Jacobian State Augmented Viable Kinematic Safety Filter

Siddharth Singh; Joshua Vaughan

cs.ROOct 11, 2026

Jacobian State Augmented Viable Kinematic Safety Filter

Authors: Siddharth Singh, Joshua Vaughan

Organizations: Manufacturing Robotics and Controls Group within the Manufacturing Science Division, Energy Science & Technology Directorate of the Oak Ridge National Lab.

Abstract

Safety Filters (SF) are leveraged to design certifiably safe controllers, which ensures forward invariance on a defined safe set when the filter is feasible. Predictive Safety Filters (PSF) embed these constraints to a closed-loop model-based optimization method to improve constraint satisfaction, and reduce feasibility loss caused by myopic, one-step filtering. Related viability-based methods emphasize approximating a viability kernel which ensures admissible control for all future time, but requires significant computational expense. This work introduces a Jacobian-based kinematic safety filter leveraging an augmented state variable with task-space velocity and filters task-space acceleration to preserve the feasibility of a low-level filter while enforcing joint position and velocity. The proposed method introduces a nested Quadratic Program (QP) formulation, defines a conservative inner approximation of viability envelope and computes a viable planner online. The method is validated in a simplified 2R planar manipulator simulation environment and shows significant improvement compared to a baseline Control Barrier Function Quadratic Program (CBF-QP) based filter. The experiments highlights the improvements in terms of computation time compared to traditional PSF and Reference Governor approach while also showing significant reduction in feasibility violations. Lastly, a simplified demonstration on a simulated 6-DoF manipulator highlights the potential scalability of the method to higher degree-of-freedom setups.

Figures & tables

Figure 1: Schematic representation of the proposed method with the two nested QPs.

Parameter		Value
Gains	[ $K_{p}$ , $K_{d}$ ]	[1.5, 1.0]
Link Lengths	$[l_{1},l_{2}]$	[0.4, 0.4] (m)
Decay rates	$[\gamma,\alpha]$	[2.0, 1.0]
Max Time	$T$	12 (s)

Table I : Design Parameters

Panel of Figure 2 — Figure 2: Experimental comparison between using a JASF with the low-level CBF-QP filter ( proposed ) and without the JASF layer and only low-level CBF-QP filter ( baseline ) for a simple $n=2$ planar manipulator in avoiding an obstacle.

Panel of Figure 3 — Figure 3: Qualitative comparison in trajectories of 6 random trials for a 2R planar manipulator.

Panel of Figure 4 — Figure 4: Quantitative Analytical comparison after 50 random trials between the baseline without JASF ( Blue ) and proposed with JASF ( Orange ). Dotted horizontal line show mean values.

Method	Metric	Value
Without JASF	Minimum $h(q)$	$3.91\times 10^{-4}$
	Safety Violations	0
	VE Violations	233
With JASF	Minimum $h(q)$	$1.316\times 10^{-3}$
	Safety Violations	0
	VE Violations	0

Table II : Safety and MCIS Viability Summary With and Without JASF

Metric	Without JASF	With JASF
CBF Violations (Steps)	$0.0\pm 0.000$	$0.0\pm 0.000$
VE Violations (Steps)	$395.360\pm 263.767$	$\mathbf{53.340\pm 1.101}$
$\text{min}\penalty\ h(q)$	$\mathbf{0.262\pm 0.311}$	$0.278\pm 0.315$
Goal dist (m)	$0.063\pm 0.075$	$\mathbf{0.043\pm 0.045}$
$\text{max}\penalty\ \xi\penalty\ \text{(rad/s)}$	$438.417\pm 865.649$	$\mathbf{15.204\pm 47.836}$

Table III : Mean data on trajectory analysis after 50 trials. (Bold values highlight the minimum of the two.)

Panel of Figure 5 — Figure 5: Performance comparison between different methods.

Metric	Baseline CBF	Ref. Gov	NMPC-PSF	JASF
VE frac.	$0.7{\pm}0.3$	$0.5{\pm}0.3$	$0.1{\pm}0.1$	$\mathbf{0.1{\pm}0.2}$
Sat. frac.	$0.4{\pm}0.3$	$0.3{\pm}0.3$	$0.1{\pm}0.1$	$\mathbf{0.0{\pm}0.0}$
min $h(q)$	$0.2{\pm}0.3$	$0.2{\pm}0.3$	$0.2{\pm}0.3$	$0.2{\pm}0.3$
Goal dist. [m]	$0.0{\pm}0.0$	$0.2{\pm}0.3$	$0.0{\pm}0.0$	$\mathbf{0.0{\pm}0.0}$
Reached [%]	$65.0$	$70.0$	$85.0$	$\mathbf{100.0}$
Solve [ $\mu$ s]	$\mathbf{66.2{\pm}7.0}$	$100.6{\pm}17.7$	$2653.3{\pm}155.4$	$172.8{\pm}22.6$

Table IV : Benchmark summary over 20 randomized trials. Values are mean

\pm

standard deviation. (Bold values highlight minimum across all four methods.)

Panel of Figure 6 — Figure 6: Comparison in compute time for JASF against NMPC-based PSF with varying horizon length over randomized 20 trials.

Panel of Figure 7 — Figure 7: Effect of $\gamma$ on viability.

Figure 8: Illustrative demonstration of proposed method on 6-DoF (UR5) robot in simulation.

Safety Filtering

Safety filtering intercepts actions or generated content to prevent harm while preserving as much useful behavior as possible.

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Safety filters provide a practical approach for enforcing safety constraints in autonomous systems. While learning-based tools scale to high-dimensional systems, their performance depends on informative data that includes states likely to lead to constraint violation, which can be difficult to efficiently sample in complex, high-dimensional systems. In this work, we characterize trajectories that barely avoid safety violations using the Pontryagin Maximum Principle. These boundary trajectories are used to guide data collection for learned Hamilton-Jacobi Reachability, concentrating learning efforts near safety-critical states to improve efficiency. The learned Control Barrier Value Function is then used directly for safety filtering. Simulations and experimental validation on a shared-control automotive racing application demonstrate PMP sampling improves learning efficiency, yielding faster convergence, reduced failure rates, and improved safe set reconstruction, with wall times around 3ms.

Abstract

Safety Filtering

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