Extending First-order Motion Planners to Second-order Dynamics

This paper extends first-order motion planners to robots governed by second-order dynamics. Two control schemes are proposed based on the knowledge of a scalar function whose negative gradient aligns with a given first-order motion planner. When such a function is known, the first-order motion planner is combined with a damping velocity vector with a dynamic gain to extend the safety and convergence guarantees of the first-order motion planner to second-order systems. If no such function is available, we propose an alternative control scheme ensuring that the error between the robot's velocity and the first-order motion planner converges to zero. The theoretical developments are supported by simulation results demonstrating the effectiveness of the proposed approaches.