Learning Two-agent Motion Planning Strategies from Generalized Nash Equilibrium for Model Predictive Control

TL;DR

This paper presents a decentralized motion planning algorithm for two agents that leverages learned game-theoretic interactions within an MPC framework, enabling competitive and cooperative behaviors.

Contribution

It introduces IGT-MPC, combining neural network predictions of game outcomes with MPC for improved multi-agent motion planning.

Findings

Successfully demonstrated competitive and cooperative behaviors in simulated scenarios

Achieved real-time planning with learned value functions guiding agent interactions

Validated the approach on head-to-head racing and intersection navigation tasks

Abstract

We introduce an Implicit Game-Theoretic MPC (IGT-MPC), a decentralized algorithm for two-agent motion planning that uses a learned value function that predicts the game-theoretic interaction outcomes as the terminal cost-to-go function in a model predictive control (MPC) framework, guiding agents to implicitly account for interactions with other agents and maximize their reward. This approach applies to competitive and cooperative multi-agent motion planning problems which we formulate as constrained dynamic games. Given a constrained dynamic game, we randomly sample initial conditions and solve for the generalized Nash equilibrium (GNE) to generate a dataset of GNE solutions, computing the reward outcome of each game-theoretic interaction from the GNE. The data is used to train a simple neural network to predict the reward outcome, which we use as the terminal cost-to-go function in an MPC scheme. We showcase emerging competitive and coordinated behaviors using IGT-MPC in scenarios such as two-vehicle head-to-head racing and un-signalized intersection navigation. IGT-MPC offers a novel method integrating machine learning and game-theoretic reasoning into model-based decentralized multi-agent motion planning.