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This paper presents a tool for addressing a key component in many algorithmsfor planning robot trajectories under uncertainty: evaluation of the safety ofa robot whose actions are governed by a closed-loop feedback policy near anominal planned trajectory. We describe an adaptive importance sampling MonteCarlo framework that enables the evaluation of a given control policy forsatisfaction of a probabilistic collision avoidance constraint which alsoprovides an associated certificate of accuracy (in the form of a confidenceinterval). In particular this adaptive technique is well-suited to addressingthe complexities of rigid-body collision checking applied to non-linear robotdynamics. As a Monte Carlo method it is amenable to parallelization forcomputational tractability, and is generally applicable to a wide gamut ofsimulatable systems, including alternative noise models. Numerical experimentsdemonstrating the effectiveness of the adaptive importance sampling procedureare presented and discussed.

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