Dual Formulation for Chance Constrained Stochastic Shortest Path with Application to Autonomous Vehicle Behavior Planning

Autonomous vehicles face the problem of optimizing the expected performance of subsequent maneuvers while bounding the risk of collision with surrounding dynamic obstacles. These obstacles, such as agent vehicles, often exhibit stochastic transitions that should be accounted for in a timely and safe manner. The Constrained Stochastic Shortest Path problem (C-SSP) is a formalism for planning in stochastic environments under certain types of operating constraints. While C-SSP allows specifying constraints in the planning problem, it does not allow for bounding the probability of constraint violation, which is desired in safety-critical applications. This work's first contribution is an exact integer linear programming formulation for Chance-constrained SSP (CCSSP) that attains deterministic policies. Second, a randomized rounding procedure is presented for stochastic policies. Third, we show that the CC-SSP formalism can be generalized to account for constraints that span through multiple time steps. Evaluation results show the usefulness of our approach in benchmark problems compared to existing approaches.