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

arXiv: https://arxiv.org/abs/2307.08602 · HTML: https://mlsanity.com/paper/2307.08602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning with End-to-End Learning](https://mlsanity.com/paper/2002.11807/) (2020)
- [Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems](https://mlsanity.com/paper/1903.01577/) (2019)
- [Control Barrier Functions for Stochastic Systems](https://mlsanity.com/paper/2003.03498/) (2020)
- [Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach](https://mlsanity.com/paper/2102.12668/) (2021)
- [Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization](https://mlsanity.com/paper/2006.04359/) (2020)
- [A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability](https://mlsanity.com/paper/2110.00693/) (2021)
- [Safe Backstepping with Control Barrier Functions](https://mlsanity.com/paper/2204.00653/) (2022)

## Abstract (arXiv)

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.