CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systems

TL;DR

CaRT introduces a hierarchical, distributed safety and robustness framework for learning-based multi-agent motion planning, ensuring safe maneuvers and robust trajectory tracking even under disturbances.

Contribution

It presents a novel hierarchical architecture with analytical safety and robust filters, guaranteeing safety and robustness in multi-agent systems using contraction theory and a log-barrier formulation.

Findings

Guarantees safety with minimal deviation from learned policies.

Ensures exponential boundedness of tracking error under disturbances.

Effective in nonlinear motion planning and multi-spacecraft reconfiguration.

Abstract

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.