Special Aspects of Control for Quadrupedal Walking based on Biological PrinciplesAndrei Vukolovassistant tutor, Pd.D. student

Bauman Moscow State Technical University

Experimental Basis: Targeting Obtain strobelight photographs of horse

walking on step allure; Treat the photographs to explore cases of

structure changing and load state of front leg; Make an assumption for structure changing

control mechanism; Make an assumption for possible method of

control (gait automatism) and sensory states.

Experiment: Planning1. Arena edge;2. Object (horse);3. Camera;4. Stroboscope;5. Holder;6. Optical system

(lens, filters);7. Lightbox;. Aperture angle;. Emission angle;

Experiment: Results

The photograph above contains record of leg kinematical chain structure changing.

Strobelight photographs obtained with 4-16 strobelight impulses on timings 0.02 – 0.3 s.Video recorded in 25fps DVCAM SD mode

Experiment: Results

Experiment: Results These graphs are

representing projections of the leg joints speed vectors on propelling speed vector axis;

Intersection of the graphs represents point of assumed leg structure changing (loading).

timing (s)

m/s

Structure Changing

1. Leg;2. Arm;3. Hoof;

Leg working inloaded state

Constant Structure Conditions

Elasticity of the Leg

1. Arm;2. Hoof;3. Stab;

- biomechanical rotary stiffness [N/(m·rad)]

Typical Schemes of Control Full Determination: the control service contains full mathematical model

of whole system behavior to calculate motion and propelling actions through onboard modeling: All aspects of motion should be represented in model; Structure of the model is nonlinear so the model is very sophisticated in case of

med and high system integrity level; Predefined Synergy: control system must calculate parameters of

behavior for each part of the mechanism according to current state of others by predefined array of equations: Requires integration of many differential equations, so high CPU class and

requirements are defined; Predicate-to-Correction mode: control system compares the incoming

sensory with table of correspondence to calculate (or play) correction: Requires optimization of search operations and onboard database; Size of correspondence table becomes extremely large in case of large sensory

data flow.

Prediction: Tabular Technique Based on ”predicate-to-correction”

behavior model and data compression principles;

Frame of incoming sensory data is being compared to full table of correspondence (database);

Matching redirects to prediction sector where strongly determined correction procedures and stored sensory predicates are defined;

Found predicate is used to determine new system state and to make a decision: should system make new entry into the database or not?

Control Model: ConceptSensory vector Represents n values (e.a. for n independent sensors) of the incoming sensory data block

Set of control procedures C(r) Implements all actions that are possible for system (procedures, macros etc.)

Table of correspondenceDynamic set of predefined vectors

Stored predicate framesLinks to selected control procedure after searching process end. Realizes prediction and feedback

Probability scalePredicate realization probability is used as weight coefficient for matching priority definition while searching in table of correspondence

Control Model: Structure After assembly of all

constant data the info block of 4 independent vectors is defined;

The rendered block provides arbitrary access to internal vectors using linear indexes m, n, k, f. In fact the sequence of such blocks is defined as non-relational database.

Each incoming frame creates the link between elements of prediction database M.

Searching criteria: rsen acts as an argument; The realization probability P

could be used as weight coefficient while selection of correction procedure;

Predicates can be used as the searching criteria to choose the proper correction procedure for each case of motion.

Templates: Static Linking

Any repeated process with similar incoming sensory creates a repeatable link (template) in the database. This link can be easily recognized and stored;

Indexing of links creates an executable objective structure (predictive sensory template) that requires only to store index set [m, n, f, k] defined constantly on long time (statistically significant set of incoming sensory frames rsen).

rsen

Resulting rsen

Templates: Structural View Template is an executable

structure; Any action defined within

control system can be represented as set of templates (metaprints);

Templates reveals similar behavior with fully automated reflex (imprints) of higher animals.

Dynamic behavior: template is not imperative control procedure because every action produces new sensory. Resulting unpredictable sensory can be used as argument to search next template.

Templates: Prediction The task of prediction could be

declared as searching for template for execution in future using probability and predicate frames from set of templates which are lying between;

Determination of the template sequence for desired action is only thing that is needed for prediction;

Now the predicate of the first template in sequence must be used for the next one as incoming data. After that we have next predicate without execution of correction procedures. To predict further iterations the system must build a chain of templates which could be executed to obtain desired behavior.

Thank you for your attention!