mlsanityData to 7 Oct 2026

Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimization

arXiv 2304.12405 ↗First posted 24 Apr 2023cs.RO cs.CV cs.LGcited by 7

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Abstract (arXiv)

We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned perception module in the feedback control loop. We leverage Lyapunov analysis to formulate the problem of synthesizing such policies. This problem is nonconvex in the policy parameters and the Lyapunov function that is used to prove the stability of the policy. To solve this problem approximately, we propose two approaches: the first solves a sequence of sum-of-squares optimization problems to iteratively improve a policy which is provably-stable by construction, while the second directly performs gradient-based optimization on the parameters of the polynomial policy, and its closed-loop stability is verified a posteriori. We extend our approach to provide stability guarantees in the presence of observation noise, which realistically arises due to errors in the learned perception module. We evaluate our approach on several underactuated nonlinear systems, including pendula and quadrotors, showing that our guarantees translate to empirical stability when controlling these systems from images, while baseline approaches can fail to reliably stabilize the system.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 16 of its 37 references that are in the map. First posted on arXiv 24 Apr 2023.

Builds on

16 of 37 references.

References · 16

  1. 2017Proximal Policy Optimization Algorithmscited by 14,441
  2. 2015End-to-End Training of Deep Visuomotor Policiescited by 847
  3. 2019kPAM: KeyPoint Affordances for Category-Level Robotic Manipulationcited by 152
  4. 2018Dense Object Nets: Learning Dense Visual Object Descriptors By and For Robotic Manipulationcited by 140
  5. 2019Key.Net: Keypoint Detection by Handcrafted and Learned CNN Filterscited by 117
  6. 2022Accelerated Policy Learning with Parallel Differentiable Simulationcited by 92
  7. 2017Robust Locally-Linear Controllable Embeddingcited by 37
  8. 2020Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functionscited by 32
  9. 2020Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constantscited by 25
  10. 2022Learning Safe, Generalizable Perception-based Hybrid Control with Certificatescited by 24
  11. 2017DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimizationcited by 19
  12. 2022Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theorycited by 18
4 more
  1. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  2. 2021Verification and Synthesis of Control Barrier Functionscited by 13
  3. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  4. 2014Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimizationcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 1; 2026: 3.

7 papers.

  1. 2024Deep Generative Models for Offline Policy Learning: Tutorial, Survey, and Perspectives on Future Directionscited by 20
  2. 2023Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matchingcited by 17
  3. 2023How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomycited by 8
  4. 2026VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesiscited by 3
  5. 2026Robustness without Wrinkles: Parallel Simulation and Robust MPC for Certified Deformable Manipulationcited by 3
  6. 2026Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPCcited by 2
  7. 2025How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomycited by 1