# Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach

arXiv: https://arxiv.org/abs/2102.12668 · HTML: https://mlsanity.com/paper/2102.12668/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 21 of 21)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Motion Planning Among Dynamic, Decision-Making Agents with Deep Reinforcement Learning](https://mlsanity.com/paper/1805.01956/) (2018)
- [Imitating Driver Behavior with Generative Adversarial Networks](https://mlsanity.com/paper/1701.06699/) (2017)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [MPC-Net: A First Principles Guided Policy Search](https://mlsanity.com/paper/1909.05197/) (2019)
- [Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach](https://mlsanity.com/paper/2006.04361/) (2020)
- [GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning with End-to-End Learning](https://mlsanity.com/paper/2002.11807/) (2020)
- [Input-to-State Safety With Control Barrier Functions](https://mlsanity.com/paper/1803.03035/) (2018)
- [Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems](https://mlsanity.com/paper/2005.04374/) (2020)
- [Safe Feedback Motion Planning: A Contraction Theory and L1-Adaptive Control Based Approach](https://mlsanity.com/paper/2004.01142/) (2020)
- [Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization](https://mlsanity.com/paper/2006.04359/) (2020)
- [Dynamic Tube MPC for Nonlinear Systems](https://mlsanity.com/paper/1907.06553/) (2019)
- [Learning Stabilizable Dynamical Systems via Control Contraction Metrics](https://mlsanity.com/paper/1808.00113/) (2018)
- [Robust Model-Free Learning and Control without Prior Knowledge](https://mlsanity.com/paper/2010.00204/) (2020)

## Built on by (most cited first, 13 of 13)

- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Demonstration-Efficient Guided Policy Search via Imitation of Robust Tube MPC](https://mlsanity.com/paper/2109.09910/) (2021)
- [A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability](https://mlsanity.com/paper/2110.00693/) (2021)
- [On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach](https://mlsanity.com/paper/2305.03608/) (2023)
- [Learning Contraction Policies from Offline Data](https://mlsanity.com/paper/2112.05911/) (2021)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects](https://mlsanity.com/paper/2208.04883/) (2022)
- [Learning-based Adaptive Control using Contraction Theory](https://mlsanity.com/paper/2103.02987/) (2021)
- [Stable Modular Control via Contraction Theory for Reinforcement Learning](https://mlsanity.com/paper/2311.03669/) (2023)
- [CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systems](https://mlsanity.com/paper/2307.08602/) (2023)
- [Bridging the Sim-to-real Gap: A Control Framework for Imitation Learning of Model Predictive Control](https://mlsanity.com/paper/2503.19228/) (2025)
- [Contraction-Aware Reinforcement Learning for Nonlinear Control with Statistical Robustness](https://mlsanity.com/paper/2506.15700/) (2025)

## Abstract (arXiv)

This paper presents Learning-based Autonomous Guidance with RObustness and Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear motion planners with formal robustness and stability guarantees, by designing a differential Lyapunov function using contraction theory. LAG-ROS utilizes a neural network to model a robust tracking controller independently of a target trajectory, for which we show that the Euclidean distance between the target and controlled trajectories is exponentially bounded linearly in the learning error, even under the existence of bounded external disturbances. We also present a convex optimization approach that minimizes the steady-state bound of the tracking error to construct the robust control law for neural network training. In numerical simulations, it is demonstrated that the proposed method indeed possesses superior properties of robustness and nonlinear stability resulting from contraction theory, whilst retaining the computational efficiency of existing learning-based motion planners.