Cross-Entropy Randomized Motion Planning

This paper is concerned with motion planning for nonlinear robotic systems operating in constrained environments. Motivated by recent developments in sampling-based motion planning and Monte Carlo optimization we propose a general randomized path planning method based on sampling in the space of trajectories. The idea is to construct a probability distribution over the set of feasible paths and to perform the search for an optimal trajectory through importance sampling. At the core of the approach lies the cross-entropy method for estimation of rare-event probabilities. The algorithm recursively approximates the optimal sampling distribution which guides the set of sampled trajectories towards regions of progressively lower cost until converging to a delta distribution at the optimum. Our main goal is to provide a framework for consistent adaptive sampling correlating the spatial structure of trajectories and their computed costs. The approach is illustrated with two simple examples--a point mass vehicle and the Dubins car, and is then applied to a simulated helicopter flying optimally in a 3-D terrain.