Data-Driven Stochastic Model Predictive Control for Nonconvex Path Planning of Vehicles

Collision-free path planning in nonconvex environments is challenging due to potential constraint violations between time steps and the difficulty of obtaining true uncertainty distributions. Although many optimization-based methods, such as Model Predictive Control (MPC), have been proposed, most rely on exact disturbance knowledge. Moreover, existing methods typically handle only open-loop uncertainty, leading to uncontrolled state covariance and overly conservative paths. This work presents a Data-driven Stochastic MPC (DSMPC) for vehicle path planning amid obstacles and unknown unbounded disturbances. DSMPC explicitly bounds failure probability, ensures recursive feasibility under weak noise assumptions, and addresses implementation via convex optimization. It controls the full state distribution, steering it from initial to target, while handling nonconvex constraints via convex reconstruction. For unknown Gaussian noise with finite variance, we derive a confidence upper-bound from samples, avoiding performance degradation due to prior knowledge deviations. We also provide a cost reduction property, asymptotic performance bound, and recursive feasibility conditions for independent and identically distributed zero-mean and bounded-variance disturbances. Simulations show DSMPC's effectiveness in obstacle-rich cases.