This work is concerned with motion planning for nonlinear robotic systems operating in constrained environments. A method for computing high-quality trajectories is proposed building upon recent developments in sampling-based motion planning and stochastic optimization. The idea is to equip sampling-based methods with a probabilistic model that serves as a sampling distribution and to incrementally update the model during planning using data collected by the algorithm. At the core of the approach lies the cross-entropy method for estimation of rare-event probabilities. The cross-entropy method is combined with rapidly-exploring random tree methods in order to handle complex environments. The main goal is to provide a framework for consistent adaptive sampling that correlates the spatial structure of trajectories and their computed costs in order to improve the performance of existing planning methods.
Example application to minimum-time planning for 12-dof underactuated helicopter in an urban terrain: