Efficient Constrained Multi-Agent Trajectory Optimization using Dynamic Potential Games

TL;DR

This paper introduces a fast, efficient trajectory optimization method for multi-agent systems with constraints, leveraging the structure of potential games to simplify the computation of Nash equilibria.

Contribution

The work develops a novel constrained game-theoretical framework that exploits the structure of multi-agent interactions to enable rapid trajectory planning in constrained environments.

Findings

Method is 20 times faster than state-of-the-art in navigation tasks.

Successfully validated on multi-agent navigation with quadrotors and humans.

Efficiently handles nonlinear state and input constraints in multi-agent settings.

Abstract

Although dynamic games provide a rich paradigm for modeling agents' interactions, solving these games for real-world applications is often challenging. Many real-world interactive settings involve general nonlinear state and input constraints that couple agents' decisions with one another. In this work, we develop an efficient and fast planner for interactive trajectory optimization in constrained setups using a constrained game-theoretical framework. Our key insight is to leverage the special structure of agents' objective and constraint functions that are common in multi-agent interactions for fast and reliable planning. More precisely, we identify the structure of agents' cost and constraint functions under which the resulting dynamic game is an instance of a constrained dynamic potential game. Constrained dynamic potential games are a class of games for which instead of solving a set of coupled constrained optimal control problems, a constrained Nash equilibrium, i.e. a Generalized Nash equilibrium, can be found by solving a single constrained optimal control problem. This simplifies constrained interactive trajectory optimization significantly. We compare the performance of our method in a navigation setup involving four planar agents and show that our method is on average 20 times faster than the state-of-the-art. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.