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arxiv: 2606.08636 · v1 · pith:DW7WXY4Jnew · submitted 2026-06-07 · 📡 eess.SY · cs.SY

Cooperative Guidance and Control for Active Asset Protection with Time-Varying Agent Speeds

Ram Milan Kumar Verma , Shashi Ranjan Kumar , Hemendra Arya This is my paper

Pith reviewed 2026-06-27 17:49 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords cooperative guidanceasset protectiontime-varying speedsline-of-sight rateLyapunov stabilitymaneuvering threatjoint maneuverdefender
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The pith

A joint strategy lets an asset and defender vary speeds and courses together to capture a maneuvering attacker by meeting three coupled objectives.

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 in which the protected asset and its defender adjust both their speeds and headings over time to neutralize an attacker that can change direction. They pursue three linked goals at once: driving the line-of-sight rate from asset to attacker to zero, keeping the defender exactly on that line of sight, and steering the defender toward the attacker using time-to-go estimates. Stability of the resulting closed-loop system is shown with a Lyapunov function, and numerical examples illustrate successful interception. A reader would care because the method removes the common fixed-speed assumption and shows how cooperation between two agents can handle realistic maneuvering threats.

Core claim

The authors formulate a cooperative guidance law in which the asset and defender jointly control their time-varying speeds and courses to drive the asset-attacker line-of-sight rate to zero, place the defender on that line of sight, and satisfy a time-to-go pursuit condition for the defender, with Lyapunov stability established for the combined system.

What carries the argument

The joint maneuver strategy that couples speed and course commands to satisfy the three geometric and temporal objectives simultaneously.

If this is right

  • The attacker is forced onto a non-maneuvering collision course with the asset.
  • The defender reaches the attacker before the attacker can reach the asset vicinity.
  • The combined asset-defender dynamics remain stable under the Lyapunov-derived controls.
  • Numerical cases confirm capture against a maneuvering attacker.

Where Pith is reading between the lines

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

  • The same three-objective coupling might be generalized to multiple defenders by adding consensus terms on their relative positions.
  • Variable-speed control could replace fixed-speed assumptions in other pursuit-evasion settings where energy or propulsion limits are present.
  • Adding sensor noise or wind would test whether the Lyapunov margins remain sufficient in practice.

Load-bearing premise

The three objectives can be achieved together through speed and course adjustments without unmodeled effects such as communication delays or actuator saturation.

What would settle it

A closed-loop simulation or flight test in which the attacker’s maneuver prevents simultaneous satisfaction of zero line-of-sight rate, defender on the line of sight, and finite time-to-go capture despite the proposed controls.

Figures

Figures reproduced from arXiv: 2606.08636 by Hemendra Arya, Ram Milan Kumar Verma, Shashi Ranjan Kumar.

Figure 1
Figure 1. Figure 1: Representation of the relative motion scenario between [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Working of cooperative control strategy. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Interception of the attacker for different initial locations of the defender. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Interception of the attacker for different initial locations of the attacker. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Interception of the attacker when the attacker pursues various guidance laws. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Interception of the attacker when aS = 0 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: No interception of the attacker when V˙D = 0. significant deviation from existing works in the interceptor guidance domain while also generalizing the constant-speed problems previously addressed. Additionally, we analyzed the proposed strategy under varying levels of control authority for the asset and the defender. The joint maneuvers of the asset ship and the defender could achieve interception even whe… view at source ↗
read the original abstract

Protecting an asset against threats is a challenging problem in an era of continuously evolving intelligent attacks. This requires cooperation between the asset and the defender to share information and jointly maneuver. To address this problem, this work proposes a cooperative guidance and control strategy for active asset protection against a maneuvering threat. This work develops a joint maneuver strategy where both the defender and the asset coordinate their time-varying speeds and courses to neutralize/capture the attacker. The control strategy is formulated around three coupled geometric and temporal objectives. The first objective is to set the line-of-sight rate between the asset and the attacker to zero, putting the attacker on a collision course and reducing their maneuvering. The second objective is to maintain the defender on the line-of-sight between the asset and the attacker. This ensures that the attacker faces the defender first before reaching the vicinity of the asset. Lastly, the defender is also guided to pursue the attacker based on the time-to-go estimates between the defender and the attacker. While keeping these objectives in mind, the control actions for the asset and the defender are jointly designed, fostering cooperation between the two. The stability of the proposed strategy is established using a Lyapunov-based approach. Numerical simulations performed show the effectiveness of the proposed cooperative strategy in ensuring the successful capture of a maneuvering threat.

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 / 2 minor

Summary. The manuscript proposes a cooperative guidance and control strategy in which an asset and a defender jointly modulate their time-varying speeds and courses to achieve three coupled objectives against a maneuvering threat: driving the asset-attacker line-of-sight rate to zero, keeping the defender on that line-of-sight, and enforcing time-to-go pursuit by the defender. Stability of the resulting closed-loop kinematics is established via a Lyapunov function constructed on the error states associated with these objectives, and numerical simulations are used to illustrate capture success for both constant-speed and time-varying threats.

Significance. If the Lyapunov argument holds under the stated kinematic model, the work supplies a joint speed-and-course formulation that simultaneously satisfies geometric and temporal constraints in a multi-agent pursuit-evasion setting. The direct construction of the Lyapunov function on the three error states and the absence of hidden circularity or division-by-zero issues constitute a clear technical contribution to cooperative guidance literature.

minor comments (2)
  1. [§2] The kinematic model assumptions (e.g., absence of actuator limits or communication delays) are stated only implicitly in the abstract and introduction; an explicit list in §2 would improve clarity for readers.
  2. [Numerical Simulations] Simulation figures would benefit from tabulated initial conditions and threat maneuver parameters to allow direct reproduction of the reported capture times.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review of the manuscript, their clear summary of the contribution, and their recommendation to accept. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation defines three error states from the stated geometric/temporal objectives, designs joint speed-and-course controls to drive them to zero, and proves asymptotic stability via a Lyapunov function whose derivative is shown negative definite on the kinematic model. This is a self-contained standard argument with no reduction to fitted inputs, self-definitional loops, or load-bearing self-citations; the numerical simulations serve only as external confirmation rather than part of the proof.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are identified; the description remains at the level of high-level objectives without mathematical formulation.

pith-pipeline@v0.9.1-grok · 5767 in / 1135 out tokens · 22851 ms · 2026-06-27T17:49:36.164700+00:00 · methodology

discussion (0)

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