Smooth Point-to-Point Trajectory Planning in $SE$ (3)with Self-Collision and Joint Constraints Avoidance

In this paper we introduce a novel point-to-point trajectory planner for serial robotic structures that combines the ability to avoid self-collisions and to respect motion constraints, while complying with the requirement of being $C^{4}$ continuous. The latter property makes our approach also suited for 4th order dynamics flexible joint robots, which gained significant practical relevance recently. In particular, we address the problem of generating a smooth, kinematically nearly time-optimal $SE$ (3)trajectory while simultaneously avoiding potential collisions of the robot end-effector with its base as well as respecting the Cartesian unreachable states induced by the joint limits of the proximal kinematic structure.