  This paper presents a novel feedback method on the motion planning for
unicycle robots in environments with static obstacles, along with an extension
to the distributed planning and coordination in multi-robot systems. The method
employs a family of 2-dimensional analytic vector fields, whose integral curves
exhibit various patterns depending on the value of a parameter lambda. More
specifically, for an a priori known value of lambda, the vector field has a
unique singular point of dipole type and can be used to steer the unicycle to a
goal configuration. Furthermore, for the unique value of lambda that the vector
field has a continuum of singular points, the integral curves are used to
define flows around obstacles. An almost global feedback motion plan can then
be constructed by suitably blending attractive and repulsive vector fields in a
static obstacle environment. The method does not suffer from the appearance of
sinks (stable nodes) away from goal point. Compared to other similar methods
which are free of local minima, the proposed approach does not require any
parameter tuning to render the desired convergence properties. The paper also
addresses the extension of the method to the distributed coordination and
control of multiple robots, where each robot needs to navigate to a goal
configuration while avoiding collisions with the remaining robots, and while
using local information only. More specifically, based on the results which
apply to the single-robot case, a motion coordination protocol is presented
which guarantees the safety of the multi-robot system and the almost global
convergence of the robots to their goal configurations. The efficacy of the
proposed methodology is demonstrated via simulation results in static and
dynamic environments.
