Kinodynamic path switching for robotic manipulators

Abstract

We extend trajectory planning methods for robotic manipulators to the more general and complex path planning problem in both the space of joints and their velocities. We consider a set of prespecified feasible paths, together with their associated, precomputed safe sets in the projected space of the dynamics restricted to the path. We ask a natural question, namely, whether we can state geometric conditions, together with their algebraic equivalents, that allow switching between paths, providing thus greater flexibility, enabling path planning capabilities. We answer affirmatively, and pose conditions whose consistency can be checked by solving a set of algebraic conditions and by computing intersections between safe sets, precisely, reach-avoid sets. Controllers can also be extracted for closed-loop switched paths. Our proof-of-concept analysis suggests that under the developed framework, composition between paths is possible, thus, potentially significantly extending the applicability of the approach and complementing existing planning methods.