Reachability based planning for robotic manipulators

Given a path, defined typically in the workspace, we recover the admissible velocity profiles and the realisable corresponding torque profiles that achieve a path traversal. To make this possible, we introduce a new torque feedback parameterisation. This enables us to construct the set where the trajectory of the projected path can be confined while reaching a target set with a feasible control action, namely, the reach-avoid set.

As a product of this procedure, we develop feedback controllers that guarantee state and input constraint satisfaction, can track reference trajectories, and can handle temporal specifications related, for example, to rendezvous and avoidance setups. Encouraging experimental evaluation of our theoretical results on a UR10 robotic manipulator suggests the framework and extensive simulation toolbox can complement and further expand the existing classical approaches.<br><br>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.<br><br>