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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.