Engineering Technical Conference, Pittsburg, PA, DETC2001:DAC-21084.


http://www-personal.engin.umich.edu/~btrease/share/Trease_Actuator_Report.doc

Kota, S., Rodgers, M.S., and Hetrick, J.A., 2001, "Compliant Displacement-Multiplying Apparatus for Microelectromechanical Systems," United States Patent No. 6,175,170. Hetrick, J. and Kota, S., 2003, "Displacement Amplification Structure and Device," United States Patent No. 6,557,436. Howell, L.L., 2001, "Compliant Mechanisms," John Wiley and Sons, Inc. Saxena, A. and Ananthasuresh, G.K., 2001, "Topology Optimization of Compliant Mechanisms with Strength Considertations," Mechanics of Structures and Machines, 29(2):199-221. Saggere, L., 1997, "Static Shape Control of Smart Structures: A New Approach Utilizing Compliant Mechanisms," Ph.D. Dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor.

14.3. Related Work Anusonti-Inthra, P., Gandhi, F. , and M. Frecker, 2003, Design of a Conformable Rotor Airfoil Using Distributed Piezoelectric Actuation, Proceedings ASME International Mechanical Engineering Congress and Exposition, Adaptive Structures Symposium, Washington, DC, November 16-21, 2003. Paper IMECE2003-42659. Bharti, S., and M. Frecker, 2003, Compliant Mechanical Amplifier Design Using Multiple Optimally Placed Actuators, Proceedings ASME International Mechanical Engineering Congress and Exposition, Adaptive Structures Symposium, Washington, DC, November 16-21, 2003. Paper IMECE2003-42658. Silva, E.C.N., 1998, “Design of Piezocomposite Materials and Piezoelectric Transducers using Topology Optimization”, PhD Dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor.

14.4. Load Path Method Akhtar, S., Tai, K., and Prasad, J., 2002, "Topology Optimization of Compliant Mechanisms Using Evolutionary Algorithm with Design Geometry Encoded as a Graph," ASME 2002 Design Engineering Technical Conferences, Montreal, Canada, DETC2002:DAC-34147. Lu, K., 2004, “Synthesis of Shape Morphing Compliant Mechanisms”, PhD Dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor. Tai, K. and Chee, T.H., 2000, "Design of Structures and Compliant Mechanisms by Evolutionary Optimization of Morphological Representations of Topology," ASME Journal of Mechanical Design, 122:560-566. Tai, K., Cui, G.Y., and Ray, T., 2002, "Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape," Journal of Mechanical Design, Transactions of the ASME, 124(3):492-500.


14.5. Biology Loomis, J. M. (1992) Distal attribution and presence. Presence: Teleoperators and Virtual Environments, 1, 113-119.

Thompson Richard Lee. "Integration of Visual and Haptic Feedback for Teleoperation". www.robots.ox.ac.uk/ActiveVision/ Papers/thompson_dphil2001/thompson_dphil2001.pdf Trease, B.P., Lu, K.J., and Kota, S., Biomimetic Compliant System for Smart Actuator-Driven Aquatic Propulsion: Preliminary Results, ASME International Mechanical Engineering Congress & Exposition, Washington, D.C., IMECE2003-41446, November 16-21, 2003


http://www.engin.umich.edu/labs/csdl/papers/imece03btrease-kjlu.pdf

http://www.engin.umich.edu/labs/csdl/papers/imece03btrease-kjlu.pdf

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Embedded Actuators, Sensors, and Structure in Adaptive and ...btrease/share/trease-prelim-proposal.pdf · Embedded Actuators, Sensors, and Structure in Adaptive and Distributed Compliant