MultiNash-PF: A Particle Filtering Approach for Computing Multiple Local Generalized Nash Equilibria in Trajectory Games

TL;DR

MultiNash-PF is an efficient particle filtering algorithm designed to identify multiple local equilibria in multi-agent trajectory planning, enabling robots to recognize and adapt to various interaction modes in real-time.

Contribution

The paper introduces MultiNash-PF, combining implicit particle filtering with game-theoretic planning to efficiently compute multiple local GNEs in multi-modal multi-agent interactions.

Findings

Reduces computation time by up to 50% compared to baseline methods.

Successfully identifies multiple interaction modes in simulated scenarios.

Effectively handles real-world human-robot interaction with multi-modal outcomes.

Abstract

Modern robotic systems frequently engage in complex multi-agent interactions, many of which are inherently multi-modal, i.e., they can lead to multiple distinct outcomes. To interact effectively, robots must recognize the possible interaction modes and adapt to the one preferred by other agents. In this work, we propose MultiNash-PF, an efficient algorithm for capturing the multimodality in multi-agent interactions. We model interaction outcomes as equilibria of a game-theoretic planner, where each equilibrium corresponds to a distinct interaction mode. Our framework formulates interactive planning as Constrained Potential Trajectory Games (CPTGs), in which local Generalized Nash Equilibria (GNEs) represent plausible interaction outcomes. We propose to integrate the potential game approach with implicit particle filtering, a sample-efficient method for non-convex trajectory optimization. We utilize implicit particle filtering to identify the coarse estimates of multiple local minimizers of the game's potential function. MultiNash-PF then refines these estimates with optimization solvers, obtaining different local GNEs. We show through numerical simulations that MultiNash-PF reduces computation time by up to 50\% compared to a baseline. We further demonstrate the effectiveness of our algorithm in real-world human-robot interaction scenarios, where it successfully accounts for the multi-modal nature of interactions and resolves potential conflicts in real-time.