Robustly Constrained Dynamic Games Via System Level Synthesis
Shuyu Zhan, Chih-Yuan Chiu, Antoine Leeman, Glen Chou
AI summary
Problem
Existing dynamic game planners for multi-agent robotics often ignore dynamics noise or fail to robustly satisfy safety constraints under uncertainty. This work addresses how to design interactive motion plans that provably remain safe despite state-dependent additive noise in nonlinear systems.
Approach
Each agent jointly optimizes a nominal trajectory and a causal affine error feedback controller using system-level synthesis to bound uncertainty propagation, then computes a robustly constrained Nash equilibrium via an iterative best response algorithm.
Key results
- Novel robustly constrained Nash equilibrium (RCNE) concept for noisy nonlinear games
- Fast SLS-based iterative best response algorithm for tractable RCNE computation
- Provable worst-case constraint satisfaction guarantees via SLS safety certificates
- Successful hardware and simulation validation on up to 24 heterogeneous robots avoiding collisions under high disturbance
Why it matters
Enables reliable, safe, and computationally efficient multi-robot coordination in real-world environments where dynamics uncertainty and strict safety constraints are critical.
Abstract
We propose a novel framework for robust dy- namic 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 experi- ments involving large numbers of robots with high-dimensional nonlinear dynamics, as well as state-dependent dynamics noise. Across all experiment settings, our method generates 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.