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arxiv: 2603.15278 · v3 · pith:AFHLOMEKnew · submitted 2026-03-16 · 📡 eess.SY · cs.RO· cs.SY

Encirclement Guaranteed Finite-Time Capture against Unknown Evader Strategies

Dinesh Patra , Prajakta Surve , Ashish R. Hota , Shaunak D. Bopardikar This is my paper

Pith reviewed 2026-05-25 06:59 UTC · model grok-4.3

classification 📡 eess.SY cs.ROcs.SY
keywords pursuit-evasionencirclementfinite-time captureconvex hullmulti-pursuerunknown evader headingguaranteed captureunbounded plane
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The pith

Pursuers can force finite-time capture of an evader while always keeping it inside their convex hull, without knowing its heading.

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

The paper develops a class of strategies for multiple pursuers to capture one evader in finite time in an unbounded two-dimensional plane. These strategies ensure the evader remains inside the convex hull formed by the pursuers' positions at every moment until capture occurs. The guarantees hold regardless of the evader's unknown heading angle or any movement strategy it chooses. An explicit upper bound on the capture time is also derived from the approach. This addresses both encirclement and capture in one framework where earlier results handled the two goals separately.

Core claim

The authors present a class of strategies for the pursuers that guarantee capture in finite time while maintaining encirclement, irrespective of the evader's strategy. They also derive an upper bound on the time to capture.

What carries the argument

Class of pursuer strategies that maintain the evader inside the convex hull of pursuer positions while driving to finite-time capture.

If this is right

  • The evader remains enclosed in the pursuer convex hull for the entire duration until capture.
  • Capture is guaranteed to occur in finite time no matter what strategy the evader selects.
  • An explicit upper bound exists on the time required for capture.
  • Numerical simulations confirm the strategies succeed against multiple different evader behaviors.

Where Pith is reading between the lines

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

  • The position-only requirement could allow implementation on agents with limited sensing that cannot measure velocities or headings.
  • The time bound might be used to plan team sizes or energy budgets for real-world pursuit tasks.
  • The same convex-hull maintenance idea could be tested in bounded domains or with moving obstacles.

Load-bearing premise

Pursuers have continuous access to the positions of the evader and each other but receive no information on the evader's heading angle.

What would settle it

An explicit evader trajectory that either exits the pursuers' convex hull before capture or forces capture time to exceed the derived upper bound when pursuers apply the proposed strategies.

Figures

Figures reproduced from arXiv: 2603.15278 by Ashish R. Hota, Dinesh Patra, Prajakta Surve, Shaunak D. Bopardikar.

Figure 1
Figure 1. Figure 1: Examples of triangulation with an evader lying inside the convex hull of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Range of strategies for the active pursuers that guarantee encirclement of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Encirclement guaranteed capture under the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Encirclement guaranteed capture under the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Encirclement guaranteed capture with three pursuers under [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Encirclement guaranteed capture under the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Performance under the closest link policy of the evader with the encirclement guaranteed sector set based robust MPC approach in [12]. The evader moves to the closest edge and remains on the edge. While the pursuers are able to maintain encirclement, it takes around t = 42 s for capture, due to the rigid sector constraints. 0 0.2 0.4 0.6 0.8 1 Time (second) 0 0.2 0.4 0.6 0.8 1 [PITH_FULL_IMAGE:figures/ful… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of the areas of the subtriangles [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distance between the nearest pursuer and the evader over time under the [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
read the original abstract

We consider a pursuit-evasion scenario involving a group of pursuers and a single evader in a two-dimensional unbounded environment. The pursuers aim to capture the evader in finite time while ensuring the evader remains enclosed within the convex hull of their positions until capture, without knowledge of the evader's heading angle. Prior works have addressed the problem of encirclement and capture separately in different contexts. In this paper, we present a class of strategies for the pursuers that guarantee capture in finite time while maintaining encirclement, irrespective of the evader's strategy. Furthermore, we derive an upper bound on the time to capture. Numerical results highlight the effectiveness of the proposed framework against a range of evader strategies.

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

0 major / 3 minor

Summary. The paper considers a pursuit-evasion game in the unbounded plane with multiple pursuers and one evader. Pursuers have access only to relative positions (no headings) and must drive the evader to capture in finite time while keeping the evader inside the convex hull of the pursuers at every instant, for any evader strategy. The central contribution is a class of pursuer strategies together with an explicit upper bound on capture time; numerical simulations illustrate performance against several evader behaviors.

Significance. If the stated guarantees hold, the work supplies a unified treatment of encirclement and finite-time capture that had previously been handled separately. The explicit time bound and the position-only sensing model are concrete strengths that could be useful for multi-agent coordination under limited information.

minor comments (3)
  1. [§3] §3, the definition of the convex-hull condition (Eq. 3) is stated only for the continuous-time trajectories; a brief remark on how the condition is preserved under the sampled-data implementation used in the simulations would remove ambiguity.
  2. [Theorem 1] The upper-bound expression in Theorem 1 depends on the initial diameter of the pursuer set; the paper should state explicitly whether this quantity is assumed known to the pursuers or is only an a-posteriori quantity used in the analysis.
  3. [Figure 4] Figure 4 caption lists four evader strategies but the legend in the figure itself uses different labels; harmonizing the notation would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading, positive summary of the contribution, and recommendation of minor revision. No major comments were provided in the report, so we have no specific points requiring response or revision at this stage.

Circularity Check

0 steps flagged

No significant circularity; derivation combines independent prior results

full rationale

The provided abstract and context state that encirclement and capture were addressed separately in prior works, with the present paper combining them into a new class of strategies plus an explicit upper bound on capture time. No equations, self-citations, or fitted parameters are shown that reduce any claimed prediction or guarantee to its own inputs by construction. The central result is presented as a novel synthesis under standard position-only sensing assumptions, with no load-bearing self-citation chains or ansatz smuggling visible. This is the expected honest non-finding for a paper whose core claim rests on external prior results rather than internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only; likely standard assumptions in the field apply but cannot be confirmed without full text.

axioms (2)
  • domain assumption The pursuers and evader follow continuous-time kinematic models in 2D plane.
    Standard in pursuit-evasion but not explicitly stated in abstract.
  • domain assumption Pursuers can obtain real-time position information of the evader and fellow pursuers.
    Required for any strategy implementation.

pith-pipeline@v0.9.0 · 5667 in / 1228 out tokens · 42859 ms · 2026-05-25T06:59:57.232724+00:00 · methodology

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Lean theorems connected to this paper

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

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Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

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