Kinodynamic planning for robotic manipulators using set-based methods

We revisit the trajectory planning problem for general N-link robotic manipulators. Our approach focuses on characterising the whole set of states that can be transferred to a target set of velocities without violating constraints. To achieve this, we work in the commonly utilized two dimensional projected space of the Lagrangian dynamics on a specific predefined path. The produced dynamics is a double integrator, with nonlinearities being pushed into a non-convex and state-dependent input constraint set. We approach the problem as a special reach-avoid set computation problem using ordering properties of the trajectories generated by a suitably parame-terised state feedback control law. Our results are illustrated in simulation using a realistic model of the UR5™ commercial robot.