Differentiable Environment-Trajectory Co-Optimization for Safe Multi-Agent Navigation

TL;DR

This paper introduces a differentiable bi-level optimization framework that jointly optimizes environment configurations and agent trajectories to enhance safety in multi-agent navigation scenarios.

Contribution

It formulates a novel bi-level problem coupling environment design with agent trajectory optimization, solved via a differentiable approach using KKT conditions and the Implicit Function Theorem.

Findings

Optimized environments improve navigation safety and efficiency.

The framework effectively handles safety-critical scenarios like warehouse logistics and urban transportation.

A new safety metric is proposed and validated through measure theory.

Abstract

The environment plays a critical role in multi-agent navigation by imposing spatial constraints, rules, and limitations that agents must navigate around. Traditional approaches treat the environment as fixed, without exploring its impact on agents' performance. This work considers environment configurations as decision variables, alongside agent actions, to jointly achieve safe navigation. We formulate a bi-level problem, where the lower-level sub-problem optimizes agent trajectories that minimize navigation cost and the upper-level sub-problem optimizes environment configurations that maximize navigation safety. We develop a differentiable optimization method that iteratively solves the lower-level sub-problem with interior point methods and the upper-level sub-problem with gradient ascent. A key challenge lies in analytically coupling these two levels. We address this by leveraging KKT conditions and the Implicit Function Theorem to compute gradients of agent trajectories w.r.t. environment parameters, enabling differentiation throughout the bi-level structure. Moreover, we propose a novel metric that quantifies navigation safety as a criterion for the upper-level environment optimization, and prove its validity through measure theory. Our experiments validate the effectiveness of the proposed framework in a variety of safety-critical navigation scenarios, inspired from warehouse logistics to urban transportation. The results demonstrate that optimized environments provide navigation guidance, improving both agents' safety and efficiency.