Source-linked AI summary
A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems
Jaime F. Fisac, Anayo K. Akametalu, Melanie N. Zeilinger, Shahab Kaynama, Jeremy Gillula, Claire J. Tomlin
TL;DR
Learning-based control needs safety guarantees despite model mismatch and delayed recomputation of safety analyses. The paper combines Bayesian disturbance estimation with safety overrides and demonstrates safe learning from a poor initial policy on a quadrotor.
Problem
Model mismatch can invalidate computed safety guarantees, while recomputing updated guarantees may take seconds or minutes, threatening timely safe intervention.
Method
The framework uses Gaussian-process regression to estimate disturbance bounds and Bayesian confidence thresholds to trigger a least-restrictive safety controller during learning.
Results
The quadrotor learned a competent controller from an extremely poor initial policy while remaining safe throughout the experiment.
Takeaways & Limitations
Online confidence-based intervention can preserve safety while allowing exploration within the computed safe set.
Takeaways & Limitations
The faster local validation method provides only a local safety guarantee and trades weaker guarantees for faster computation.
Abstract
from arXiv · showhide
The proven efficacy of learning-based control schemes strongly motivates their application to robotic systems operating in the physical world. However, guaranteeing correct operation during the learning process is currently an unresolved issue, which is of vital importance in safety-critical systems. We propose a general safety framework based on Hamilton-Jacobi reachability methods that can work in conjunction with an arbitrary learning algorithm. The method exploits approximate knowledge of the system dynamics to guarantee constraint satisfaction while minimally interfering with the learning process. We further introduce a Bayesian mechanism that refines the safety analysis as the system acquires new evidence, reducing initial conservativeness when appropriate while strengthening guarantees through real-time validation. The result is a least-restrictive, safety-preserving control law that intervenes only when (a) the computed safety guarantees require it, or (b) confidence in the computed guarantees decays in light of new observations. We prove theoretical safety guarantees combining probabilistic and worst-case analysis and demonstrate the proposed framework experimentally on a quadrotor vehicle. Even though safety analysis is based on a simple point-mass model, the quadrotor successfully arrives at a suitable controller by policy-gradient reinforcement learning without ever crashing, and safely retracts away from a strong external disturbance introduced during flight.
A Gaussian process
The framework uses Gaussian-process Bayesian inference to update disturbance bounds and validate Hamilton-Jacobi safety guarantees online. It combines global and local intervention criteria, balancing probabilistic safety guarantees, computational cost, and learning freedom.
- Bayesian disturbance modeling: The disturbance bound ˆD(x) is constructed as confidence intervals whose desired marginal coverage is controlled by p.Higher p produces larger bounds and may shrink or eliminate the computed safe set, while lower p enlarges the set but weakens reliability under later observations.
- Bayesian disturbance modeling: Gaussian-process regression estimates each disturbance component from residuals between observed dynamics and model predictions.The posterior provides an expected disturbance value and uncertainty at arbitrary query states.
- Safety validation: A global validation criterion can trigger intervention when the posterior confidence in the safety conditions falls below γ0, preserving a lower bound on all-time safety probability.The guarantee remains probabilistic because safety may still hold even when the corollary’s hypotheses fail.
- Computational and experimental considerations: The local validation method trades weaker guarantees for faster computation, while reachability and Gaussian-process methods remain computationally intensive in high-dimensional spaces.The tradeoff is especially relevant when safety validation must run on onboard processors.
- Safety validation: A faster local criterion allows exploration while local model reliability exceeds λ0 and intervenes to maintain or increase the computed safety value with probability at least λ0.This local guarantee is not globally sufficient by itself, but it can become global when the relevant hypotheses hold.
- Computational and experimental considerations: In the quadrotor experiment, the safety controller overrode an initially free-falling policy near the floor, enabling learning without collision from a poor initial controller.The authors emphasize safe competent task performance rather than the learned controller’s quality after only a few seconds.
Altitude (m)
The experiment reports that the safety controller maintained safety throughout flight, while local Bayesian analysis detected the fan disturbance and avoided the affected region.
- Altitude (m): The fan’s airflow is quickly detected during flight.
- Altitude (m): The vehicle avoids entering the affected region after the disturbance is detected.
- Altitude (m): The safety controller succeeds in maintaining safety throughout the experiment.The reported experiment provides strong evidence for this outcome.
- Altitude (m): The local Bayesian analysis provides a strictly local safety guarantee and serves as an effective best-effort approach beyond its theoretical guarantees.
APPENDIX
The appendix establishes that state-dependent Gaussian-process disturbance bounds preserve the regularity needed for well-defined dynamics and differential-game safety analysis. Lipschitz assumptions yield continuous trajectories and Hausdorff-continuous disturbance sets.
- APPENDIX: State-dependent disturbance bounds raise existence and uniqueness questions for Carathéodory solutions because classical theorems assume fixed control sets.
- APPENDIX: Lipschitz Gaussian-process priors make posterior means and standard deviations Lipschitz continuous in the state.This supports the regularity of the inferred disturbance bound.
- APPENDIX: Assumption 1 requires each state-dependent disturbance set to be a closed deformation retract of the original disturbance set.The deformation map starts at any original disturbance and ends within the state-dependent bound while fixing points already in the bound.
- APPENDIX: Assumption 2 requires the retraction map to be Lipschitz in state and uniformly continuous in disturbance.This prevents abrupt changes in the disturbance bound across the state space.
- APPENDIX: The retraction construction transforms state-dependent disturbance constraints into standard fixed-input dynamics for applying differential-game results.
- APPENDIX: Under the Gaussian-process assumptions, the disturbance bound satisfies the regularity assumptions and is Lipschitz continuous under the Hausdorff distance.The resulting dynamics are bounded, uniformly continuous, and Lipschitz in the state, enabling differential-game analysis.