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

In this article, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty unknown. We propose novel model-predictive (MPC) method limiting risk unsafety even obstacles’ movements deviates, within an ambiguity set , from empirical obtained using limited amount sample data. By choosing ambiguity set as statistical ball with its radius measured by xmlns:xlink="http://www.w3.org/1999/xlink">Wasserstein metric we achieve probabilistic guarantee xmlns:xlink="http://www.w3.org/1999/xlink">out-of-sample risk evaluated new data generated independently training To resolve infinite-dimensionality issue inherent in distributionally robust MPC problem, reformulate it finite-dimensional nonlinear program modern optimization techniques based on Kantorovich duality principle. find globally optimal solution case affine dynamics and output equations, spatial branch-and-bound algorithm designed McCormick relaxation. The performance proposed demonstrated analyzed through simulation studies dynamic kinematic vehicle models linearized quadrotor model. results indicate that, size small, can successfully out-of-sample risk, while average approximation counterpart fails do so.