Time-optimal obstacle avoidance

This paper presents a method for generating near-time optimal trajectories in cluttered environments for manipulators with invariant inertia matrices. For one obstacle, the method generates the time-optimal trajectory by minimizing the time-derivative of the return (cost) function for this problem, satisfying the Hamilton-Jacobi-Bellman (HJB) equation. For multiple obstacles, the trajectory is generated using the pseudo return function, which is an approximation of the return function for the multi-obstacle problem. The pseudo return function avoids one obstacle at a time, producing near-optimal trajectories that are guaranteed to avoid the obstacles and satisfy the actuator constraints. An example with circular obstacles demonstrates close correlation between the near-optimal and optimal paths, requiring computational efforts that are suitable for on-line implementations