Robustly Constrained Dynamic Games for Uncertain Nonlinear Dynamics

We propose a novel framework for robust dynamic games with nonlinear dynamics corrupted by state-dependent additive noise, and nonlinear agent-specific and shared constraints. Leveraging system-level synthesis (SLS), each agent designs a nominal trajectory and a causal affine error feedback law to minimize their own cost while ensuring that its own constraints and the shared constraints are satisfied, even under worst-case noise realizations. Building on these nonlinear safety certificates, we define the novel notion of a robustly constrained Nash equilibrium (RCNE). We then present an Iterative Best Response (IBR)-based algorithm that iteratively refines the optimal trajectory and controller for each agent until approximate convergence to the RCNE. We evaluated our method on simulations and hardware experiments involving large numbers of robots with high-dimensional nonlinear dynamics, as well as state-dependent dynamics noise. Across all experiment settings, our method generated trajectory rollouts which robustly avoid collisions, while a baseline game-theoretic algorithm for producing open-loop motion plans failed to generate trajectories that satisfy constraints.