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In this paper, a risk-aware motion control scheme is considered for mobilerobots to avoid randomly moving obstacles when the true probabilitydistribution of uncertainty is unknown. We propose a novel model predictivecontrol (MPC) method for limiting the risk of unsafety even when the truedistribution of the obstacles' movements deviates, within an ambiguity set,from the empirical distribution obtained using a limited amount of sample data.By choosing the ambiguity set as a statistical ball with its radius measured bythe Wasserstein metric, we achieve a probabilistic guarantee of theout-of-sample risk, evaluated using new sample data generated independently ofthe training data. To resolve the infinite-dimensionality issue inherent in thedistributionally robust MPC problem, we reformulate it as a finite-dimensionalnonlinear program using modern distributionally robust optimization techniquesbased on the Kantorovich duality principle. To find a globally optimal solutionin the case of affine dynamics and output equations, a spatial branch-and-boundalgorithm is designed using McCormick relaxation. The performance of theproposed method is demonstrated and analyzed through simulation studies using anonlinear car-like vehicle model and a linearized quadrotor model.

Wasserstein Distributionally Robust Motion Control for Collision Avoidance Using Conditional Value-at-Risk