Racing miniature cars: Enhancing performance using Stochastic MPC and disturbance feedback

Abstract

We study and compare different Stochastic Model Predictive Control (MPC) approaches for driving miniature race cars, where the goal is to race the cars as fast as possible around a known track. Designing such controllers is generally challenging since the models are not entirely accurate due to linearization errors and model mismatch. Consequently, deterministic MPC tends to be optimistic, causing the cars to leave the race track, resulting in accidents. To mitigate these shortcomings, methods based on Stochastic MPC have been proposed that ensure constraint satisfaction with high probability. Furthermore, one can reduce conservatism of the solution by optimizing over feedback policies at the expense of increased computational time. While methods based on affine state feedback policies have been shown to perform well, their performance critically depends on the choice of the feedback matrix. One way to ensure computational tractability is to fix the feedback matrix in an a-priori computation which is typically obtained via trial-and-error. To overcome this issue, we investigate the benefits of disturbance feedback policies, which allows us to (indirectly) optimize over the state feedback matrices. We verify the benefits of disturbance feedback policies in simulations, and also implement a heuristic variant on the actual system in experiment. Both studies suggest that Stochastic MPC with disturbance feedback is an attractive alternative to existing methods, due to its ability to increase performance and robustness compared to deterministic methods.