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.

翻译：环境通过施加空间约束、规则和限制，在多智能体导航中扮演关键角色，智能体必须绕过这些约束。传统方法将环境视为固定不变，未探索其对智能体性能的影响。本研究将环境配置视为决策变量，与智能体动作共同优化，以实现安全导航。我们构建了一个双层问题：下层子问题优化智能体轨迹以最小化导航成本，上层子问题优化环境配置以最大化导航安全性。我们开发了一种可微优化方法，迭代地使用内点法求解下层子问题，并使用梯度上升法求解上层子问题。关键挑战在于解析地耦合这两个层级。通过利用KKT条件和隐函数定理，我们计算了智能体轨迹对环境参数的梯度，从而实现了整个双层结构的可微化。此外，我们提出了一种新指标，量化导航安全性作为上层环境优化的准则，并通过测度论证明了其有效性。实验验证了所提框架在多种安全关键导航场景中的有效性，这些场景灵感来源于仓库物流到城市交通。结果表明，优化后的环境提供了导航引导，同时提高了智能体的安全性和效率。