Game-Theoretic Control with Constrained Potential Surgery

Abstract

Constrained general-sum dynamic games are a popular formulation for highly interactive multi-agent planning problems. In recent years, Generalized Nash Equilibrium (GNE) solvers have achieved real-time performance for small dynamic games. However, solution speed still remains a bottleneck, and controlling even a small number of agents (e.g., more than four) in a dynamic task remains elusive. In addition, Newton solvers that focus on the first-order conditions are vulnerable to non-Nash saddle points, limiting the usefulness of the provided solution. In this work, we propose a fast and versatile interior point solver for constrained dynamic games, along with a computationally efficient second-order correction that increases the probability of converging to a local GNE solution in constrained dynamic games. The performance of the proposed method is evaluated on numerical benchmarks and a physical experiment involving scaled race cars.