This paper presents CART, an analytical method to augment a learning-based, distributed motion planning policy of a nonlinear multi-agent system with real-time collision avoidance and robust tracking guarantees, independently of learning errors. We first derive an analytical form of an optimal safety filter for Lagrangian systems, which formally ensures a collision-free operation in a multi-agent setting in a disturbance-free environment, while allowing for its distributed implementation with minimal deviation from the learned policy. We then propose an analytical form of an optimal robust filter for Lagrangian systems to be used hierarchically with the learned collision-free target trajectory, which also enables distributed implementation and guarantees exponential boundedness of the trajectory tracking error for safety, even under the presence of deterministic and stochastic disturbance. These results are shown to extend further to general control-affine nonlinear systems using contraction theory. Our key contribution is to enhance the performance of the learned motion planning policy with collision avoidance and tracking-based robustness guarantees, independently of its original performance such as approximation errors and regret bounds in machine learning. We demonstrate the effectiveness of CART in motion planning and control of several examples of nonlinear systems, including spacecraft formation flying and rotor-failed UAV swarms.

翻译：摘要：本文提出CART，一种解析方法，用于增强基于学习的非线性多智能体系统分布式运动规划策略，使其在实时碰撞规避和鲁棒跟踪方面具有保障，且该保障独立于学习误差。首先，我们为拉格朗日系统推导出最优安全滤波器的解析形式，该滤波器能在无扰动环境中正式确保多智能体场景下的无碰撞运行，同时支持分布式实现，并最小化对学习策略的偏离。随后，我们提出拉格朗日系统的最优鲁棒滤波器的解析形式，该滤波器与学习得到的无碰撞目标轨迹分层结合，同样支持分布式实现，并确保即使在确定性和随机扰动存在下，轨迹跟踪误差仍呈指数有界以保证安全性。利用收缩理论，这些结果可进一步推广至一般控制仿射非线性系统。我们的核心贡献是：在不依赖机器学习原有性能（如逼近误差和遗憾界）的前提下，通过学习策略中引入碰撞规避和基于跟踪的鲁棒性保障，显著提升其性能。通过多个非线性系统（包括航天器编队飞行和转子故障无人机集群）的运动规划与控制实例，验证了CART的有效性。