Time-optimal sampling-based motion planning for manipulators with acceleration limits

Abstract

Robot actuators have physical limitations in how fast they can change their velocity. The more accurately planning algorithms consider these limitations, the better the robot is able to perform.

Sampling-based algorithms have been successful in geometric domains, which ignore actuator limitations. They are simple, parameter-free, probabilistically complete and fast. Even though some algorithms like RRTs were specifically designed for kinodynamic problems, which take actuator limitations into account, they are less efficient in these domains or are, as we show, not probabilistically complete.

A common approach to this problem is to decompose it, first planning a geometric path and then time-parameterizing it such that actuator constraints are satisfied. We improve the reliability of the latter step. However, the decomposition approach can neither deal with non-zero start or goal velocities nor provides an optimal solution.

We demonstrate that sampling-based algorithms can be extended to consider actuator limitations in the form of acceleration limits while retaining the same advantageous properties as in geometric domains. We present an asymptotically optimal planner by combining a steering method with the RRT* algorithm. In addition, we present hierarchical rejection sampling to improve the efficiency of informed kinodynamic planning in high-dimensional spaces.