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arxiv: 1906.11153 · v1 · pith:7N4BV7U6new · submitted 2019-06-26 · 📡 eess.SY · cs.SY

Distributed Optimal Guidance Laws for Multiple Unmanned Aerial Vehicles Attacking A Moving Target

Xiaoqian Wei , Jianying Yang , Xiangru Fan This is my paper

Pith reviewed 2026-05-25 15:47 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords cooperative guidance lawssimultaneous attackunmanned aerial vehiclesmoving targetdistributed controlline of sighttwo-point boundary value
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The pith

Distributed guidance laws allow multiple UAVs to attack a moving target simultaneously by equalizing relative distance reduction rates along lines of sight.

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

This paper develops two cooperative guidance laws for multiple unmanned aerial vehicles to perform simultaneous attacks on a moving target, covering cases with both known and unknown target acceleration. The laws require only that the communication network contains a directed spanning tree and that at least one attacker observes the target. Acceleration components along each attacker-target line of sight reduce the relative remaining distance at the same speed for all attackers, enabling simultaneous impact without computing remaining time. Perpendicular components make normal overload zero, producing smooth trajectories that avoid collisions among attackers.

Core claim

The central claim is that the acceleration components along the attacker-target line of sight in the novel guidance laws reduce the relative remaining distance between each of the attackers and the target at the same speed, thus completing simultaneous attack and avoiding the calculation of the remaining time, while the components perpendicular to the attacker-target line of sight make the normal overload of relative motion zero so that the trajectory will be smooth and the collision problem within the attackers can be avoided.

What carries the argument

Two-point boundary value based cooperative guidance laws that decompose acceleration into line-of-sight components equalizing closing rates and perpendicular components nulling normal overload.

If this is right

  • Simultaneous attack occurs without explicit calculation of remaining flight time.
  • Trajectories remain smooth because normal overload in relative motion is zero.
  • Intra-attacker collisions are avoided by the perpendicular acceleration design.
  • The laws function for both known and unknown target acceleration.
  • Only minimal network connectivity and partial target observation are needed.

Where Pith is reading between the lines

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

  • The same decomposition could apply to other multi-agent synchronization tasks where arrival timing matters more than individual paths.
  • Eliminating time-to-go estimates may reduce real-time computational demands on vehicle processors.
  • The approach could be tested for robustness by adding communication delays to the directed spanning tree condition.
  • Hardware flight tests with actual UAVs would check whether the zero-overload property holds under wind and sensor noise.

Load-bearing premise

The multi-attacker communication network contains a directed spanning tree and at least one attacker can observe the target.

What would settle it

A simulation run with the proposed laws on a communication network lacking a directed spanning tree in which the attackers fail to reach the target at the same time.

Figures

Figures reproduced from arXiv: 1906.11153 by Jianying Yang, Xiangru Fan, Xiaoqian Wei.

Figure 1
Figure 1. Figure 1: Geometry for TA engagement [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Geometry for an attacker and its neighbors. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Then, j-th attacker can obtain the relative distan [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trajectories. 0 5 10 15 −2 −1.5 −1 −0.5 0 0.5 Time(s) Velocity Vr(km/s) Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Velocities Vr. 0 5 10 15 −2 −1.5 −1 −0.5 0 0.5 Time(s) Velocity Vλ(km/s) Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Velocities Vλ. target velocity is time-varying (atλ = 0.1sin(10t) km/s 2 ). Then the acceleration components along and perpendicular to the LOS of the attackers are AT r = atr cos φ − atλ sin φ and AT λ = atr sin φ + atλ cos φ. Attention should be paid to the fact that the accelerations of the target and the attacker are perpendicular to their respective velocity directions, which means that the speeds of … view at source ↗
Figure 8
Figure 8. Figure 8: Inputs AMr. 0 5 10 15 −4 −3 −2 −1 0 1 2 3 4 5 t(s) AMλ(km/s 2 ) AMλ1 AMλ2 AMλ3 AMλ4 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Inputs AMλ. 0 5 10 15 −3 −2 −1 0 1 2 3 4 5 Time(s) Line−of−sight angle λ (rad) Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Line of sight angle λ. and the attacker are Vi = 0.7 (km/s) and VT = 1 (km/s). In this example, four low-speed attackers attack a high-speed target at the same time. The guidance law in equation (3) is adopted, in which matrices P1i = P2i = IN , t0 = 0(s), tf = 15(s), R0 and Rf are listed in [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 16
Figure 16. Figure 16: Velocities Vλ. 0 1 2 3 4 5 6 7 8 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Time(s) Input AMr Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p009_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Inputs AMr. 0 1 2 3 4 5 6 7 8 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 Time(s) Input AMλ Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p009_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Inputs AMλ. Similar to the above, the relative distance and relative speed of the attacker-target are consistent, and the simultaneous attack task can be completed in a limited time. VI. CONCLUSIONS Distributed guidance laws based on two-point boundary value problem are designed in this paper, which can be used by multiple low-speed attackers to coordinate around or attack [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 19
Figure 19. Figure 19: Line of sight angle λ. 0 1 2 3 4 5 6 7 8 −0.05 0 0.05 0.1 0.15 0.2 Time(s) Costate parameter ρ R Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p010_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Costate parameter ρR. 0 1 2 3 4 5 6 7 8 −0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 Time(s) Costate parameter ρ Vλ Agent1 Agent2 Agent3 Agent4 [PITH_FULL_IMAGE:figures/full_fig_p010_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Costate parameter ρV λ. a high-speed moving target precisely at the same time. The acceleration of the target can be observed by an observer. At least one attacker can observe the information of the target, while the other attackers can obtain the information of the relative movement of the attacker-target indirectly from the communication network containing a directed spanning tree. The novel guidance la… view at source ↗
read the original abstract

In this paper, two cooperative guidance laws based on two-point boundary value are designed to deal with the problem of cooperative encirclement and simultaneous attack under condition of both known target acceleration and unknown target acceleration. The only requirement for the multi-attacker communication network is that it contains a directed spanning tree. The guidance laws can function properly as long as at least one attacker can observed the target. The acceleration components along the attacker-target line of sight in the novel guidance laws can reduce the relative remaining distance between each of the attackers and the target at the same speed, thus completing simultaneous attack and avoiding the calculation of the remaining time. The components of the guidance laws perpendicular to the attacker-target line of sight can make the normal overload of relative motion zero, so that the trajectory will be smooth and the collision problem within the attacker can be avoided. Simulation results verified the practicability of the novel guidance laws.

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 / 1 minor

Summary. The manuscript proposes two cooperative guidance laws derived from two-point boundary value methods for multiple UAVs to achieve simultaneous attack (and encirclement) on a moving target. The laws are distributed, requiring only a directed spanning tree in the communication graph with at least one attacker observing the target; they decompose commanded acceleration into line-of-sight (LOS) and perpendicular components. The LOS terms are asserted to reduce each attacker-target range at identical rates, thereby guaranteeing equal arrival times without explicit time-to-go computation, while the perpendicular terms null normal overload to produce smooth, collision-free trajectories. Verification is stated to rest on simulation results.

Significance. If the central range-reduction mechanism can be shown to equalize impact times for arbitrary initial ranges, the approach would supply a distributed, time-to-go-free guidance law that leverages only standard boundary-value techniques and minimal network connectivity. This would be of interest for multi-agent intercept problems where explicit synchronization is undesirable. The manuscript does not, however, supply machine-checked derivations, reproducible code, or falsifiable analytic predictions that would strengthen the result.

major comments (2)
  1. [Abstract] Abstract (third sentence): the assertion that the LOS acceleration components 'reduce the relative remaining distance between each of the attackers and the target at the same speed, thus completing simultaneous attack and avoiding the calculation of the remaining time' is not supported for unequal initial ranges. If the closing rates are identical while the initial ranges differ, the individual times-to-go (= range / closing rate) necessarily differ; the perpendicular components are stated only to null normal overload and do not compensate for timing mismatch. Because this range-reduction property is presented as the mechanism that replaces explicit time-to-go computation, the claim is load-bearing for the headline result.
  2. [Abstract] Abstract (final sentence) and throughout: the verification statement 'Simulation results verified the practicability of the novel guidance laws' supplies no information on initial conditions (in particular whether ranges are identical), network topology realization, baseline comparators, error metrics, or Monte-Carlo statistics. Without these details the distributed claim and the range-equalization property cannot be assessed.
minor comments (1)
  1. [Abstract] Abstract: the two laws (known vs. unknown target acceleration) are introduced but never distinguished in the provided description; a brief statement of their structural difference would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. Below we respond to each major comment and indicate planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (third sentence): the assertion that the LOS acceleration components 'reduce the relative remaining distance between each of the attackers and the target at the same speed, thus completing simultaneous attack and avoiding the calculation of the remaining time' is not supported for unequal initial ranges. If the closing rates are identical while the initial ranges differ, the individual times-to-go (= range / closing rate) necessarily differ; the perpendicular components are stated only to null normal overload and do not compensate for timing mismatch. Because this range-reduction property is presented as the mechanism that replaces explicit time-to-go computation, the claim is load-bearing for the headline result.

    Authors: We agree that the abstract phrasing is imprecise and potentially misleading for unequal initial ranges. The two-point boundary-value formulation incorporates boundary conditions chosen to enforce simultaneous arrival; the distributed implementation propagates this coordination via the spanning-tree topology. Nevertheless, describing the LOS components as reducing distance 'at the same speed' does not correctly capture the mechanism when ranges differ. We will revise the abstract (and the corresponding sentence in the introduction) to state the mechanism accurately without relying on that wording. revision: yes

  2. Referee: [Abstract] Abstract (final sentence) and throughout: the verification statement 'Simulation results verified the practicability of the novel guidance laws' supplies no information on initial conditions (in particular whether ranges are identical), network topology realization, baseline comparators, error metrics, or Monte-Carlo statistics. Without these details the distributed claim and the range-equalization property cannot be assessed.

    Authors: We accept that the abstract's verification statement is too terse. In the revised manuscript we will expand the abstract to mention representative initial conditions (including unequal ranges), the directed spanning-tree topologies employed, and the quantitative metrics used. The simulation section will be augmented with explicit descriptions of the network realizations, performance statistics, and any comparative runs. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard two-point boundary value methods

full rationale

The paper designs distributed guidance laws via two-point boundary value problems to enforce cooperative attack conditions under a directed spanning tree network. The stated LOS-component property (reducing relative distances at equal speed) is presented as an outcome of that design rather than a self-referential definition or a fitted parameter renamed as a prediction. No self-citation load-bearing steps, uniqueness theorems imported from the authors' prior work, or ansatzes smuggled via citation appear in the abstract or described chain. The central result therefore remains independent of its own inputs and is self-contained against external optimal-control benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from multi-agent systems and optimal control; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption The multi-attacker communication network contains a directed spanning tree.
    Invoked to ensure information propagation for distributed guidance; stated as the only network requirement.
  • domain assumption At least one attacker can observe the target.
    Required for the guidance laws to function when target acceleration is unknown.

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