mlsanityData to 14 Oct 2026

Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems

arXiv 2212.06874 ↗First posted 13 Dec 2022cs.RO cs.LGcited by 11

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Abstract (arXiv)

We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a dynamics dataset, our method jointly learns a mean dynamics model, a spatially-varying disturbance bound that captures the effect of noise and model mismatch, and a feedback controller based on contraction theory that stabilizes the learned dynamics. We propose a sampling-based planner that uses the mean dynamics model and simultaneously bounds the closed-loop tracking error via a learned disturbance bound. We employ techniques from Extreme Value Theory (EVT) to estimate, to a specified level of confidence, several constants which characterize the learned components and govern the size of the tracking error bound. This ensures plans are guaranteed to be safely tracked at runtime. We validate that our guarantees translate to empirical safety in simulation on a 10D quadrotor, and in the real world on a physical CrazyFlie quadrotor and Clearpath Jackal robot, whereas baselines that ignore the model error and stochasticity are unsafe.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 26 of its 36 references that are in the map. First posted on arXiv 13 Dec 2022.

Builds on

26 of 36 references.

References · 26

  1. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  2. 2017Hamilton-Jacobi Reachability: A Brief Overview and Recent Advancescited by 201
  3. 2020Neural Lyapunov Controlcited by 142
  4. 2018Learning-based Model Predictive Control for Safe Explorationcited by 120
  5. 2020Learning Stable Deep Dynamics Modelscited by 111
  6. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  7. 2020Learning Certified Control using Contraction Metriccited by 49
  8. 2020Learning Stability Certificates from Datacited by 45
  9. 2015Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Designcited by 39
  10. 2016Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processescited by 39
  11. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
  12. 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
14 more
  1. 2016Funnel Libraries for Real-Time Robust Feedback Motion Planningcited by 29
  2. 2020Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constantscited by 25
  3. 2020Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approachcited by 23
  4. 2022Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theorycited by 19
  5. 2020Deep Learning Tubes for Tube MPCcited by 14
  6. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  7. 2020Safe Feedback Motion Planning: A Contraction Theory and L1-Adaptive Control Based Approachcited by 11
  8. 2021Learning Density Distribution of Reachable States for Autonomous Systemscited by 11
  9. 2020Uncertainty-Aware Constraint Learning for Adaptive Safe Motion Planning from Demonstrationscited by 10
  10. 2013Technical Report: Convex Optimization of Nonlinear Feedback Controllers via Occupation Measurescited by 8
  11. 2022Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic Nonlinear Systems in Uncertain Environmentscited by 8
  12. 2021Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrationscited by 6
  13. 2016Nonlinear Stabilization via Control Contraction Metrics: a Pseudospectral Approach for Computing Geodesicscited by 3
  14. 2019Contraction Metrics in Adaptive Nonlinear Controlcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 0; 2025: 1; 2026: 8.

11 papers.

  1. 2023Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matchingcited by 17
  2. 2026Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Controlcited by 9
  3. 2023Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimizationcited by 7
  4. 2026Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesiscited by 7
  5. 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
  6. 2026Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPCcited by 4
  7. 2026VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesiscited by 3
  8. 2025Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilizationcited by 2
  9. 2026Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllerscited by 2
  10. 2026Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guaranteescited by 1
  11. 2026Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systemscited by 0