A Stochastic Nonlinear Model Predictive Control with an Uncertainty Propagation Horizon for Autonomous Vehicle Motion Control

Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in high-dimensional systems with extended prediction horizons, such as autonomous vehicles. To enhance closed-loop performance and feasibility in SNMPCs, we introduce the Uncertainty Propagation Horizon (UPH) concept. The UPH limits the time for uncertainty propagation through system dynamics, preventing the divergence of uncertain states' evolution and too tightened constraints, leveraging feedback loop advantages, and reducing computational overhead. Our SNMPC approach utilizes Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates nonlinear hard constraints on state expectations and nonlinear probabilistic constraints. We transform the probabilistic constraints into deterministic constraints by estimating the nonlinear constraints' expectation and variance and then formulate a general SNMPC problem. We showcase our algorithm's effectiveness in real-time control of a high-dimensional, highly nonlinear system-the motion control of an autonomous passenger vehicle, modeled with a dynamic nonlinear single-track model. Experimental results demonstrate our approach's robust capability to follow an optimal racetrack trajectory at speeds up to 37.5m/s while dealing with state estimation disturbances, achieving a minimum solving frequency of 97Hz. Additionally, our experiments illustrate that limiting the UPH renders previously infeasible SNMPC problems feasible, even when incorrect uncertainty assumptions or strong disturbances exist. The code used in this research is publicly accessible as open-source software: https://github.com/bzarr/TUM-CONTROL