In motion planning problems (e.g., robotics, autonomous driving) we need to design controllers that can guarantee satisfaction of safety critical contraints (e.g., collision avoidance). This problem becomes increasingly challenging if nonlinear and uncertain systems are considered. Model predictive control (MPC) is an optimization based control strategy that can directly deal with general nonlinear dynamics and safety critical constraints. However, the presence of model uncertainty causes additional feasibility and stability issues, thus invalidating the a priori safety guarantees.
In this talk, we present a robust design method for MPC schemes to overcome the issues given by model uncertainty, with a particular focus on nonlinear system. We discuss how incremental stability is a natural tool to study the uncertainty propagation of nonlinear systems. Based on this tool, we derive a general robust tubebased framework for nonlinear uncertain systems. Then, we provide a constraint tightening approach which is simpler to implement and also ensures safety. One of the core features of this modification is the fact that the online computational demand remains essentially the same as in nominal MPC (contrary to most of the state-of-theart approaches). Finally, we also discuss how this robust MPC approach can be improved by using additional adaptation and learning methods, without sacrificing safety.
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