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

cs.ROMar 7, 2026

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

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

Organizations: Global College, Shanghai Jiao Tong University, Shanghai, China · Department of Computer Science and Engineering, The Chinese University of Hong Kong, HongKong, China · Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Massachusetts, America

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.

Figures & tables

Fig. 1 : Safety-guaranteed Surgical Policy Framework: We propose a safety-guaranteed surgical policy framework, which learns robust and safe executions of surgical actions.

Fig. 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.

Panel of Figure 3 — Fig. 3 : Surgical Environments: The four unconstrained simulation environments in SurRoL used for evaluation.

Panel of Figure 4 — Fig. 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.

		CLF Only	Combined CLF-OKCBF Control
Path Type	Len. (m)	Avg. Dev. ( $10^{-4}$ m)	CLF Dev. ( $10^{-4}$ m)	CBF Dev. ( $10^{-2}$ m)	Total Dev. ( $10^{-3}$ m)
Straight	$0.35$	$0.939$	$1.00$	$7.89$	$3.23$
Circular	$0.75$	$4.24$	$3.00$	$0.230$	$0.341$
Triangular	$0.30$	$4.34$	$4.00$	$3.05$	$1.35$

TABLE I : Comprehensive Reference Path Following Results: Average trajectory tracking deviation from the reference path under CLF control and CLF CBF control.

Ablation Study (CLF)		Ablation Study (CBF)
Beta ( $\beta$ )	Avg. Tracking Dev. (m)	Gamma ( $\gamma$ )	Avg. Safe Margin (m)
$5$	$2.75\times 10^{-4}$	$5$	$9.94\times 10^{-2}$
$10$	$1.36\times 10^{-4}$	$\mathbf{10}$	$\mathbf{7.89\times 10^{-2}}$
$\mathbf{15}$	$\mathbf{9.39\times 10^{-5}}$	$15$	$7.35\times 10^{-2}$
$20$	$1.26\times 10^{-4}$	$20$	$5.85\times 10^{-2}$
$25$	$1.34\times 10^{-4}$	$25$	$4.83\times 10^{-2}$

TABLE II : Ablation Studies: Impact of CLF Gain

\beta

(Left) and CBF Gain

\gamma

(Right) on System Performance.

Panel of Figure 7 — Fig. 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).

Constraint	Task	Method	Task Performance			Safety / Efficiency
			Mean Success Rate $\uparrow$		Collision $\downarrow$	Time $\downarrow$	Safe Margin $\uparrow$	$\dot{s}$ Error $\downarrow$	$s$ Error $\downarrow$
			(w/ Violation)	(w/o Violation)	Collision $\downarrow$	(ms)	( $\times 10^{-3}$ )	( $\times 10^{-3}$ )	( $\times 10^{-4}$ )
Cylinder No-Go Zones	NeedleReach	CLF [ 22 ]	$1.00\!\pm\!0.00$	$0.08\!\pm\!0.02$	$0.92\!\pm\!0.02$	$3.33\!\pm\!0.28$	$-15.5\!\pm\!1.47$	$1299\!\pm\!7.94$	$1295\!\pm\!7.87$
		DP [ 28 ]	$1.00\!\pm\!0.01$	$0.42\!\pm\!0.03$	$0.58\!\pm\!0.03$	$6.96\!\pm\!0.36$	$-1.20\!\pm\!1.61$	$\mathbf{4.83\!\pm\!0.18}$	$\mathbf{4.79\!\pm\!0.17}$
		DEX [ 4 ]	$1.00\!\pm\!0.00$	$0.50\!\pm\!0.00$	$0.50\!\pm\!0.00$	$\mathbf{1.73\!\pm\!0.09}$	$1.71\!\pm\!0.89$	$6.60\!\pm\!0.29$	$6.68\!\pm\!0.33$
		SSP-CLF (Proposed)	$1.00\!\pm\!0.00$	$0.27\!\pm\!0.09$	$0.17\!\pm\!0.02$	$5.17\!\pm\!0.09$	$2.24\!\pm\!0.79$	$1074\!\pm\!5.80$	$1071\!\pm\!5.93$

TABLE III : Evaluation Results. Mean success rate (with / without violation), collision rate, inference time, and safety margin. Results are averaged over 3 seeds with 20 rollouts each.

\uparrow

\downarrow

indicate higher / lower is better. The quantitative results demonstrate the critical efficacy of the proposed framework in enforcing safety without severely compromising task performance.

Method		PSM Tasks				Overall
Method		NeedleReach	GauzeRetrieve	NeedlePick	PegTransfer	Aggregate
Reinforcement Learning	SAC [ 29 ]	1.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)
Reinforcement Learning	DDPG [ 30 ]	1.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)
Imitation Learning	BC [ 31 ]	1.00 ( $\pm$ .00)	0.07 ( $\pm$ .05)	0.21 ( $\pm$ .06)	0.56 ( $\pm$ .11)	0.40 ( $\pm$ .05)
	SQIL [ 32 ]	0.07 ( $\pm$ .09)	0.00 ( $\pm$ .00)	0.00 ( $\pm$ .00)	0.02 ( $\pm$ .05)	0.00 ( $\pm$ .00)
	VINN [ 33 ]	0.89 ( $\pm$ .06)	0.01 ( $\pm$ .02)	0.02 ( $\pm$ .02)	0.05 ( $\pm$ .04)	0.02 ( $\pm$ .02)

TABLE IV : Performance of Different Learning Algorithms in Surgical Environments: The quantitative results demonstrate the proposed framework achieves comparable performance compared to other unconstrained baselines while guaranteeing safety.

Panel of Figure 10 — Fig. 6 : Real World Experiments of Needle and Gauze Picking with No-Go Zones: Sampled frames evaluating RL with safety constraints guaranteed by CBF. The rows show (a) needle pick with a sphere, (b) needle pick with a cylinder, (c) gauze retrieve with a sphere, and (d) gauze retrieve with a cylinder.

Panel of Figure 11 — Fig. 7 : Real World Experiments on dVRK. (a) Multi stage suturing sequence (RL + CLF). The task is decomposed into an RL based grasp phase for robust needle acquisition, followed by a CLF based insertion phase. (b) and (c) Lung tumor resection task with safety constraints (Top and Side views, CLF + CBF). The CLF generates a nominal cutting trajectory, while the CBF enforces a hard safety constraint to prevent penetration into a spherical vascular safety region ( $r=90$ mm). The controller smoothly deviates to avoid the no-go zone and converges back to the path.

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PPO-EAL: Exact Augmented Lagrangian Proximal Policy Optimization for Safe Robotic Control

Jiatao Ding, Songqun Gao, Andrea Del Prete, Matteo Saveriano

Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38123, Trento, Italy

Robotic Control Constrained RL Robot Safety Proximal Policy Optimization Safe RL

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Reinforcement learning (RL) has emerged as a promising solution to accomplish complex robotic control tasks; however, most of the current work ignores the safety requirements. Safe RL seeks to maximize task performance while satisfying explicit physical constraints, but current algorithms struggle to learn the policy efficiently with precise constraint satisfaction. This work proposes PPO-EAL, a novel first-order constrained policy optimization framework that integrates exact augmented Lagrangian optimization into proximal policy optimization for safe robotic control. By combining clipped policy updates with exact quadratic penalty terms, PPO-EAL achieves theoretically grounded constraint enforcement without requiring impractically large penalty factors. A momentum-regulated multiplier update further improves dual-variable stability, reducing constraint oscillation and unsafe behavior while preserving task performance. We provide exactness and convergence analysis under standard stochastic approximation assumptions. Extensive validation across diverse GPU-accelerated robotic benchmarks-including cart-pole balancing, cart-double-pendulum stabilization, 7-DoF Franka end-effector reaching, and quadrupedal locomotion-demonstrates superior safety precision and reward performance compared with state-of-the-art first-order safe RL baselines. Finally, we demonstrate zero-shot sim-to-real deployment in a contact-rich gear assembly task, where PPO-EAL substantially improves task success, reduces peak contact force, and enhances operational robustness. These results establish PPO-EAL as a general and practically deployable safe RL framework for diverse safety-critical robotic systems.

Abstract

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