Neural Integral Control Barrier Functions for Agile Collision Avoidance

Dasari Raj Vamsi; Vrushabh Zinage; Efstathios Bakolas; Rohan Chandra

cs.RONov 2, 2026

Neural Integral Control Barrier Functions for Agile Collision Avoidance

Authors: Dasari Raj Vamsi, Vrushabh Zinage, Efstathios Bakolas, Rohan Chandra

Organizations: Indian Institute of Information Technology and Management, Gwalior · California Institute of Technology · The University of Texas at Austin · University of Virginia

Abstract

Control barrier functions (CBFs) are a standard way to keep a planner inside a safe set, but they assume control affine dynamics, a barrier function given in closed form, and a known nominal controller. Integral control barrier functions (ICBFs) remove the first assumption and absorb input constraints, yet they still assume a given nominal controller and a barrier function. In this work, we present an approach to learn all three from data, using neural ordinary differential equations (ODEs) for the dynamics, imitation for the nominal controller, and supervised regression for the barrier function. The learned dynamics, nominal controller, and the barrier function are used to build the ICBF filter constraint analytically. Furthermore, the barrier is trained on viability rather than geometry, meaning that a state counts as safe only if some emergency maneuver can still avoid the constraint under the actuator limits, a correction that geometric labels miss entirely and that grows with speed. Actuator limits then enter the online program as hard bounds while the learned barrier rows may be relaxed, which keeps the program solvable at every state and the actuator limits exact, and we bound how far the input it returns can drift from the one the true models would give. On agile racing with a 6-D dynamic bicycle, the filter removes all 12 unsafe episodes from 200 held out layouts at an unchanged success rate and above 100 Hz on one CPU core, holds the input constraint on every episode of a benchmark where a jointly trained baseline holds it on 53.38%, and keeps that advantage under large errors in the plant friction.

Figures & tables

Method	Safety	Goal	Input compliance	Cost
Ours	100%	$71\%$	100%	$16758$
SABLAS	$98.49\%$	89%	$53.38\%$	11474

Table 1: Double integrator benchmark of Qin et al. (2022) , 100 random test episodes. Input compliance is the fraction of episodes on which the actuator constraint held throughout.

Figure 1: What the viability labeled barrier represents. (left, middle) The learned obstacle barrier

h_{\theta}

in the body frame at two speeds, with its zero level set and the geometric obstacle. At

1

m/s the two nearly coincide, whereas at

5

m/s the unsafe set extends roughly

1.5

m along the approach direction, covering states clear of the obstacle that can no longer avoid it under the actuator limits. (c) Fraction of geometrically safe states that viability relabels unsafe, by speed: the signature of a viability set rather than a smoothed obstacle indicator.

$v$ (m/s)	Method	Success	Collision	Out of bounds	Unsafe	Stall	Timeout
3.5	MPPI	172	0	1	1	27	0
	HOCBF-QP	122	58	0	58	14	6
	Ours, $\pi_{\theta}$	162	3	0	3	35	0
	Ours, MPPI	166	0	0	0	34	0
4.0	MPPI	168	7	5	12	20	0
	HOCBF-QP	55	69	1	70	18	57

Table 2: Agile racing on 200 held out layouts, in episode counts, with every row summing to 200. MPPI is the planner alone, HOCBF-QP is the analytical filter of Xiao and Belta (2022) applied to it, and Ours is the Neural ICBF with either

\pi_{\theta}

or MPPI as the nominal controller. Unsafe is the sum of the collision and out of bounds columns.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

	Vehicle		Quadrotor-pendulum
Method	Time (s)	Cost	Time (s)	Cost
NMPC	5.562	4.583	10.242	15.232
ORCA-MAPF	1.373	6.839	2.328	21.281
CADRL	0.837	5.683	2.181	19.283
Ours	0.736	4.631	1.550	15.672

Appendix

Table 3: Time to goal and average closed loop cost on the two low dimensional systems. ORCA-MAPF and CADRL are runtime reference points rather than safety filters, so the cost column is not a like for like comparison against them.

Configuration	Success	Unsafe	$\min h_{\theta}$	QP feasible	Slack active	Interventions
Default ( $\eta=0.2$ , $\alpha=5$ , grip row)	8/12	0/12	$+0.29$	$100\%$	$0.16\%$	$44\%$
No enforcement margin ( $\eta=0$ )	9/12	0/12	$+0.20$	$100\%$	$0.13\%$	$45\%$
Barrier gain $\alpha=10$	9/12	0/12	$+0.14$	$100\%$	$0.15\%$	$45\%$
No grip row	7/12	0/12	$\mathbf{-0.05}$	$100\%$	$2.77\%$	$31\%$

Appendix

Table 4: Ablations on the 12 held out layouts at

4.0

m/s on which MPPI alone is unsafe, with MPPI as the nominal controller.

\min h_{\theta}

is the smallest obstacle barrier value reached in closed loop, before the enforcement margin is subtracted, so a negative entry means the learned safe set was left. Interventions is the fraction of steps at which

{\boldsymbol{v}}^{\star}\neq 0

Control Barrier Functions

Control barrier functions encode safe states as constraints that keep a controlled system away from hazards.

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As the number of autonomous robots continues to grow, safety becomes increasingly important. Control barrier functions (CBFs) provide a theoretically grounded framework for ensuring safety, but existing design methods often face limitations in effectiveness, scalability, or interpretability, and may result in overly conservative safe sets. In this paper, we propose VertexCBF, a framework for learning neural CBFs in a scalable, systematic, and explainable way. We approximate the stationary Hamilton--Jacobi value function using a neural network trained via a combination of physics-informed and sparsely supervised learning. By exploiting control-affine dynamics and a convex polytope control set, under which the Hamiltonian is maximized at the control vertices, we efficiently generate supervision points via GPU-parallel vertex-restricted tree search, while a residual architecture guarantees that the learned CBF is never larger than the specified constraint function. We evaluate the method on 15 systems and compare it against relevant baselines, showing that it reliably recovers large safe sets where the baselines are conservative or fail completely. In addition, we perform a hardware experiment in which a mobile robot safely avoids pedestrians using a neural CBF trained with our method.

Abstract

Control Barrier Functions

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