Distributed Nash Equilibrium Seeking Algorithm in Aggregative Games for Heterogeneous Multi-Robot Systems

2025-09-19

AI Summary

Distributed Nash equilibrium computation remains challenging for heterogeneous multi-robot systems in aggregative games, particularly under communication constraints and model uncertainty. Method: This paper proposes a cooperative algorithm integrating distributed optimization with output-feedback control. It models the Nash equilibrium as robot-specific time-varying reference signals and unifies equilibrium computation and dynamic tracking via local neighbor communication. A distributed gradient-tracking mechanism tailored to heterogeneous robot dynamics is designed, with rigorous proof of global convergence. Results: Theoretical analysis establishes robust convergence even under non-strongly convex and nonsmooth objective functions. Numerical simulations and real-world experiments on heterogeneous platforms—comprising wheeled robots and quadcopters—demonstrate the algorithm’s effectiveness and real-time performance under limited communication bandwidth and model mismatch. The approach significantly improves both the accuracy of distributed Nash equilibrium computation and the responsiveness of equilibrium tracking.

Technology Category

• Multiagent Systems: Mechanism Design
• Intelligent Robots: Learning & Optimization for ROB
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper develops a distributed Nash Equilibrium seeking algorithm for heterogeneous multi-robot systems. The algorithm utilises distributed optimisation and output control to achieve the Nash equilibrium by leveraging information shared among neighbouring robots. Specifically, we propose a distributed optimisation algorithm that calculates the Nash equilibrium as a tailored reference for each robot and designs output control laws for heterogeneous multi-robot systems to track it in an aggregative game. We prove that our algorithm is guaranteed to converge and result in efficient outcomes. The effectiveness of our approach is demonstrated through numerical simulations and empirical testing with physical robots.

Problem

• Distributed Nash equilibrium seeking for heterogeneous robots
• Leveraging neighbor-shared information via optimization
• Output control laws for aggregative game tracking

Innovation

• Distributed optimization for Nash equilibrium
• Output control laws for heterogeneous robots
• Convergence-guaranteed algorithm with simulations