Wasserstein Distributionally Robust Risk-Constrained Iterative MPC for Motion Planning: Computationally Efficient Approximations

This paper considers a risk-constrained motion planning problem and aims to find the solution combining the concepts of iterative model predictive control (MPC) and data-driven distributionally robust (DR) risk-constrained optimization. In the iterative MPC, at each iteration, safe states visited and stored in the previous iterations are imposed as terminal constraints. Furthermore, samples collected during the iteration are used in the subsequent iterations to tune the ambiguity set of the DR constraints employed in the MPC. In this method, the MPC problem becomes computationally burdensome when the iteration number goes high. To overcome this challenge, the emphasis of this paper is to reduce the realtime computational effort using two approximations. First one involves clustering of data at the beginning of each iteration and modifying the ambiguity set for the MPC scheme so that safety guarantees still holds. The second approximation considers determining DR-safe regions at the start of iteration and constraining the state in the MPC scheme to such safe sets. We analyze the computational tractability of these approximations and present a simulation example that considers path planning in the presence of randomly moving obstacle.