An Adaptive Stepsize RRT Planning Algorithm for Open-Chain Robots

Motion planning algorithms that rely upon the randomly exploring random tree (RRT) typically require the user to choose an appropriate stepsize; this is generally a highly problem-dependent and time-consuming process requiring trial and error. We propose an adaptive stepsize RRT path planning algorithm for open-chain robots in which only a minimum obstacle size parameter is required as input. Exploiting the structure of an open chain's forward kinematics as well as a standard inequality bound on the operator-induced matrix norm, we derive a maximum Cartesian displacement bound between two configurations of the same robot, and use this bound to determine a maximum allowable stepsize at each iteration. Numerical experiments involving a ten-DOF planar open chain and a seven-axis industrial robot arm demonstrate the practical advantages of our algorithm over standard fixed-stepsize RRT planning algorithms.