Chance-constrained Linear Quadratic Gaussian Games for Multi-robot Interaction under Uncertainty

2025-03-09

AI Summary

Addressing the safety-coordination challenge in multi-robot systems under uncertainty—arising from coupled constraints and modeling errors—this paper proposes the first multi-agent Linear-Quadratic-Gaussian (LQG) game framework incorporating chance constraints. Methodologically, it embeds probabilistic safety constraints directly into the Nash equilibrium computation, introduces an analytically reconstructible chance-constraint formulation, and develops a provably convergent distributed dual ascent algorithm that guarantees equilibrium solutions strictly satisfy coupled safety requirements. The approach unifies stochastic optimal control, generalized Nash equilibrium computation, and distributed model predictive control. Evaluated in autonomous driving simulations and real-world multi-robot experiments, the method achieves superior safety–performance trade-offs: compared to single-agent MPC, it enables more aggressive and responsive trajectory planning while ensuring higher safety assurance.

Technology Category

• Multiagent Systems: Mechanism Design
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Multi-Robot Systems

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

Abstract

We address safe multi-robot interaction under uncertainty. In particular, we formulate a chance-constrained linear quadratic Gaussian game with coupling constraints and system uncertainties. We find a tractable reformulation of the game and propose a dual ascent algorithm. We prove that the algorithm converges to a generalized Nash equilibrium of the reformulated game, ensuring the satisfaction of the chance constraints. We test our method in driving simulations and real-world robot experiments. Our method ensures safety under uncertainty and generates less conservative trajectories than single-agent model predictive control.

Problem

• Safe multi-robot interaction under uncertainty
• Chance-constrained linear quadratic Gaussian game
• Generalized Nash equilibrium with safety guarantees

Innovation

• Chance-constrained linear quadratic Gaussian game
• Dual ascent algorithm for equilibrium
• Safety ensured in multi-robot interaction