Safe Set-Based Trajectory Planning for Robotic Manipulators

Inspired by the line of seminal works on projected path dynamics and time-optimal control of robots, which originated in the 1980s, and recent advances on the computation of safe sets for complex systems in control, we present a new trajectory planning framework for
$N$
-link robotic manipulators. Given a path, defined typically in the workspace, we recover the admissible velocity profiles and the realizable corresponding torque profiles that achieve a path traversal. To make this possible, we introduce a new torque feedback parameterization. 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 proof-of-concept experimental evaluation of the theory on a UR10 robotic manipulator suggests the framework can complement and further expand the existing classical approaches.