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SSP: Safety-guaranteed Surgical Policy via Joint Optimization of Behavioral and Spatial Constraints

Jianshu Hu, ZhiYuan Guan, Lei Song, Kantaphat Leelakunwet, Hesheng Wang, Wei Xiao, Qi Dou, Yutong Ban

TL;DR

This paper utilizes Neural Ordinary Differential Equations (Neural ODEs) to learn an uncertainty-aware dynamics model that underpins a robust Control Barrier Function (CBF) safety controller, which minimally alters the actions of a surgical policy to ensure strict safety under uncertainty.

Abstract

The paradigm of robot-assisted surgery is shifting toward data-driven autonomy, where policies learned via Reinforcement Learning (RL) or Imitation Learning (IL) enable the execution of complex tasks. However, these ``black-box" policies often lack formal safety guarantees, a critical requirement for clinical deployment. In this paper, we propose the Safety-guaranteed Surgical Policy (SSP) framework to bridge the gap between data-driven generality and formal safety. We utilize Neural Ordinary Differential Equations (Neural ODEs) to learn an uncertainty-aware dynamics model from demonstration data. This learned model underpins a robust Control Barrier Function (CBF) safety controller, which minimally alters the actions of a surgical policy to ensure strict safety under uncertainty. Our controller enforces two constraint categories: behavioral constraints (restricting the task space of the agent) and spatial constraints (defining surgical no-go zones). We instantiate the SSP framework with surgical policies derived from RL, IL and Control Lyapunov Functions (CLF). Validation on in both the SurRoL simulation and da Vinci Research Kit (dVRK) demonstrates that our method achieves a near-zero constraint violation rate while maintaining high task success rates compared to unconstrained baselines.

SSP: Safety-guaranteed Surgical Policy via Joint Optimization of Behavioral and Spatial Constraints

TL;DR

This paper utilizes Neural Ordinary Differential Equations (Neural ODEs) to learn an uncertainty-aware dynamics model that underpins a robust Control Barrier Function (CBF) safety controller, which minimally alters the actions of a surgical policy to ensure strict safety under uncertainty.

Abstract

The paradigm of robot-assisted surgery is shifting toward data-driven autonomy, where policies learned via Reinforcement Learning (RL) or Imitation Learning (IL) enable the execution of complex tasks. However, these ``black-box" policies often lack formal safety guarantees, a critical requirement for clinical deployment. In this paper, we propose the Safety-guaranteed Surgical Policy (SSP) framework to bridge the gap between data-driven generality and formal safety. We utilize Neural Ordinary Differential Equations (Neural ODEs) to learn an uncertainty-aware dynamics model from demonstration data. This learned model underpins a robust Control Barrier Function (CBF) safety controller, which minimally alters the actions of a surgical policy to ensure strict safety under uncertainty. Our controller enforces two constraint categories: behavioral constraints (restricting the task space of the agent) and spatial constraints (defining surgical no-go zones). We instantiate the SSP framework with surgical policies derived from RL, IL and Control Lyapunov Functions (CLF). Validation on in both the SurRoL simulation and da Vinci Research Kit (dVRK) demonstrates that our method achieves a near-zero constraint violation rate while maintaining high task success rates compared to unconstrained baselines.
Paper Structure (26 sections, 1 theorem, 35 equations, 7 figures, 4 tables, 1 algorithm)

This paper contains 26 sections, 1 theorem, 35 equations, 7 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Policy Learning for Surgical Robot
  4. Neural ODE for Dynamics Modeling
  5. CBF for Safety Guarantee
  6. Background
  7. Neural Ordinary Differential Equations
  8. Control Barrier Function and Control Lyapunov Function
  9. Methodology
  10. Safety-guaranteed Surgical Policy Framework
  11. Dynamics Model Learning with Uncertainty Quantification
  12. Demonstration-guided Surgical Policy Learning
  13. Robust CBF Safety Controller
  14. Implementation
  15. Reference Path Following with CLF
  16. ...and 11 more sections

Key Result

Theorem 1

If the robot is initially safe, then the CBF-based controller (eq:cbf optimization problem) ensures the safety of the robot with the learned neural ODE model (eq:neural ode for whole state) and the corresponding uncertainty quantification (eqn:un1) (eqn:un2).

Figures (7)

  • Figure 1: Safety-guaranteed Surgical Policy Framework: We propose a safety-guaranteed surgical policy framework, which learns robust and safe executions of surgical actions.
  • Figure 2: Overview of the Safety-guaranteed Surgical Policy (SSP) Framework: This architecture decouples task performance from safety assurance by wrapping "black-box" surgical policies within a theoretically guaranteed safety layer. The framework utilizes Neural Ordinary Differential Equations (Neural ODEs) to learn a continuous dynamics model with uncertainty quantification, which underpins a Robust Control Barrier Function (CBF) controller. By solving a quadratic program that jointly optimizes for behavioral constraints (restricting the agent to the valid task space) and spatial constraints (avoiding no-go zones), the system minimally deviates from nominal actions to ensure strict safety during deployment.
  • Figure 3: Surgical Environments: The four unconstrained simulation environments in SurRoL used for evaluation.
  • Figure 4: Visualization of the Trajectory and Corresponding Safe Margin: (a) The circular path following task and (c) the safe margin along the path. With CLF combined with CBF, the agent successfully follow the circular path while avoid the red sphere no-go zone. (b) Path following for NeedlePick task and (d) the safe margin along the path. With CLF combined with CBF, the agent successfully finish the NeedlePick task while avoid the cylinder no-go zone. The margin values remain strictly positive ($b(x) > 0$), quantitatively verifying that the safety constraints are strictly satisfied throughout the execution.
  • Figure 5: Surgical Environments with Constraints in SurRoL used to evaluate safety. The rows correspond to the four tasks: (a) NeedleReach, (b) NeedlePick, (c) GauzeRetrieve, and (d) PegTransfer. The columns illustrate the two different No-Go Zones geometries (Cylinder vs. Sphere).
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1: Control Barrier Function 7782377
  • Definition 2: Control Lyapunov Function ames2012control
  • Theorem 1