Evaluating Trajectory Collision Probability through Adaptive Importance Sampling for Safe Motion Planning

This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal planned trajectory. We describe an adaptive importance sampling Monte Carlo framework that enables the evaluation of a given control policy for satisfaction of a probabilistic collision avoidance constraint which also provides an associated certificate of accuracy (in the form of a confidence interval). In particular this adaptive technique is well-suited to addressing the complexities of rigid-body collision checking applied to non-linear robot dynamics. As a Monte Carlo method it is amenable to parallelization for computational tractability, and is generally applicable to a wide gamut of simulatable systems, including alternative noise models. Numerical experiments demonstrating the effectiveness of the adaptive importance sampling procedure are presented and discussed.