Safe Motion Planning for Serial-Chain Robotic Manipulators via Invariant Sets

Ongoing research is focused on developing autonomous motion-planning algorithms capable of addressing nonlinear robot manipulator dynamics and non-convex collision avoidance constraints. This letter extends the application of the invariant-set motion planner (ISMP) to robot motion planning. We broaden the proof of output admissibility for configuration-space bubbles, accommodating robots with both prismatic and revolute joints. We derive a constraint admissible positive invariant (CAPI) subset within the configuration-space bubble for closed-loop system dynamics, integrating proportional-derivative joint controllers. Furthermore, we outline conditions for CAPI sets to be input admissible. Utilizing random exploring tree techniques, we identify a sequence of CAPI sets to guide the robot from an initial configuration to a goal equilibrium state while avoiding collisions. We illustrate the effectiveness and feasibility of the ISMP through a simulation involving the Universal Robots UR5e mounted on an actuated rail, modeled as a prismatic joint. Simulation results validate that ISMP for robot motion planning.