In this paper, we investigate methods for steering systems with
nonholonomic constraints between arbitrary configurations. Early work
by Brockett derives the optimal controls for a set of canonical systems
in which the tangent space to the configuration manifold is spanned by
the input vector fields and their first order Lie brackets. Using
Brocket's result as motivation, we derive suboptimal trajectories for
systems which are not in canonical form and consider systems in which
it takes more than one level of bracketing to achieve controllability.
These trajectories use sinusoids at integrally related frequencies to
achieve motion at a given bracketing level. We define a class of
systems which can be steered using sinusoids (chained systems) and give
conditions under which a class of two-input systems can be converted
into this form.
Real Time Feedback Control for Nonholonomic Mobile Robots With Obstacles We introduce a method for constructing smooth feedback laws for a
nonholonomic robot in a 2-dimensional polygonal workspace. First, we
compute a smooth feedback law in the workspace without taking the
nonholonomic constraints into account. We then give a general technique
for using this to construct a new smooth feedback law over the entire
3- dimensional configuration space (consisting of position and
orientation). The trajectories of the resulting feedback law will be
smooth and will stabilize the position of the robot in the plane,
neglecting the orientation. Our method is suitable for real time
implementation and can be applied to dynamic environments. |