Online-Learning-Enabled Distributionally Robust Motion Control via Uncertainty Propagation and Ambiguity Set Compression

We develop a safe, efficient, and flexible motion control framework for collision-free navigation of robots in uncertain and dynamic environments. With the gathered real-time data at each control time, the motion distribution of obstacles is estimated from data streams by leveraging the Dirichlet process mixture model. We propose a novel uncertainty propagation method, which theoretically admits the derivation of obstacle position distributions over the entire prediction horizon only based on the current position and motion distribution of obstacles. To enhance the robustness against estimated distribution errors, an ambiguity set utilizing local-moment information of position distributions is constructed. Additionally, we introduce a compression scheme to automatically adjust the complexity (granularity) of the ambiguity set by aggregating distributions that are close in Wasserstein space, thereby flexibly striking a trade-off between control performance and computation time. The distributionally robust collision avoidance constraint based on the compressed ambiguity set is reformulated into separating hyperplanes, which are applied in the model predictive controller to obtain the optimal collision-free trajectory. To resolve the infinite-dimensionality issue inherent in the computation of the separating hyperplanes, we equivalently derive a tractable semi-definite programming formulation exploiting distributionally robust optimization techniques. The efficacy of the proposed framework is demonstrated through simulation.