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Lecture 2:

Introduction to Concepts in Robotics

In this lecture, you will learn:

- Basic Robotics Concepts

- Start discussion on geometric aspects:frames, positions, orientations.

- Homogenous transforms

- Some math recap

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Reading Assignment

for Weeks 1-2

To cover History of Robotics and Basic Concepts,(Lectures 1-3)

Required Reading is:

- Chapters 1 F. Lewis

- Chapter 1 R. Murray

- Chapter 1 McKerrow

- Chapter 1 JJ Craig

To cover Intro to Robot Kinematics Geometry,

Frames, Transformations (Lectures 3, 4)Required Reading is:

- Chapter 2.5 from F. Lewis text

- Chapter 2.1-2.6 from J. J. Craig text

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Robot Subsystems

A mechanical structure. For manipulators this structure consists of a set of rigid bodies (links), connected

by means of articulations (joints). Links and joints can also be described interms of an arm (for mobility), a wrist (for dexterity) and an end-effector (forperforming the task).

For mobile robots, the structure consists of a chassis with a locomotionmechanism, in the form of legs, wheels, rotor blades, etc.

Actuators. These set the robot in motion through actuation of its joints, andare typical electric or hydraulic.

Sensors. These measure the status of the manipulator (propriceptivesensors) and the status of the environment (heteroceptive sensors).

A control system. This enables control and supervision of the robot, and isusually a computer with a graphical user interface, and/or a pendant.

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Typical Industrial Robot

6 DOFs

Controller

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Mechanics of Manipulators

We describe robotic manipulators in terms of theirdegrees of freedom(DOFs). 6 DOFs are needed to position and orient an object in a unique way in the 3D

space.

Most robots have no more than 6 degrees of freedom. If they do, they arecalled redundant robots. Redundant robots can be ideal for situations

requiring reaching out behind certain obstacles. The manipulator links are connected together in chains. Chains can beopen or closed.

Manipulators with open chains are also called serial, while the ones withclosed chains are called parallel.

Joints allow relative motion between links, and can be rotary (revolute R )or linear (prismaticP ).

The workspace of the manipulator is the total volume swept out by the end-effector of the manipulator. The workspace may be constrained by the fact that not all joints can rotate 360

degrees.

The workspace is defined in terms of point reachable with arbitrary orientations(dextrous workspace) or fixed orientations (reachable workspace).

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Examples of industrial

manipulator geometries

Revolute

RRR

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Cartesian

PPP

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Spherical

RRP

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SCARA

3R+P

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Parallel

Stewart platform

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Workspace Examples

Revolute

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Workspace Examples

Cartesian, Scara

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Properties of Manipulators

The most important considerations for the application of an industrialrobot are: Manipulator performance

System integration

Reconfigurability/modularity

Manipulator performance is defined as: Reach (size of workspace), and dexterity (angular displacement of

individual joints). Some robots can have unuseable workspace due todead-zones, singular poses, wrist-wrap poses.

Payload (weight that can be carried). Inertial loading for rotational wristaxes can be specified for extreme velocity and reach conditions.

Quickness (how fast it can move). Critical in determining robotthroughput but rarely specified. Maximum speeds of joints are usuallyspecified, but average speeds while carrying payloads in a workingcycle is of interest.

Duty-cycle (how fast it can repeat motions without breaking down).

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Properties of Manipulators

Precision is defined by using 3 metrics: resolution, repeatability andaccuracy.

These concepts are usually static, and dynamic precision is usually notspecified.

Accuracy is defined as how close the manipulator can come to a given pointwithin its workspace.

Accuracy varies with the location of the point Repeatability is how close the manipulator returns to the same point in

space.

Most present day manipulators are highly repeatable but not veryaccurate.

Repeatability for the manipulator is also defined as the ability to returnto a so called taught position.

Resolution is defined as the minimum motion increment that the manipulatorcan perform and detect.

example: a robot controller has 12-bit storage capacity, the fullrange of the robot = 1.0 cm for one joint

spatial resolution = 1.0cm/212 = 1.0 cm/4096 = 2.44 m

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Basic Concepts

In robotics we are constantly concerned with the location of objectsin 3D space. In order to describe it we attach a coordinate frame rigidly to an object,

or to the manipulator. We then transform the position and orientationfrom one frame to another. The frame associated with the non-movingparts of the manipulator is called the base frame, and the one attached

to the end-effector is called the tool frame.

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Basic Concepts

Kinematics is the science of motion based on geometric description, regardless ofthe forces which cause it. Kinematics deals with positions and its derivatives(velocity/acceleration).

The number ofDOFs of the manipulator equals the number of independent positionvariables that would have to be specified in order to locate all parts of themechanism. It equals the number of joints in an open kinematic chain.

Forward Kinematics refers to the problem of computing the position and orientationof the end-effector relative to the base frame given a set of joint angles.

Cartesian space (or task space, operational space) is the usual 3D Euclidian spacefor position and orientation (6 DOFs). The joint space (or configuration space) is thespace in which the manipulator is described by its joint angles.

Inverse kinematics is the problem of inverse mapping between end-effectorpositions and orientation and the joint angles. We need to map locations in taskspace to the robots internal joint space. Early robots lacked this algorithm and theywere simply taught joint spaces by moving the end-effector (by hand) to the desiredposition. The inverse kinematics problem is considerably harder than forwardkinematics because it involves solving a non-linear equation which may not have aclosed form solution. Also, no solution, or multiple solutions may exist.

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Basic Concepts

The manipulator Jacobian is a matrix that relates the velocities of thejoints to the velocities of the end-effector. When this matrix becomessingular (non-invertible), such points are called singularities. Example:WW I rear gunner.

Open chain manipulators are designed as a cascade of revolute or

prismatic joints. They usually have up to six degrees of freedom dependingon the task. For example a pick and place tasks from a 2D plane requiresonly 4 degrees of freedom. A welding operation on a car requires all 6degreed of freedom. By using two manipulators to carry a load, one forms aclosed kinematic chain. By using multiple kinematic chains, one can formmuch stiffer and precise robots called parallel manipulators.

Manipulators dont always move through free space. They are sometimesrequired to touch a workpiece and apply a force. It turns out that we can usethe manipulator Jacobian to calculate the relationship between joint torquesand the forces exerted.

The joint actuators of the manipulators are electric or hydraulic motorsused to create motion of the joints.

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Basic Concepts

Dynamics is devoted to studying the forces required to cause motion. The relationship between the joint actuator torques, the accelerations of the

robot, and the other external forces (gravity of links and payload, external forcesexerted) is studied within the context of dynamics.

Dynamics is important if we use high velocities to actuate the system.

If there is no motion involved, the force/torque balancing analysis is also calledmanipulatorstatics

Kinematics is usually sufficient if the robot is gravity compensated and moves atslow speeds.

Dynamics is necessary for simulation and control.

Motion planning refers to the study of generating motion for the robot toaccomplish a task. This consists of : Path planning - generating a feasible path from an initial position to a final

position by describing the geometric position and orientation of the robot during

the transition. Sometimes this path must avoid obstacles in the task space, and itmay be described by intermediate points (also called via-points). Sometimes thepath is a spline (e.g. a smooth function that passes through a set of via points).

Trajectory generation attaching a time frame to the paths generates atrajectory. The trajectory not only describes the position of the robot duringmotion, but also how that position changes with time.

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Basic Concepts

Manipulator control refers to a closed-loop feedback system that usessensory information to control the motion of the manipulator. A controlleraccomplishes : Trajectory tracking following the prescribed trajectory for the manipulation. End-point control - reaching a goal configuration in either task or joint space

irrespective of the trajectory it is achieved. This is also called the stabilizationproblem.

Position/velocity control

compensates for errors in knowledge of the systemsparameters and suppresses disturbances. Control algorithms can be linear ornonlinear.

Force control Controlling the force exerted by the manipulator onto an objectin a single or multiple degrees of freedom. Can be reduced to position control ifthe stiffness of the manipulator and object are known, but it usually requires forcesensing. Sometimes a scheme called hybrid control is used, e.g. controllingforce along certain DOFs and position along other DOFs.

Robot Programming Modern robots use robot programming languagesto describe tasks from users. Programming could be on-line (with the robotattached) and off-line (with a dynamic simulation model of the robot). Theissue of safety should be carefully considered when implementing on-linerobot motion. Often time robotic cells have interlocked protective enclosuresand fences.

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Robot Control Architectures

1) Functional (deliberative) vs. 2) Behavioral Model:

1) Sense-Think-Act cycle in serial mode with five

Think functional modules:

- Perception, Modeling, Planning, Task Execution, MotorControl.

Internal model maintenance/update consumes resources. This

model has problems with long reaction times.

Symbols are used to represent knowledge and generateactions.

This approach dominated robotics in the first 30 years.

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Robot Control Architectures

2) Sense-Think-Act cycle is decentralized in parallelmode. Brooks proposes a subsumption architecture(1985) with 8 behaviors:

- reason about objects, plan changes to world,identify objects, monitor changes, build maps,explore, wander, avoid objects.

Advantages: quick reaction, multiple goals, no conflict

resolution needs, easy to extend, debug, etc.Disadvantages: sub-optimal, not clear how to

describe and implement complex plans.

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Recap of Math Concepts

Vector space

Subspace

Vector norm

Matrix norm Inner product

Groups

Special matrices Eigenvectors, eigenvalues

Singular value decomposition

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