The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the analytical form of our CaRT safety filter formally ensures safe maneuvers of nonlinear multi-agent systems, optimally with minimal deviation from the learning-based policy. Second, in off-nominal settings, the analytical form of our CaRT robust filter optimally tracks the certified safe trajectory, generated by the previous layer in the hierarchy, the CaRT safety filter. We show using contraction theory that CaRT guarantees safety and the exponential boundedness of the trajectory tracking error, even under the presence of deterministic and stochastic disturbance. Also, the hierarchical nature of CaRT enables enhancing its robustness for safety just by its superior tracking to the certified safe trajectory, thereby making it suitable for off-nominal scenarios with large disturbances. This is a major distinction from conventional safety function-driven approaches, where the robustness originates from the stability of a safe set, which could pull the system over-conservatively to the interior of the safe set. Our log-barrier formulation in CaRT allows for its distributed implementation in multi-agent settings. We demonstrate the effectiveness of CaRT in several examples of nonlinear motion planning and control problems, including optimal, multi-spacecraft reconfiguration.

翻译：我们分析方法CaRT的关键创新在于建立了一种新的分层分布式架构，以保障给定基于学习的运动规划策略的安全性与鲁棒性。首先，在标称设定下，CaRT安全滤波器的解析形式能正式确保非线性多智能体系统的安全机动，并以最小偏离学习策略的方式实现最优性。其次，在非标称设定下，CaRT鲁棒滤波器的解析形式则可最优跟踪由层级结构中上一层（即CaRT安全滤波器）生成的认证安全轨迹。我们利用收缩理论证明，即使在确定性与随机扰动存在的情况下，CaRT也能保证安全性以及轨迹跟踪误差的指数有界性。此外，CaRT的层级特性使其仅通过卓越的认证安全轨迹跟踪能力即可增强安全鲁棒性，因而适用于存在大幅扰动的非标称场景。这与传统安全函数驱动方法形成重大区别——后者鲁棒性源于安全集合的稳定性，可能使系统过度保守地退入安全集合内部。CaRT中的对数障碍函数公式化使其能够在多智能体场景中实现分布式部署。我们通过包括最优多航天器重构在内的多个非线性运动规划与控制问题实例，验证了CaRT的有效性。