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arxiv: 2606.04518 · v1 · pith:SEYJD34Fnew · submitted 2026-06-03 · 💻 cs.RO

Cooperative Circumnavigation for Multiple Unmanned Surface Vehicles Without External Localization

Xueming Liu , Lin Li , Xiang Zhou , Tianjiang Hu , Qingrui Zhang This is my paper

Pith reviewed 2026-06-28 06:25 UTC · model grok-4.3

classification 💻 cs.RO
keywords unmanned surface vehiclescooperative circumnavigationformation controlKalman filterpersistent excitationobservabilityonboard sensingtarget tracking
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The pith

Multiple USVs maintain circular formation around a target using only onboard sensors by making relative motions persistently exciting for their Kalman filters.

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

This paper develops a cooperative framework in which several unmanned surface vehicles circle a non-cooperative target at a fixed radius while keeping equal spacing, all without GPS or other external positioning. The vehicles measure distances and displacements to one another through active sensing and communication, and obtain bearings to the target with passive sensors. Two Kalman filters produce the needed position estimates, while a coupled-oscillator controller shapes the vehicles' motion so that those estimates remain observable. The approach is shown to work in simulation and rests on a theoretical guarantee that the chosen motion satisfies the persistent-excitation condition required by the filters.

Core claim

The coupled oscillator-based formation controller ensures that the relative motions between the USVs, as well as between each USV and the target, satisfy the persistent excitation condition, thereby guaranteeing observability of the Maximum Correntropy Kalman Filter and the Pseudo-Linear Kalman Filter used for position estimation.

What carries the argument

Coupled oscillator-based formation controller that enforces the persistent excitation condition on relative motions to guarantee observability of the two Kalman filters.

If this is right

  • The USVs achieve and hold a uniform circular formation of any chosen radius around the target.
  • Relative positions among the vehicles and to the target are estimated continuously by the respective Kalman filters.
  • The entire system functions without external localization infrastructure.
  • Numerical simulations confirm that the controller simultaneously achieves the formation and keeps the filters observable.

Where Pith is reading between the lines

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

  • The same motion-design principle could be tested on other vehicle types that must circle a target with limited sensors.
  • If the persistent-excitation guarantee holds over long durations, estimation drift would remain bounded without external corrections.
  • The separation of active inter-vehicle sensing from passive target sensing may simplify hardware requirements in other multi-agent formation tasks.

Load-bearing premise

The heterogeneous perception strategy supplies enough relative-range, displacement, and bearing measurements for the chosen Kalman filters to produce usable position estimates.

What would settle it

A run in which the USVs' relative trajectories are altered so the persistent-excitation condition is violated and the position estimates from either filter diverge or become unbounded.

Figures

Figures reproduced from arXiv: 2606.04518 by Lin Li, Qingrui Zhang, Tianjiang Hu, Xiang Zhou, Xueming Liu.

Figure 1
Figure 1. Figure 1: Illustration of the multi-USV cooperative circum [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic diagram illustrating the geometric re [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: RMSE of relative position estimation under log [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: RMSE of relative position estimation with real [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 4
Figure 4. Figure 4: RMSE of relative position estimation under Gaus [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: USV target tracking trajectories under different [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Error evolution for the constant-velocity target [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Multi-USV circumnavigation a varying-velocity [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Error evolution for the varying-velocity target [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 14
Figure 14. Figure 14: Trajectories of the USVs and the target in the [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Multi-USV circumnavigation a varying [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Trajectories of the USVs and the target in the [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Error evolution for the USV dropout scenario. [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
read the original abstract

This paper proposes a cooperative target circumnavigation framework for multiple unmanned surface vehicles (USVs) operating without external localization. The objective is to maintain a uniform circular formation of a specified radius around a target using only limited onboard sensing. The framework adopts a heterogeneous perception strategy that distinguishes between the asymmetric sensing relationships with the target and among the USVs. Specifically, the USVs obtain relative range and displacement measurements through active perception and inter-vehicle communication, while bearing measurements to a non-cooperative target are acquired via passive sensors. To estimate relative positions--both among USVs and between each USV and the target--we employ a Maximum Correntropy Kalman Filter and a Pseudo-Linear Kalman Filter, respectively. A coupled oscillator-based formation controller is designed to ensure system observability while achieving circumnavigation. Theoretical analysis demonstrates that the controller ensures the relative motions between the USVs, as well as that between each USV and the target, satisfy the persistent excitation condition, thereby guaranteeing observability of the Kalman-based filters. The effectiveness of the proposed approach is validated through numerical simulations.

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

2 major / 2 minor

Summary. The paper proposes a cooperative circumnavigation framework for multiple USVs without external localization. It uses heterogeneous perception (active range/displacement among USVs via comms, passive bearing to target), MCKF for USV-USV relative position estimation, PLKF for USV-target estimation, and a coupled oscillator controller designed to induce persistent excitation (PE) in relative motions to guarantee observability of the filters. Effectiveness is shown via numerical simulations and theoretical analysis claiming controller-induced PE ensures filter observability.

Significance. If the PE guarantees transfer rigorously to the modified filters (accounting for correntropy in MCKF and linearization in PLKF), the work would offer a useful contribution to decentralized marine robotics by tightly coupling formation control with estimation observability in GPS-denied settings. The heterogeneous sensing and oscillator-based design are practical strengths, though the result's impact depends on closing the gap between standard linear PE theory and the specific nonlinear filter properties.

major comments (2)
  1. [Theoretical analysis] Theoretical analysis section: The claim that the coupled oscillator controller ensures relative motions satisfy the PE condition (thereby guaranteeing observability of MCKF and PLKF) invokes standard results for linear time-varying systems, but does not re-derive the excitation condition or observability Gramian under the correntropy-based cost in MCKF (which alters the information matrix) or the pseudo-linear approximation in PLKF (which introduces linearization error). This leaves the central observability guarantee unverified for the actual filters used.
  2. [Controller design] Controller design and observability proof: The design couples the oscillator dynamics to relative motions to enforce PE, but the manuscript does not explicitly address whether this creates circularity (i.e., the controller assumes the excitation it must induce) or whether the resulting trajectories satisfy the filter-specific persistence conditions required for MCKF convergence and PLKF bias analysis.
minor comments (2)
  1. Notation for the heterogeneous measurements (range, displacement, bearing) should be unified across the estimation and control sections to avoid ambiguity in the observability analysis.
  2. [Numerical simulations] Simulation section: Include quantitative metrics (e.g., estimation RMSE, formation error) comparing against a baseline without the PE-inducing controller to strengthen the validation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the theoretical analysis and controller design. We provide point-by-point responses below.

read point-by-point responses

  1. Referee: [Theoretical analysis] Theoretical analysis section: The claim that the coupled oscillator controller ensures relative motions satisfy the PE condition (thereby guaranteeing observability of MCKF and PLKF) invokes standard results for linear time-varying systems, but does not re-derive the excitation condition or observability Gramian under the correntropy-based cost in MCKF (which alters the information matrix) or the pseudo-linear approximation in PLKF (which introduces linearization error). This leaves the central observability guarantee unverified for the actual filters used.

    Authors: We agree that the manuscript applies standard PE results for LTV systems without an explicit re-derivation of the observability Gramian accounting for the correntropy cost function in the MCKF or the linearization in the PLKF. The analysis focuses on the underlying relative-motion regressors satisfying PE, which is intended to ensure positive definiteness of the information matrix for the base linear models. To strengthen the presentation, we will revise the theoretical analysis section to include additional discussion on the transfer of the PE condition to the modified filters, citing supporting results from robust filtering literature where appropriate. revision: yes

  2. Referee: [Controller design] Controller design and observability proof: The design couples the oscillator dynamics to relative motions to enforce PE, but the manuscript does not explicitly address whether this creates circularity (i.e., the controller assumes the excitation it must induce) or whether the resulting trajectories satisfy the filter-specific persistence conditions required for MCKF convergence and PLKF bias analysis.

    Authors: The coupled oscillator is embedded in the control law to generate trajectories with persistent relative motion by design; the PE proof is carried out on the closed-loop kinematic equations and holds for the motion trajectories independently of the instantaneous filter estimates. This structure avoids circularity because the excitation is enforced at the trajectory level, which then enables filter convergence. We will revise the manuscript to add an explicit clarification paragraph separating the control-induced PE from the filter convergence analysis and confirming that the resulting trajectories meet the required conditions for both the MCKF and PLKF. revision: yes

Circularity Check

0 steps flagged

No significant circularity; controller design and PE proof are independent

full rationale

The abstract states that a coupled oscillator controller is designed to achieve circumnavigation while ensuring PE, with separate theoretical analysis demonstrating that relative motions satisfy the PE condition to guarantee filter observability. This is a standard non-circular control design pattern (design for dual objectives, then prove satisfaction of excitation conditions) rather than any self-definitional reduction, fitted input renamed as prediction, or load-bearing self-citation chain. No equations or claims in the provided text reduce the observability guarantee to an assumption by construction. The derivation remains self-contained against standard linear time-varying system results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract, the main assumptions are standard in the field of control and estimation; no new entities invented. The radius is a design choice but not fitted to data in the description.

pith-pipeline@v0.9.1-grok · 5725 in / 1152 out tokens · 52153 ms · 2026-06-28T06:25:30.738409+00:00 · methodology

discussion (0)

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