Dynamic Constraint Tightening for Nonlinear MPC for Autonomous Racing via Contraction Analysis

TL;DR

The paper addresses robust nonlinear MPC for autonomous racing at the handling limits under uncertain tire dynamics by starting from a perturbed dynamic single track model and deriving a Control Contraction Metric (CCM) via offline Sum-of-Squares optimization. This CCM is used to parameterize a dynamic, homothetic tube for constraint tightening, enabling robust MPC with only a single additional state in the prediction model and improved feasibility near constraint bounds. The approach is demonstrated on a demanding Yas Marina racetrack with Pacejka-based perturbations and disturbances, showing reduced constraint violations and enhanced stability at the expense of some speed, while maintaining real-time computational feasibility (~288 Hz). Overall, the method offers a practical, less conservative alternative to rigid-tube or linearized-robust MPC for high-speed autonomous racing with strong robustness guarantees.

Abstract

This work develops a robust nonlinear Model Predictive Control (MPC) framework for path tracking in autonomous vehicles operating at the limits of handling utilizing a Control Contraction Metric (CCM) derived from a perturbed dynamic single track model. We first present a nonlinear MPC scheme for autonomous vehicles. Building on this nominal scheme, we assume limited uncertainty in tire parameters as well as bounded force disturbances in both lateral and longitudinal directions. By simplifying the perturbed model, we optimize a CCM for the uncertain model, which is validated through simulations at the dynamic limits of vehicle performance. This CCM is subsequently employed to parameterize a homothetic tube used for constraint tightening within the MPC formulation. The resulting robust nonlinear MPC is computationally more efficient than competing methods, as it introduces only a single additional state variable into the prediction model compared to the nominal scheme. Simulation results demonstrate that the homothetic tube expands most significantly in regions where the nominal scheme would otherwise violate constraints, illustrating its ability to capture all uncertain trajectories while avoiding unnecessary conservatism.

Figures (7)

• Figure 1: Visualization of homothetic uncertainty tube in different driving conditions
• Figure 2: Dynamic single track model in curvilinear coordinates
• Figure 3: Sketch of tire curve uncertainty model
• Figure 4: Predicted tube sizes and lateral tire grip demand at selected sampling points over the finite horizons during the first corner at Yas Marina Circuit (Sketch on the right)
• Figure 5: Yaw rate $\dot{\psi}$, orthogonal path deviation $d$ (Limits green dashed) and total velocity $v$ for the progress along the path $s$) during slip test in first corner of Yas Marina Circuit as in Figure \ref{['fig:STMRes1']} using the nominal and robustified algorithm