Fast and Scalable Game-Theoretic Trajectory Planning with Intentional Uncertainties

TL;DR

This paper introduces a scalable, efficient game-theoretic trajectory planning method that models multi-agent interactions with intentional uncertainties as a Bayesian game, solved via a distributed ADMM algorithm for real-time applications.

Contribution

It models intentional uncertainties as a Bayesian game and demonstrates that the equilibrium can be found through a unified optimization, with a distributed algorithm enhancing scalability and real-time performance.

Findings

Outperforms existing methods in scalability and efficiency.

Achieves real-time trajectory planning under intentional uncertainties.

Validated through simulations and experiments across various scenarios.

Abstract

Trajectory planning involving multi-agent interactions has been a long-standing challenge in the field of robotics, primarily burdened by the inherent yet intricate interactions among agents. While game-theoretic methods are widely acknowledged for their effectiveness in managing multi-agent interactions, significant impediments persist when it comes to accommodating the intentional uncertainties of agents. In the context of intentional uncertainties, the heavy computational burdens associated with existing game-theoretic methods are induced, leading to inefficiencies and poor scalability. In this paper, we propose a novel game-theoretic interactive trajectory planning method to effectively address the intentional uncertainties of agents, and it demonstrates both high efficiency and enhanced scalability. As the underpinning basis, we model the interactions between agents under intentional uncertainties as a general Bayesian game, and we show that its agent-form equivalence can be represented as a potential game under certain minor assumptions. The existence and attainability of the optimal interactive trajectories are illustrated, as the corresponding Bayesian Nash equilibrium can be attained by optimizing a unified optimization problem. Additionally, we present a distributed algorithm based on the dual consensus alternating direction method of multipliers (ADMM) tailored to the parallel solving of the problem, thereby significantly improving the scalability. The attendant outcomes from simulations and experiments demonstrate that the proposed method is effective across a range of scenarios characterized by general forms of intentional uncertainties. Its scalability surpasses that of existing centralized and decentralized baselines, allowing for real-time interactive trajectory planning in uncertain game settings.