Improving the robustness of an MPC-based obstacle avoidance algorithm to parametric uncertainty using worst-case scenarios

Previous work by the authors focused on obstacle avoidance in large, high-speed autonomous ground vehicles within unknown and unstructured environments. This work resulted in a nonlinear model predictive control based algorithm that simultaneously optimises both the speed and steering commands. The algorithm can exploit the dynamic limits of the vehicle to navigate it to a target position as quickly as possible without compromising safety. In the algorithm, a model of the vehicle is used explicitly to predict and optimise future actions, but in practice the model parameter values are not known exactly. Thus, in this paper, the robustness of the algorithm to parametric uncertainty is evaluated. It is first demonstrated that using nominal parameter values in the algorithm leads to safety issues in 24% of the evaluated scenarios with the considered parametric uncertainty distributions. To improve the algorithm's robustness, a novel double-worst-case formulation is developed that simultaneously accounts for the robust satisfaction of the two safety requirements of high-speed obstacle avoidance: collision-free and no-wheel-lift-off. Results from simulations with stratified random scenarios and worst-case scenarios show that the double-worst-case formulation renders the algorithm robust to all uncertainty realisations tested. The trade-off between robustness and the task completion performance is also quantified.