Distributed 3D Leader-Follower Formation Control with Field-of-View Safety via Control Barrier Functions

Bin Hu; Immanuel R. Santjoko; Miao Pan; Richie R. Suganda

arxiv: 2605.17533 · v1 · pith:KF6FQILUnew · submitted 2026-05-17 · 📡 eess.SY · cs.RO· cs.SY

Distributed 3D Leader-Follower Formation Control with Field-of-View Safety via Control Barrier Functions

Immanuel R. Santjoko , Richie R. Suganda , Miao Pan , Bin Hu This is my paper

Pith reviewed 2026-05-19 22:26 UTC · model grok-4.3

classification 📡 eess.SY cs.ROcs.SY

keywords leader-follower formationcontrol barrier functionsfield of view safetymulti-UAV systemsdistributed controlperception-aware control3D formation trackingsafety filters

0 comments

The pith

Control barrier functions enforce field-of-view safety in 3D leader-follower UAV formations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a distributed control method for multiple UAVs to maintain 3D formations while ensuring each follower can always see the leader with its onboard camera. It starts with a relative kinematic model using line-of-sight coordinates to design a formation tracking controller that uses only local information. The key step is wrapping this controller inside a quadratic program based on control barrier functions that changes the velocities as little as possible to keep the leader in view. A sympathetic reader would care because losing sight of the leader breaks vision-based coordination, and this method builds in the guarantee by design rather than reacting after the fact.

Core claim

The central claim is that embedding a nominal 3D leader-follower formation tracking controller into a Control Barrier Function-based Quadratic Program safety filter minimally modifies the commanded velocities to maintain the leader inside the follower's camera frustum while preserving formation tracking whenever feasible. This architecture is derived from a relative kinematic model in line-of-sight coordinates and validated through Gazebo simulations and Crazyflie hardware experiments showing accurate tracking and effective FOV enforcement even when nominal commands conflict with visibility.

What carries the argument

The Control Barrier Function-based Quadratic Program (CBF-QP) safety filter, which takes the nominal formation velocity commands and finds the closest safe velocities that satisfy the field-of-view constraint.

If this is right

The leader stays visible to the follower at all times under the safety filter.
Formation tracking performance is preserved as long as the visibility constraint allows.
The method works in distributed fashion using only relative states.
Hardware experiments on Crazyflie drones confirm the approach in real conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This method could be combined with other safety constraints like collision avoidance for more complex swarm behaviors.
Extensions to non-holonomic vehicles or different sensor models might require adjusted barrier functions.
Guaranteeing feasibility of the QP under all operating conditions would allow fully reliable deployment without fallback strategies.

Load-bearing premise

The control barrier function quadratic program always admits a feasible solution at each time step under the conditions of the formation task.

What would settle it

A scenario or simulation where the desired formation geometry and velocities make it impossible for any velocity adjustment to keep the leader in the camera frustum, leading to either visibility loss or controller failure.

Figures

Figures reproduced from arXiv: 2605.17533 by Bin Hu, Immanuel R. Santjoko, Miao Pan, Richie R. Suganda.

**Figure 2.** Figure 2: Leader–follower geometry and camera frustum. The leader position [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Perception-aware safe 3D-LFF control architecture. A high-level distributed 3D-LFF controller tracks the desired state [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Multi-UAV leader–follower navigation in a Gazebo cave environment. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Gazebo simulation of the three-stage task. A comparison of 3D [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Gazebo simulation of abrupt leader motion. A comparison of 3D [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: Trajectories of the leader and the followers during the three-stage [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: Hardware experiment of the three-stage task. A comparison of 3D [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

read the original abstract

This letter proposes a distributed 3D leader-follower formation (3D-LFF) control framework for multi-UAV systems that achieves formation tracking while enforcing perception safety constraints. Maintaining safe, vision-based 3D-LFF is challenging because onboard cameras impose strict Field-of-View (FOV) limitations, and demanding formation commands can drive the leader outside the follower's camera frustum, resulting in loss of visibility. To address this issue, we develop a perception-aware safe control architecture that guarantees visibility by construction. First, we derive a relative kinematic model in a line-of-sight coordinate representation and design a distributed 3D-LFF tracking controller using only locally available relative states. Next, we embed the nominal formation controller within a Control Barrier Function-based Quadratic Program (CBF-QP) safety filter that minimally modifies the commanded velocities to maintain the leader inside the follower's camera frustum while preserving formation tracking whenever feasible. Gazebo simulations and Crazyflie hardware experiments validate the proposed approach, demonstrating accurate formation tracking and effective FOV enforcement, including scenarios in which the nominal desired formation conflicts with visibility constraints.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Standard CBF-QP filter on a line-of-sight 3D formation model, with sim and Crazyflie tests, but no evidence the QP stays feasible under the tested commands.

read the letter

The paper takes a distributed 3D leader-follower formation controller and wraps it in a CBF-QP safety filter to keep the leader inside the follower's camera frustum. They first build a relative kinematic model in line-of-sight coordinates, design a nominal tracker that uses only local relative states, then solve a quadratic program at each step that minimally changes the commanded velocities to satisfy the FOV barrier while trying to stay close to the formation goal. Gazebo simulations and Crazyflie flights are shown, including cases where the nominal formation would otherwise lose visibility. That combination of the 3D LOS model with the perception constraint is the concrete new piece; prior CBF work on formations usually stays in 2D or ignores camera limits. The experiments appear to run without crashes and demonstrate the filter activating when needed. The main gap is on feasibility. The abstract says the filter works “whenever feasible,” yet the write-up gives no proof that the feasible set stays non-empty for the closed-loop relative dynamics, and the reported results do not include solver status, constraint slack values, or counts of infeasible steps. Without those numbers it is hard to know how often the safety layer actually has to back off or whether it ever fails silently. The quantitative tracking errors and FOV margin plots are also thin. This is useful reading for anyone building vision-based UAV teams who already knows CBF-QP basics and wants a worked 3D example. It is not a foundational result, but the method is concrete enough and the hardware trials are real, so it belongs in review rather than a desk reject.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a distributed 3D leader-follower formation (3D-LFF) control framework for multi-UAV systems. It derives a relative kinematic model in line-of-sight coordinates, designs a nominal distributed formation tracking controller using local relative states, and embeds this controller in a CBF-QP safety filter that minimally modifies commanded velocities to enforce a field-of-view (FOV) constraint keeping the leader inside the follower's camera frustum. The approach is claimed to guarantee visibility by construction while preserving formation tracking whenever feasible, and is validated via Gazebo simulations and Crazyflie hardware experiments including conflict scenarios.

Significance. If the QP feasibility analysis and experimental verification are strengthened, the work offers a practical perception-aware safety filter for vision-based UAV formations that combines standard CBF theory with distributed formation control. This addresses a relevant engineering gap where demanding formation commands can violate onboard camera constraints.

major comments (1)

[Abstract and §4] Abstract and §4 (Safety Filter Design): the central guarantee of visibility 'by construction' is qualified by 'whenever feasible,' yet the manuscript supplies neither a proof that the feasible set of the CBF-QP is non-empty for the closed-loop relative dynamics under the tested formation commands nor empirical verification (solver status flags, minimum constraint margins, or infeasibility counts) from the Gazebo and Crazyflie experiments.

minor comments (2)

[Experiments] Experiments section: validation is described only qualitatively; quantitative metrics (e.g., RMS formation tracking error, percentage of time the FOV constraint is active, or histograms of QP slack variables) with error bars or statistical summaries across trials are absent.
[§3] Notation and §3 (Relative Kinematics): the precise definition of the FOV barrier function h(x) derived from the line-of-sight angles and the choice of class-K function in the CBF inequality should be stated explicitly with the corresponding equation numbers.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the constructive feedback. We address the major comment below.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (Safety Filter Design): the central guarantee of visibility 'by construction' is qualified by 'whenever feasible,' yet the manuscript supplies neither a proof that the feasible set of the CBF-QP is non-empty for the closed-loop relative dynamics under the tested formation commands nor empirical verification (solver status flags, minimum constraint margins, or infeasibility counts) from the Gazebo and Crazyflie experiments.

Authors: We agree that the manuscript does not contain a formal proof that the CBF-QP feasible set remains non-empty under the closed-loop relative dynamics for the tested formation commands; deriving such a guarantee for the nonlinear distributed system is non-trivial. We will revise the manuscript to add empirical verification using data from the Gazebo simulations and Crazyflie experiments. This will include QP solver feasibility status, time histories of the minimum CBF value h(x), and confirmation of zero infeasibility events in the reported trials. The abstract and Section 4 will be updated to clarify that the visibility guarantee holds subject to QP feasibility, which is supported empirically for the presented scenarios. revision: partial

standing simulated objections not resolved

Formal proof that the CBF-QP feasible set is non-empty for the closed-loop relative dynamics under the tested formation commands

Circularity Check

0 steps flagged

No circularity; derivation uses standard CBF-QP on relative kinematics

full rationale

The paper derives a relative kinematic model in line-of-sight coordinates, designs a distributed nominal 3D-LFF tracking controller from locally available states, and then embeds that controller inside a standard CBF-QP safety filter whose barrier function enforces the FOV constraint. None of these steps reduce the claimed visibility guarantee to a fitted parameter, a self-referential definition, or a load-bearing self-citation whose validity depends on the present work. The 'whenever feasible' qualifier is an explicit acknowledgment of QP feasibility rather than a hidden circular assumption. The overall architecture therefore remains self-contained against external CBF theory and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from nonlinear control and optimization; no new physical entities are introduced. The main free parameters are the CBF class-K functions and QP weights that trade off formation error versus safety margin.

free parameters (2)

CBF gain and class-K function parameters
These define the strictness of the FOV barrier and are chosen to make the QP feasible; their specific values are not given in the abstract.
QP weighting matrices
Trade-off between nominal formation velocity and safety correction; must be tuned for each formation geometry.

axioms (2)

domain assumption The relative kinematic model in line-of-sight coordinates is accurate and the only states needed for control are locally measurable.
Invoked when the distributed controller is designed using only relative states.
ad hoc to paper The quadratic program is feasible whenever the nominal formation command would violate the FOV constraint.
The abstract qualifies the guarantee with 'whenever feasible' but does not prove non-emptiness of the feasible set.

pith-pipeline@v0.9.0 · 5744 in / 1651 out tokens · 42260 ms · 2026-05-19T22:26:53.659753+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

embed the nominal formation controller within a Control Barrier Function-based Quadratic Program (CBF-QP) safety filter that minimally modifies the commanded velocities to maintain the leader inside the follower's camera frustum
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Definition 1 (Control Barrier Function). A continuously differentiable function h is a valid CBF ... sup_u [nabla h^T (f + g u) + kappa(h)] >= 0

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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R. R. Suganda and B. Hu, “Formation-aware adaptive conformalized perception for safe leader-follower multi-robot systems,”arXiv preprint arXiv:2603.08958, 2026

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Distributed implementation of con- trol barrier functions for multi-agent systems,

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Neural graph control barrier functions guided distributed collision-avoidance multi-agent control,

S. Zhang, K. Garg, and C. Fan, “Neural graph control barrier functions guided distributed collision-avoidance multi-agent control,” inConfer- ence on robot learning, pp. 2373–2392, PMLR, 2023

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A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,”IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2016

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Learning for layered safety-critical control with predictive control barrier functions,

W. D. Compton, M. H. Cohen, and A. D. Ames, “Learning for layered safety-critical control with predictive control barrier functions,”arXiv preprint arXiv:2412.04658, 2024

work page arXiv 2024

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Crazysim: A software-in-the-loop simulator for the crazyflie nano quadrotor,

C. Llanes, Z. Kakish, K. Williams, and S. Coogan, “Crazysim: A software-in-the-loop simulator for the crazyflie nano quadrotor,” in2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 12248–12254, 2024. APPENDIX Formulating the kinematics of the spherical states˙ x ij = [ ˙Lij, ˙ϕij, ˙ξij,˙αij]⊤ relies on determining the Cartesian rel...

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