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arxiv: 2604.17995 · v2 · submitted 2026-04-20 · 💻 cs.MA

Multi-UAV Path Following using Vector-Field Guidance

Gautam Kumar , Amit Shivam , Ashwini Ratnoo This is my paper

Pith reviewed 2026-05-10 03:54 UTC · model grok-4.3

classification 💻 cs.MA
keywords multi-UAVpath followingvector field guidancecollision avoidanceuniform spacingdecentralized controlrotational repulsion
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The pith

A decentralized vector-field method with rotational repulsion guides multiple UAVs to a path while guaranteeing no collisions and uniform spacing.

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

The paper develops a guidance approach for several UAVs to track the same reference path without colliding and while keeping equal distances between them. Each vehicle is driven to the path by a vector field, repelled from others through a rotation term that uses only local distance and bearing measurements, and sped up or slowed down according to its spacing error relative to neighbors. Mathematical analysis shows that the repulsion term prevents all collisions during the approach to the path and that the spacing errors decay to zero. The result matters for applications such as coordinated surveillance or mapping, where fleets must stay safely spread out along a route without a central coordinator.

Core claim

A vector-field guidance law steers each UAV to the reference path; a rotational repulsion term constructed from relative distance and bearing between UAVs prevents collisions throughout convergence; and a velocity command proportional to the inter-UAV spacing error drives the errors to zero, yielding uniform separation along the path. The authors prove collision avoidance and asymptotic convergence of the spacing errors under the assumed kinematic model.

What carries the argument

Vector-field path guidance combined with a rotational repulsion mechanism (using relative distance and bearing) and an inter-UAV spacing-error velocity controller.

If this is right

  • Collisions are provably avoided for any initial positions outside a minimum separation distance.
  • Inter-UAV spacing errors converge asymptotically to zero regardless of the number of vehicles.
  • The scheme requires only local relative-position measurements and no global coordination.
  • Uniform spacing is achieved along both straight and curved reference paths under the kinematic assumptions.
  • The method extends the single-UAV vector-field guidance literature to the multi-vehicle case with explicit safety guarantees.

Where Pith is reading between the lines

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

  • The same repulsion term could be adapted to handle moving obstacles or time-varying paths if the bearing calculation is updated continuously.
  • Real-world robustness would depend on how well the kinematic model matches actual UAV dynamics under wind or actuator limits.
  • The approach offers a building block for larger multi-agent formation problems where agents must follow a common curve while preserving order.
  • Integration with altitude or formation-shape controllers would require checking whether the repulsion still dominates in three dimensions.

Load-bearing premise

The vector-field law successfully drives every UAV onto the reference path and the rotational repulsion stays active and unopposed by path curvature or disturbances throughout the entire convergence.

What would settle it

A numerical simulation or flight test in which at least one pair of UAVs collides or the spacing errors fail to converge to zero while following the stated control laws.

Figures

Figures reproduced from arXiv: 2604.17995 by Amit Shivam, Ashwini Ratnoo, Gautam Kumar.

Figure 1
Figure 1. Figure 1: Path following scenario: (a) straight line path, and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: UAV control input and spacing error for straight [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Inter-UAV distance parameter E for straight line path and sinusoidal curve following [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 2
Figure 2. Figure 2: UAV trajectories for straight line path following [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: UAV trajectories for sinusoidal curve following. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: UAV control input and spacing error for sinusoidal [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

This paper presents a decentralized, collision-free framework for path following guidance of multiple uncrewed aerial vehicles (UAVs), while maintaining uniform spacing along a reference path. A vector field-based guidance law is employed to drive each UAV toward the reference path. A rotational repulsion mechanism, utilizing relative distance and bearing between UAVs, is proposed to avoid collisions during convergence to the path, and an inter-UAV spacing error-based velocity control law is presented to achieve uniform separation along the path. Analytical guarantees are established for collision avoidance and convergence of the inter-UAV spacing errors to zero, ensuring uniform separation along the path. Numerical simulations demonstrate the efficacy of the proposed method.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a decentralized multi-UAV path-following framework that combines a vector-field guidance law to drive each vehicle to a reference path, a rotational repulsion term based on relative distance and bearing to enforce collision avoidance during convergence, and an inter-UAV spacing-error velocity controller to achieve uniform separation along the path. Analytical guarantees are claimed for collision avoidance (via a distance-based Lyapunov argument) and asymptotic convergence of spacing errors to zero, with numerical simulations used to illustrate performance under the combined laws.

Significance. If the claimed guarantees hold for the full closed-loop system, the work would provide a useful decentralized approach to safe, coordinated path following for UAV teams, with explicit Lyapunov-based safety and convergence results. The separation of path guidance, repulsion, and spacing control is a reasonable modular design, and the provision of analytical (rather than purely empirical) guarantees is a positive feature for the multi-agent control literature.

major comments (1)
  1. [§5 (Stability Analysis)] §5 (Stability Analysis) and the associated Lyapunov arguments: the proof of collision avoidance under the rotational repulsion law (Eq. (12) or equivalent) is developed for the vector-field guidance alone and does not explicitly verify that the safe set remains invariant when the spacing velocity law (Eq. (18)) modulates forward speed. Because the spacing controller alters the magnitude of the velocity vector along the path tangent while repulsion acts on the relative bearing, the sign condition on the distance derivative can change; a combined closed-loop vector-field analysis or invariance argument is required to support the joint claim of collision avoidance and spacing convergence.
minor comments (2)
  1. [§2 (Problem Formulation)] The kinematic model assumptions (e.g., whether wind or actuator dynamics are neglected) should be stated explicitly in the problem formulation section before the control laws are introduced.
  2. [§6 (Simulations)] Simulation figures would benefit from explicit labeling of the reference path curvature and initial spacing errors to allow readers to assess how the repulsion and spacing laws interact under non-straight paths.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the work's significance. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§5 (Stability Analysis)] §5 (Stability Analysis) and the associated Lyapunov arguments: the proof of collision avoidance under the rotational repulsion law (Eq. (12) or equivalent) is developed for the vector-field guidance alone and does not explicitly verify that the safe set remains invariant when the spacing velocity law (Eq. (18)) modulates forward speed. Because the spacing controller alters the magnitude of the velocity vector along the path tangent while repulsion acts on the relative bearing, the sign condition on the distance derivative can change; a combined closed-loop vector-field analysis or invariance argument is required to support the joint claim of collision avoidance and spacing convergence.

    Authors: We agree that the collision-avoidance argument in Section 5 was developed for the vector-field guidance plus rotational repulsion and did not explicitly incorporate the forward-speed modulation introduced by the spacing-error velocity law. Because the spacing controller changes the magnitude of the tangential velocity component, the relative-velocity projection that appears in the distance derivative can in principle be affected. In the revision we will therefore supply a combined closed-loop analysis: we will recompute the time derivative of the inter-UAV distance under the full control law (vector-field guidance + repulsion + spacing modulation), bound the speed variation induced by the spacing term, and show that the repulsion term still guarantees that the safe set remains invariant whenever the distance falls below a prescribed threshold. The revised Section 5 will contain the extended Lyapunov (or invariance) argument together with the necessary technical lemmas that jointly establish collision avoidance and asymptotic spacing convergence. revision: yes

Circularity Check

0 steps flagged

No circularity: analytical guarantees derived from stated kinematic model and Lyapunov arguments without reduction to fitted inputs or self-definitions.

full rationale

The paper's central claims rest on vector-field guidance, rotational repulsion, and spacing-velocity laws applied to a kinematic model, with collision avoidance and spacing convergence shown via Lyapunov analysis. No quoted step reduces a prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness result, or renames an input as an output. The derivation chain remains independent of the target results.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on standard kinematic models for UAVs and convergence properties of vector fields; no new entities are postulated, but control gains and path assumptions are implicit.

free parameters (1)
  • control gains for vector field, repulsion, and velocity laws
    Gains are part of the guidance and control laws and typically require tuning for performance, though not explicitly fitted in the abstract description.
axioms (2)
  • domain assumption UAVs obey point-mass or simple kinematic dynamics without higher-order effects
    Standard assumption in guidance law design for path following.
  • domain assumption Reference path is sufficiently smooth for vector field to be well-defined
    Required for the guidance law to drive UAVs to the path.

pith-pipeline@v0.9.0 · 5406 in / 1358 out tokens · 35892 ms · 2026-05-10T03:54:14.201164+00:00 · methodology

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Reference graph

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