  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 real-time 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.
