Distributionally Robust Sampling-Based Motion Planning Under Uncertainty

We propose a distributionally robust incremental sampling-based method for kinodynamic motion planning under uncertainty, which we call distributionally robust RRT (DR-RRT). In contrast to many approaches that assume Gaussian distributions for uncertain parameters, here we consider moment-based ambiguity sets of distributions with given mean and covariance. Chance constraints for obstacle avoidance and internal state bounds are then enforced under the worst-case distribution in the ambiguity set, which gives a coherent assessment of constraint violation risks. The method generates risk-bounded trajectories and feedback control laws for robots operating in dynamic, cluttered, and uncertain environments, explicitly incorporating localization error, stochastic process disturbances, unpredictable obstacle motion, and uncertain obstacle location. We show that the algorithm is probabilistically complete under mild assumptions. Numerical experiments illustrate the effectiveness of the algorithm.