Page 89 - Dynamic Vision for Perception and Control of Motion

3.4 Behavioral Capabilities for Locomotion 73

ment of the most powerful brain found on our planet. Some species even use their
tail to improve climbing and swinging performance in trees.
Without locomotion of the body, subjects with articulated bodies in both the
biological and the technical realm are able to move their limbs for some kind of
behavior. Grasping for objects nearby may be found in both areas (arm motion of
animals or of industrial robots). Humans may use their arms for conveying infor-
mation to a partner or to opponents. Cranes move their arms for loading and un-
loading vehicles or for lifting goods.
This may suffice to show the generality of the approach for understanding dy-
namic scenes by body shapes, their articulations, and their degrees of freedom for
motion, controlled by some actuators with constrained motion capabilities, which
get their commands from some data and knowledge processing device. Species
may be recognized by their stereotypical motion behaviors, beside their appearance
with 3-D shape and surface properties.

3.4.1 The General Model: Control Degrees of Freedom

To enable the link between image sequence interpretation and understanding mo-
tion processes with subjects in the real world, a few basic properties of control ap-
plication are discussed here. Again, it is not intended to treat all possible classes of
subjects but to concentrate on just one class of technical subjects from which a lot
of experience has been gained by our group over the last two decades: Road vehi-
cles (and air vehicles not treated here).

3.4.1.1 Differential Equations with Control Variables

As mentioned in the introduction, control variables are the variables in a dynamic
system that distinguishes subjects from objects (proper). Control variables may be
changed at each time “at will”. Any kind of discontinuities are allowed; however,
very frequently control time histories are smooth with a few points of discontinuity
when certain events occur.
Differential equations describe constraints on temporal changes in the system,
including the effects of control input. Again, standard forms are n equations of first
order (“state equations”) for an nth order system. In the transformed frequency
domain, they are usually given as a set of transfer functions of nth order for linear
systems. There is an infinite variety of (usually nonlinear) differential equations for
describing the same temporal process. System parameters p allow us to adapt the
representation to a class of problems
dX/dt = f (X , U , p , t ) . (3.2)
Since real-time performance usually requires short cycle times for control, lin-
earization of the equations of motion around a nominal set point (index N) is suffi-
ciently representative of the process, if the set point is adjusted along the trajectory.
With the substitutions
X = X + x , U = U + u , (3.3)
N
N