Time-optimal obstacle avoidance for robotic manipulators

摘要

This thesis presents a method for the on-line generation of near-time optimal trajectories for robotic manipulators with actuator constraints moving in a cluttered environment. The near-time optimal trajectories are generated by avoiding obstacles one at a time using the pseudo return function. This reduces the computationally complex time-optimal obstacle avoidance problem to m simple sub-problems, facilitating on-line implementation. In spite of its simplicity, this approach is guaranteed to yield trajectories terminating at the target for all initial states under very unrestrictive conditions. Examples with circular and elliptical obstacles demonstrate close correlation between the exact and near-time optimal trajectories, and the computational efficiency of the proposed approach. An on-line method for generating near-shortest paths in a cluttered environment is also presented. Here, near-shortest paths are generated by following the negative gradient of the pseudo return function for the Kinematic Problem. As a result, the computation of the path is independent of the number of obstacles at all but a finite number of points. These paths are guaranteed to terminate at the goal for all initial conditions. The computational efficiency of this approach is demonstrated for a large number of circular and polygonal obstacles. This thesis also presents a new sufficient condition for time-optimal control, which generalizes the existing sufficient conditions for time-optimal control, the Hamilton-Jacobi-Bellman equation and Nahi's Theorem. A potential field-based method for generating near-time optimal paths on-line is also included.