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

Wasserstein distributionally robust risk-constrained iterative MPC for motion planning: computationally efficient approximations