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

2024-11-21

arXiv.org

AI Summary

This work addresses real-time motion planning for two agents operating in mixed competitive-cooperative scenarios. We propose Implicit Game-Theoretic Model Predictive Control (IGT-MPC), a decentralized framework that avoids explicit opponent modeling. Methodologically, we introduce the first data-driven neural network approximation of the Generalized Nash Equilibrium (GNE) solution as a reward function embedded in the MPC terminal cost. This enables implicit game-theoretic reasoning within an optimization-based planner. The framework unifies treatment of adversarial and cooperative behaviors under coupled state and control constraints. Evaluated on challenging tasks—including unsignalized intersection crossing and head-on racing—IGT-MPC consistently emergently generates coordinated yielding and strategic competition. It achieves real-time planning frequencies suitable for onboard automotive deployment and significantly outperforms non-game-theoretic MPC baselines in both safety and efficiency metrics.

Technology Category

• Multiagent Systems: Adversarial Agents
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Decentralized two-agent motion planning using game theory.
• Predicting interaction outcomes via neural network learning.
• Applying MPC for competitive and cooperative multi-agent scenarios.

Innovation

• Decentralized algorithm for two-agent motion planning
• Learned value function predicts game-theoretic outcomes
• Neural network predicts reward outcomes for MPC