Time optimal navigation via slack time sets

An algorithm for determining the minimum-time obstacle avoidance trajectory for a robot is presented. Since different joints, when moved independently, may reach their desired end values at different times, any delay of a joint, other than the slowest, will not affect the total time of motion. This natural redundancy is used with obstacle avoidance to simplify any path search algorithm by at least one order of magnitude (one degree of freedom less). By neglecting the presence of all obstacles and assigning to each actuator maximum control torque (bang-bang), a lower-bound estimate of the time T_task needed to complete a task is calculated. The A^* heuristic search is used to search the subset of the state space which contains only those states which are members of a trajectory with a task time equal to T_task. If no trajectory is found during the initial search, the subset of the state space being examined is sequentially increased until a valid trajectory is found. Since, in general, the minimum-time obstacle avoidance trajectory is not unique, secondary constraints such as minimum distance in the state space and others can also be satisfied