Tube model predictive control for an autonomous race car

Abstract

Nonlinear effects and external disturbances can severely impact the control of an autonomous race car at the handling limits. State-of-the-art approaches do not take these uncertainties explicitly into account in the design process and are therefore prone to failure. To overcome this limitation, we present a robust control design based on tube model predictive control (TMPC). It is based on a simplified friction limited point-mass model and an additive disturbance for the lateral and longitudinal dynamics. Instead of nominal predictions, it leverages an approximate tube of reachable sets over the prediction horizon to guarantee constraint satisfaction. The resulting optimisation problem can be posed in the form of a standard quadratic programme by tightening the input and state constraints. The computational burden is therefore the same as in the nominal case. We benchmark our controller on a Hardware-in-the-Loop testbench with a nonlinear dual-track model and a combined Pacejka tyre model. The results demonstrate that the TMPC controller reduces the constraint violations while achieving comparable lap-times in contrast to an MPC controller and an infinite time LQR controller. It manages to apply caution when needed while maintaining a similar level of performance and is therefore considered to be superior in practical applications.