# Safe Feedback Motion Planning: A Contraction Theory and L1-Adaptive Control Based Approach

arXiv: https://arxiv.org/abs/2004.01142 · HTML: https://mlsanity.com/paper/2004.01142/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2020.

## Built on by (most cited first, 11 of 11)

- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach](https://mlsanity.com/paper/2102.12668/) (2021)
- [Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems](https://mlsanity.com/paper/2104.08695/) (2021)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [Neural Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2206.10397/) (2022)
- [Federated reinforcement learning for robot motion planning with zero-shot generalization](https://mlsanity.com/paper/2403.13245/) (2024)
- [Robust Model Based Reinforcement Learning Using L1 Adaptive Control](https://mlsanity.com/paper/2403.14860/) (2024)
- [Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy](https://mlsanity.com/paper/2512.17899/) (2025)
- [Robustifying Reinforcement Learning Policies with L1 Adaptive Control](https://mlsanity.com/paper/2106.02249/) (2021)
- [Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation](https://mlsanity.com/paper/2112.08222/) (2021)
- [Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems](https://mlsanity.com/paper/2603.07092/) (2026)

## Abstract (arXiv)

Autonomous robots that are capable of operating safely in the presence of imperfect model knowledge or external disturbances are vital in safety-critical applications. In this paper, we present a planner-agnostic framework to design and certify safe tubes around desired trajectories that the robot is always guaranteed to remain inside of. By leveraging recent results in contraction analysis and L1-adaptive control we synthesize an architecture that induces safe tubes for nonlinear systems with state and time-varying uncertainties. We demonstrate with a few illustrative examples how contraction theory-based L1-adaptive control can be used in conjunction with traditional motion planning algorithms to obtain provably safe trajectories.