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arxiv: 2507.13647 · v2 · submitted 2025-07-18 · 💻 cs.RO · cs.AI

Improved particle swarm optimization algorithm: multi-target trajectory optimization for swarm drones

Minze Li , Wei Zhao , Ran Chen , Mingqiang Wei This is my paper

Pith reviewed 2026-05-19 04:52 UTC · model grok-4.3

classification 💻 cs.RO cs.AI
keywords particle swarm optimizationUAV trajectory planningdrone swarmsB-spline curvesreal-time optimizationmulti-agent systemsgenetic algorithmobstacle avoidance
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The pith

PE-PSO adds persistent exploration and entropy-based tuning to PSO for real-time multi-UAV trajectory planning.

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

The paper introduces PE-PSO, a modified particle swarm optimization method for online trajectory planning of drone swarms in changing environments. It keeps the swarm diverse through persistent exploration instead of early convergence and adjusts parameters dynamically using an entropy measure. Paths are represented as B-spline curves to produce smooth trajectories with fewer variables. A distributed setup pairs this with genetic algorithm task allocation so multiple agents can generate coordinated plans in parallel. Simulations show gains over standard PSO in path quality, energy use, obstacle clearance, and run time.

Core claim

The authors establish that PE-PSO, by combining a persistent exploration mechanism to maintain swarm diversity with an entropy-driven parameter adjustment rule applied to B-spline parameterized trajectories inside a distributed multi-agent framework that uses genetic algorithms for task allocation, produces higher-quality, smoother, and more efficient real-time trajectories for UAV swarms than conventional PSO and other swarm planners.

What carries the argument

PE-PSO algorithm that uses a persistent exploration mechanism to preserve swarm diversity together with entropy-based parameter adjustment on B-spline curves, embedded in a distributed multi-agent architecture with genetic algorithm task allocation.

If this is right

  • Real-time performance becomes feasible through parallel computation across agents.
  • Energy efficiency improves because trajectories are optimized for lower consumption.
  • Obstacle avoidance strengthens in dynamic settings due to faster adaptation.
  • Computation time drops, allowing more frequent replanning during flight.
  • Scalable coordination emerges among multiple UAVs without centralized bottlenecks.

Where Pith is reading between the lines

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

  • The same structure could extend to ground or water vehicles that face similar real-time constraints.
  • Sensor noise and model mismatch in hardware would likely require targeted robustness checks beyond the simulations shown.
  • Decentralized control might reduce single-point failures in large swarms compared with fully centralized planners.

Load-bearing premise

The simulation environments and performance metrics accurately predict how the algorithm behaves on physical UAVs in real dynamic conditions without major retuning or hardware adjustments.

What would settle it

Running the planner on physical UAVs in a test area containing moving obstacles and verifying that measured energy use, collision avoidance rates, and replanning times match or exceed the reported simulation results.

Figures

Figures reproduced from arXiv: 2507.13647 by Mingqiang Wei, Minze Li, Ran Chen, Wei Zhao.

Figure 1
Figure 1. Figure 1: Schematic of Multi-UAV Trajectory Optimization Framework Integrating Task Allocation and PE-PSO. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Multi-UAV Trajectory Planning Results: 3D and 2D Representations of PE-PSO Optimized Paths. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of Trajectory between PE-PSO and Other Algorithms. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Feasibility verification of PE-PSO in XTDrone. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of Convergence between PE-PSO and [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of Convergence between PE-PSO and [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of convergence between PE-PSO and [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

Real-time trajectory planning for unmanned aerial vehicles (UAVs) in dynamic environments remains a key challenge due to high computational demands and the need for fast, adaptive responses. Traditional Particle Swarm Optimization (PSO) methods, while effective for offline planning, often struggle with premature convergence and latency in real-time scenarios. To overcome these limitations, we propose PE-PSO, an enhanced PSO-based online trajectory planner. The method introduces a persistent exploration mechanism to preserve swarm diversity and an entropy-based parameter adjustment strategy to dynamically adapt optimization behavior. UAV trajectories are modeled using B-spline curves, which ensure path smoothness while reducing optimization complexity. To extend this capability to UAV swarms, we develop a multi-agent framework that combines genetic algorithm (GA)-based task allocation with distributed PE-PSO, supporting scalable and coordinated trajectory generation. The distributed architecture allows for parallel computation and decentralized control, enabling effective cooperation among agents while maintaining real-time performance. Comprehensive simulations demonstrate that the proposed framework outperforms conventional PSO and other swarm-based planners across several metrics, including trajectory quality, energy efficiency, obstacle avoidance, and computation time. These results confirm the effectiveness and applicability of PE-PSO in real-time multi-UAV operations under complex environmental conditions.

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

3 major / 2 minor

Summary. The manuscript proposes PE-PSO, an enhanced PSO algorithm for real-time multi-target trajectory optimization in swarm drones. It adds a persistent exploration mechanism to preserve diversity, an entropy-based parameter adjustment strategy, B-spline curve modeling for smooth trajectories, GA-based task allocation, and a distributed multi-agent execution framework. Comprehensive simulations are reported to show outperformance versus conventional PSO and other swarm planners on trajectory quality, energy efficiency, obstacle avoidance, and computation time, supporting claims of effectiveness for real-time multi-UAV operations in complex environments.

Significance. If the simulation-based outperformance claims hold under scrutiny, the work could advance online planning for UAV swarms by mitigating premature convergence and latency issues in standard PSO. The distributed architecture and B-spline representation are constructive elements for scalability and smoothness. The approach offers a plausible path toward adaptive, coordinated drone operations, though its impact hinges on stronger empirical grounding beyond simulations.

major comments (3)
  1. [Abstract] Abstract: the central claim that 'comprehensive simulations demonstrate that the proposed framework outperforms conventional PSO and other swarm-based planners across several metrics' is asserted without any quantitative values, statistical tests, baseline algorithm names, or ablation results. This directly weakens support for the outperformance conclusion that the paper treats as load-bearing.
  2. [Conclusions] Simulation results and conclusions: the assertion that results 'confirm the effectiveness and applicability of PE-PSO in real-time multi-UAV operations under complex environmental conditions' rests on the unexamined assumption that simulation metrics (trajectory quality, energy, avoidance, time) predict physical UAV behavior. No modeling of sensor noise, actuator lag, communication delays, or sim-to-real degradation analysis is provided, making the applicability claim unsupported.
  3. [Proposed Method] Method description (persistent exploration and entropy adjustment): the two free parameters (exploration persistence coefficient and entropy adjustment rate) are introduced as independent enhancements, yet no derivation shows how claimed performance gains reduce directly to these quantities rather than to other implementation choices or tuning.
minor comments (2)
  1. [Figures and Tables] Figure captions and tables should explicitly list all compared algorithms, environment parameters, and run counts to allow reproducibility assessment.
  2. [Notation] Notation for B-spline control points and the distributed execution protocol could be clarified with a short pseudocode block or explicit equation references.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the work.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'comprehensive simulations demonstrate that the proposed framework outperforms conventional PSO and other swarm-based planners across several metrics' is asserted without any quantitative values, statistical tests, baseline algorithm names, or ablation results. This directly weakens support for the outperformance conclusion that the paper treats as load-bearing.

    Authors: We agree that the abstract would be strengthened by greater specificity. In the revised manuscript, we will incorporate key quantitative results from the simulations, including average percentage improvements in trajectory quality, energy consumption, and computation time relative to standard PSO, along with the names of the other swarm-based planners used as baselines. We will also note that results were averaged over multiple independent runs with statistical significance assessed via paired t-tests. revision: yes

  2. Referee: [Conclusions] Simulation results and conclusions: the assertion that results 'confirm the effectiveness and applicability of PE-PSO in real-time multi-UAV operations under complex environmental conditions' rests on the unexamined assumption that simulation metrics (trajectory quality, energy, avoidance, time) predict physical UAV behavior. No modeling of sensor noise, actuator lag, communication delays, or sim-to-real degradation analysis is provided, making the applicability claim unsupported.

    Authors: This is a fair criticism. The current work relies on simulation results, and we do not claim direct equivalence to physical UAV performance. In the revision, we will moderate the language in the conclusions and abstract to emphasize simulation-based performance while adding a brief discussion of potential sim-to-real gaps, such as the effects of sensor noise and communication delays. A full degradation analysis would require new hardware experiments that are outside the scope of this study. revision: partial

  3. Referee: [Proposed Method] Method description (persistent exploration and entropy adjustment): the two free parameters (exploration persistence coefficient and entropy adjustment rate) are introduced as independent enhancements, yet no derivation shows how claimed performance gains reduce directly to these quantities rather than to other implementation choices or tuning.

    Authors: We acknowledge the need for clearer justification of these parameters. They were selected through systematic empirical tuning guided by prior adaptive PSO studies to balance exploration and convergence. In the revised method section, we will add an explanation of their roles together with a parameter sensitivity study demonstrating their specific contributions to swarm diversity and optimization stability, separate from other implementation details. revision: yes

standing simulated objections not resolved
  • Full sim-to-real degradation analysis including explicit modeling of sensor noise, actuator lag, and communication delays, as this would require physical UAV experiments not performed in the present simulation-focused study.

Circularity Check

0 steps flagged

No circularity: enhancements and simulation metrics are independent additions

full rationale

The paper defines PE-PSO via explicit new mechanisms (persistent exploration to preserve diversity, entropy-based adaptation, B-spline trajectory modeling, GA task allocation, distributed execution) and evaluates them through external simulation metrics (trajectory quality, energy, obstacle avoidance, computation time) against conventional PSO baselines. No equation reduces a claimed gain to a quantity defined by the paper's own fitted parameters or prior self-citations; the performance claims rest on comparative simulation runs rather than tautological re-derivations. The derivation chain is therefore self-contained against the stated benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The approach depends on standard optimization assumptions and a small number of tunable algorithmic parameters whose values are not reported.

free parameters (2)
  • exploration persistence coefficient
    Controls how long diversity is maintained; value chosen to balance search behavior
  • entropy adjustment rate
    Governs dynamic parameter changes; specific thresholds or scaling factors required for the strategy
axioms (2)
  • domain assumption B-spline curves maintain smoothness while lowering optimization dimensionality
    Invoked when modeling UAV trajectories to reduce complexity
  • domain assumption Distributed GA-plus-PE-PSO architecture scales with swarm size while preserving real-time performance
    Basis for the multi-agent coordination claim
invented entities (1)
  • PE-PSO variant no independent evidence
    purpose: Real-time trajectory planner with built-in diversity preservation
    New algorithmic construct introduced to address premature convergence

pith-pipeline@v0.9.0 · 5745 in / 1281 out tokens · 63611 ms · 2026-05-19T04:52:33.847665+00:00 · methodology

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Reference graph

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