The presentation is dedicated to special theoretical aspects of control for quadrupedal walking. The assumed case of control on high abstraction level includes usage of peculiarities of mechanisms with changeable structure (with consideration of biological analog - horse front legs and gait), characteristics of sensory and suggestion of control concept realization. This concept based on special developed technique that uses biological principle of imprinting and probability control (predictive sensory templates) with auto recomplication possibility. Predictive sensory templates allow the control system to work and to allocate all necessary functions using low-end level of CPU speed. Presentation includes slides of experiment that was conducted with walking horse on step allure using strobelight photography.

1. Special Aspects of Control
for Quadrupedal Walking
based on Biological
Principles
Andrei Vukolov
assistant tutor, Pd.D. student
Bauman Moscow State Technical University

2. 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.

3. Experiment: Planning
1. Arena edge;
2. Object (horse);
3. Camera;
4. Stroboscope;
5. Holder;
6. Optical system
(lens, filters);
7. Lightbox;
α. Aperture angle;
β. Emission angle;

4. 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

5. Experiment: Results

6. 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

7. Structure Changing
1. Leg;
2. Arm;
3. Hoof;
Leg working in
loaded state

8. Constant Structure Conditions

9. Elasticity of the Leg
1. Arm;
2. Hoof;
3. Stab;
σ - biomechanical rotary stiffness [N/(m·rad)]

10. 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.

11. 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?

12. Control Model: Concept
Sensory 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 correspondence
Dynamic set of predefined vectors
Stored predicate frames
Links to selected control procedure after searching
process end. Realizes prediction and feedback
Probability scale
Predicate realization probability is used as weight
coefficient for matching priority definition while
searching in table of correspondence

13. 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.

14. 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

15. 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.

16. 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.

17. Thank you for your attention!