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Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems

arXiv 2104.08695 ↗First posted 18 Apr 2021cs.RO cs.LG cs.SYcited by 13

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Abstract (arXiv)

We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset, our method learns a deep control-affine approximation of the dynamics. To find a trusted domain where this model can be used for planning, we obtain an estimate of the Lipschitz constant of the model error, which is valid with a given probability, in a region around the training data, providing a local, spatially-varying model error bound. We derive a trajectory tracking error bound for a contraction-based controller that is subjected to this model error, and then learn a controller that optimizes this tracking bound. With a given probability, we verify the correctness of the controller and tracking error bound in the trusted domain. We then use the trajectory error bound together with the trusted domain to guide a sampling-based planner to return trajectories that can be robustly tracked in execution. We show results on a 4D car, a 6D quadrotor, and a 22D deformable object manipulation task, showing our method plans safely with learned models of high-dimensional underactuated systems, while baselines that plan without considering the tracking error bound or the trusted domain can fail to stabilize the system and become unsafe.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 17 of its 29 references that are in the map. First posted on arXiv 18 Apr 2021.

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17 of 29 references.

References · 17

  1. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  2. 2018Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approachcited by 181
  3. 2018Learning-based Model Predictive Control for Safe Explorationcited by 116
  4. 2020Learning Stable Deep Dynamics Modelscited by 110
  5. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  6. 2020Learning Certified Control using Contraction Metriccited by 48
  7. 2020Learning Stability Certificates from Datacited by 45
  8. 2015Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Designcited by 38
  9. 2016Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processescited by 38
  10. 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
  11. 2020Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constantscited by 25
  12. 2020Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approachcited by 22
5 more
  1. 2020Deep Learning Tubes for Tube MPCcited by 14
  2. 2020Safe Feedback Motion Planning: A Contraction Theory and L1-Adaptive Control Based Approachcited by 11
  3. 2019GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programmingcited by 9
  4. 2015Asymptotically Optimal Planning by Feasible Kinodynamic Planning in State-Cost Spacecited by 8
  5. 2016Nonlinear Stabilization via Control Contraction Metrics: a Pseudospectral Approach for Computing Geodesicscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 2; 2024: 0; 2025: 0; 2026: 6.

13 papers.

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  1. 2022Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theorycited by 18
  2. 2023Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matchingcited by 17
  3. 2022Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertaintycited by 11
  4. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  5. 2023Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimizationcited by 7
  6. 2026Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesiscited by 7
  7. 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
  8. 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Modelscited by 3
  9. 2026VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesiscited by 3
  10. 2026Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllerscited by 2
  11. 2026Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPCcited by 2
  12. 2026Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guaranteescited by 1
1 more
  1. 2021Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimationcited by 0