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

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.