mlsanityData to 7 Oct 2026

Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants

arXiv 2010.08993 ↗First posted 18 Oct 2020cs.RO cs.LG cs.SYcited by 25

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Abstract (arXiv)

We present a method for feedback motion planning of systems with unknown dynamics which provides probabilistic guarantees on safety, reachability, and goal stability. To find a domain in which a learned control-affine approximation of the true dynamics can be trusted, we estimate the Lipschitz constant of the difference between the true and learned dynamics, and ensure the estimate is valid with a given probability. Provided the system has at least as many controls as states, we also derive existence conditions for a one-step feedback law which can keep the real system within a small bound of a nominal trajectory planned with the learned dynamics. Our method imposes the feedback law existence as a constraint in a sampling-based planner, which returns a feedback policy around a nominal plan ensuring that, if the Lipschitz constant estimate is valid, the true system is safe during plan execution, reaches the goal, and is ultimately invariant in a small set about the goal. We demonstrate our approach by planning using learned models of a 6D quadrotor and a 7DOF Kuka arm. We show that a baseline which plans using the same learned dynamics without considering the error bound or the existence of the feedback law can fail to stabilize around the plan and become unsafe.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 3; 2023: 4; 2024: 3; 2025: 4; 2026: 7.

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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. 2021Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approachcited by 14
  4. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  5. 2022Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertaintycited by 11
  6. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  7. 2023How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomycited by 8
  8. 2026Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Controlcited by 8
  9. 2023Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimizationcited by 7
  10. 2026Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesiscited by 7
  11. 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
  12. 2025Reimagination with Test-time Observation Interventions: Distractor-Robust World Model Predictions for Visual Model Predictive Controlcited by 6
13 more
  1. 2021Formal Verification of Unknown Dynamical Systems via Gaussian Process Regressioncited by 5
  2. 2023Promises of Deep Kernel Learning for Control Synthesiscited by 4
  3. 2024Q-Distribution guided Q-learning for offline reinforcement learning: Uncertainty penalized Q-value via consistency modelcited by 4
  4. 2021Learning Contraction Policies from Offline Datacited by 3
  5. 2024Certified Training with Branch-and-Bound for Lyapunov-stable Neural Controlcited by 3
  6. 2026VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesiscited by 3
  7. 2025Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilizationcited by 2
  8. 2025Data-driven Acceleration of MPC with Guaranteescited by 2
  9. 2026Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllerscited by 2
  10. 2026Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPCcited by 2
  11. 2024Robust Model Based Reinforcement Learning Using L1 Adaptive Controlcited by 1
  12. 2025How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomycited by 1
  13. 2026Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guaranteescited by 1