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This paper presents a novel feedback method on the motion planning forunicycle robots in environments with static obstacles, along with an extensionto the distributed planning and coordination in multi-robot systems. The methodemploys a family of 2-dimensional analytic vector fields, whose integral curvesexhibit various patterns depending on the value of a parameter lambda. Morespecifically, for an a priori known value of lambda, the vector field has aunique singular point of dipole type and can be used to steer the unicycle to agoal configuration. Furthermore, for the unique value of lambda that the vectorfield has a continuum of singular points, the integral curves are used todefine flows around obstacles. An almost global feedback motion plan can thenbe constructed by suitably blending attractive and repulsive vector fields in astatic obstacle environment. The method does not suffer from the appearance ofsinks (stable nodes) away from goal point. Compared to other similar methodswhich are free of local minima, the proposed approach does not require anyparameter tuning to render the desired convergence properties. The paper alsoaddresses the extension of the method to the distributed coordination andcontrol of multiple robots, where each robot needs to navigate to a goalconfiguration while avoiding collisions with the remaining robots, and whileusing local information only. More specifically, based on the results whichapply to the single-robot case, a motion coordination protocol is presentedwhich guarantees the safety of the multi-robot system and the almost globalconvergence of the robots to their goal configurations. The efficacy of theproposed methodology is demonstrated via simulation results in static anddynamic environments.

Motion planning and Collision Avoidance using Non-Gradient Vector Fields. Technical Report