Path Planning for a UAV Swarm Using Formation Teaching-Learning-Based Optimization

Manh Duong Phung; Van Truong Hoang

REVIEW 3 major objections 4 minor 18 references

Path Planning for a UAV Swarm Using Formation Teaching-Learning-Based Optimization

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper's central claim is that FTLBO, an enhanced TLBO with mutation, elite selection, and multi-subject learning, produces collision-free triangular paths for a three-UAV survey and beats GA, TLBO, and θ-PSO in cost.

desk verdict A plausible but incremental extension of the authors' own single-UAV TLBO planner to a three-UAV triangle formation, undermined by a safety cost that checks obstacles only on the centroid path, not on the individual UAV offsets. read the letter →

arxiv 2501.09357 v1 pith:A4VLG2BP submitted 2025-01-16 cs.RO cs.SYeess.SY

Van Truong Hoang , Manh Duong Phung This is my paper · ORCID

classification cs.ROcs.SYeess.SY

keywords UAVswarmformationpathplanningteaching-learning-basedoptimizationFTLBOcollisionavoidancemulti-objectivefitnessfunctionorchardmonitoring3D

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that a modified Teaching-Learning-Based Optimization (FTLBO) can solve the path-planning problem for a small UAV swarm that must keep a fixed triangular formation while surveying an area. It treats formation flight as an optimization problem: minimize a fitness function that rewards short paths, low collision risk with cylindrical obstacles, and staying within altitude limits. The authors add mutation, elite selection, and multi-subject learning to TLBO to avoid local optima. In a satellite-based orchard scenario with three UAVs, FTLBO converges to a cost of 94.70, lower than θ-PSO (100.63), TLBO (108.31), and GA (129.04), and the generated paths keep the desired triangle at every waypoint. A reader would care because the approach converts formation geometry into a single centroid path, making planning tractable, and claims feasibility on real UAVs.

What carries the argument

The carrier of the argument is the FTLBO algorithm: the standard two-phase TLBO (teaching update S_new_i = S_old_i + w0(T − λA), and peer-learning update) augmented with (i) a mutation step using a chaotic logistic sequence z = 2×X_n − 1 with probability μ = 1 − ξ/ξ_max, (ii) an elite strategy that replaces the worst student when the mutated solution improves fitness, and (iii) a multi-subject learning update S_new_{i,j} = S_old_{i,j} + w_{i,j}|S_{i,j} − S_{k,j}|. The formation-to-path reduction is also central: UAV n's position is P_n = P_F + ΔP_n, with constraints d_n = r_F and equal neighbor distances, so planning the centroid path P_F automatically defines all individual paths.

What would settle it

Recompute the obstacle-violation cost for each individual UAV path, not just the centroid path, in the same scene: if any waypoint's offset position lies within distance R_k of a cylinder center, or any segment between offset waypoints intersects a cylinder, the safety claim fails. A direct check is to plot the three offset paths from Figure 5 against the obstacle cylinders of Figure 3 and measure the minimum distances.

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Extended reading notes

Core claim

The central claim is that FTLBO generates valid, collision-free paths for three UAVs flying in a triangle, and that in the reported benchmark it converges to the lowest fitness value among GA, TLBO, and θ-PSO (94.70 after 107 iterations versus 100.63 for θ-PSO after 96). The method works by planning one path for the formation's centroid and deriving each UAV's route from fixed offsets ΔP1, ΔP2, ΔP3, so formation maintenance reduces to tracking the centroid. The fitness function sums path length, obstacle-violation cost (based on distance from path segments to cylinder centers), and altitude/task costs, weighted by coefficients α, β, and γ. The result is tested both in simulation and by uploading planned paths to three 3DR Solo quadcopters via Mission Planner; the authors report that the planned paths are smooth enough for autonomous flight and avoid obstacles.

Load-bearing premise

The paper assumes that keeping the formation's centroid path away from obstacle cylinders is enough to keep all three UAVs safe, even though the UAVs are offset by up to 3 meters from that centroid.

Editorial extensions

If this is right

In this scenario FTLBO reaches fitness 94.70 in 107 iterations, lower than θ-PSO (100.63), TLBO (108.31), and GA (129.04), so the enhancements do not hurt convergence in this benchmark.
The centroid-path formulation means the same planner can adapt to other formations by changing the ΔP_n offsets, with no change to the core algorithm.
Real-aircraft validation suggests the planned paths are smooth enough to be followed autonomously, indicating practical deployability for surveying tasks.
The fitness function can be reused with different obstacle models by replacing the cylinder-distance cost with other collision metrics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The safety guarantee is only as strong as the assumption that centroid clearance implies offset-path clearance; with offsets up to 3 m, a rigorous planner should check per-UAV clearance or inflate obstacle radii.
The comparison is a single test scenario, so the claimed advantage over θ-PSO likely depends on scene difficulty, obstacle density, and waypoint count; testing on randomized maps would tell.
The multi-subject and chaotic-mutation mechanisms are generic enough to be applied to other metaheuristics such as PSO or GA, so the observed gain may come from the enhancements more than from TLBO itself.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know this is a modest, honest paper, not a breakthrough. The new piece is small but legitimate: the authors take their earlier single-UAV TLBO path planner, add mutation, elite selection, and multi-subject learning, and plan a formation by optimizing a centroid path, then deriving each UAV's path as a fixed offset from that centroid. The formation model (Eq. 4) is sound by construction: if the centroid path is feasible under the fitness function, the triangle shape is preserved by definition. For a reader in the metaheuristic path-planning niche, that is a workable recipe.

What it does well: the problem formulation is clean, the pseudo-code is detailed enough to reimplement the method, and the authors actually flew three 3DR Solos along the generated paths. Most papers in this genre stop at simulation. The convergence comparison against GA, TLBO, and θ-PSO on a single scenario shows FTLBO at the lowest cost, which is interesting if not statistically robust.

The soft spots are real, and one is load-bearing. The safety cost in Eqs. (8)-(9) computes distance from each obstacle to the centroid path segment only. The individual UAVs are offset by up to 3 m horizontally (ΔP2 = [3,0,-1], ΔP3 = [-3,0,-1]), so a centroid path that clears a cylinder does not imply the offset paths do. The paper's claim of "safe operation" for all UAVs is therefore not supported by the defined fitness. This is not a subtle math error; it's a mismatch between what the cost measures and what the text claims. Second, the fitness weights α, β, γ in Eq. (5) are never reported, which makes the exact objective indeterminate. Third, the real-UAV validation is qualitative: no measured clearance, no deviation, just "the paths navigate the UAVs to avoid obstacles." Those quantitative gaps would all be fixable in revision.

Who is this for? Anyone working on TLBO variants or formation path planning with metaheuristics who wants another data point. It is not going to change how you plan swarms. But it is not a waste of time either: the formulation is clear, the method is plausible, and the single-scenario comparison, while weak, is at least a fair attempt against three baselines.

My recommendation: this deserves a serious referee, not a desk reject. The safety-cost flaw is exactly what peer review should catch, and the paper is short enough that a careful reviewer can verify the derivation. Send it out, but expect the authors to need to add obstacle checks on the actual UAV paths and report their weights before I would trust the safety claim.

Referee Report

3 major / 4 minor

Summary. The paper addresses 3D path planning for a three-UAV group that must maintain a triangular formation while performing an inspection task. The formation is modeled by fixing each UAV's position as the group centroid plus a constant offset (Eq. (4)), and the planning problem is cast as the minimization of a weighted fitness function (Eq. (5)) comprising path length (Eq. (7)), obstacle-violation cost on the centroid path (Eqs. (8)-(9)), and an altitude/task cost (Eq. (10)). The authors propose an enhanced teaching-learning-based optimizer (FTLBO) with mutation, elite selection, and multi-subject learning, compare its converged fitness against GA, TLBO, and θ-PSO, and report a qualitative real-UAV validation. The central claim is that FTLBO generates safe, collision-free formation paths at lower cost than the comparison algorithms.

Significance. If fully established, the paper would provide an incremental but practical formation-path-planning baseline: the kinematic formation construction in Eq. (4) is sound, the optimization formulation is transparent, and the inclusion of a real-UAV flight test is a strength that goes beyond pure simulation. The paper also explicitly compares against three metaheuristic baselines and reports convergence statistics. However, the central safety claim is not supported by the obstacle-cost formulation because safety is evaluated only on the centroid path, not on the actual offset UAV paths, and several parameter values needed for reproducibility are omitted. Thus the contribution is a reasonable engineering study whose main claim requires additional verification before it can be accepted.

major comments (3)

[Section 2.2, Eqs. (8)-(9)] The obstacle-violation cost d_{j,k} is computed only for the centroid path q. In Section 5.1 the individual UAV positions are P_n = P_F + ΔP_n, with ΔP_2 = [3,0,-1] m and ΔP_3 = [-3,0,-1] m, so a centroid segment that clears a cylinder does not imply that the offset UAV paths are collision-free. Since Eq. (8) assigns infinite cost only when the centroid path itself penetrates a cylinder and contains no term depending on ΔP_n, the fitness values reported in Table 1 and the convergence comparison in Figure 8 do not establish safe operation for all three UAVs. The real-UAV validation in Section 5.3 is qualitative and reports no measured clearance distances, so it does not close this gap. The authors should either compute violation costs for each individual UAV path or equivalently inflate obstacle radii by the maximum formation offset, then rerun the optimization and the comparisons.
[Section 2.2, Eq. (5)] The weight coefficients α, β, and γ in the fitness function are never assigned numerical values anywhere in the text, in the experimental setup of Section 5.1, or in Table 1. Because the converged fitness value depends directly on these weights, the reported comparison between FTLBO, GA, TLBO, and θ-PSO is not reproducible, and no sensitivity analysis is provided. The authors should state the exact weight values used in the experiments and ideally report how the ranking of algorithms changes over a modest range of weightings.
[Section 2.2, Eq. (10)] The altitude cost uses h_i^j, the altitude of UAV i at viewpoint j, but the optimization variable q is the centroid path. It is not explained how each UAV's altitude is derived from q and the fixed offsets ΔP_n. Without an explicit link, the task-cost term is either incompletely specified or depends on additional degrees of freedom that are not part of the optimized path. Please define h_i^j operationally in terms of q and ΔP_n, or revise the fitness formulation so that all terms are functions of the same decision variables.

minor comments (4)

[Section 2.1, Eqs. (2)-(4)] The statement that the triangular formation is maintained follows directly from the construction: since ΔP_n are constant, Eq. (4) gives the same offsets at every waypoint by definition. This is not a limitation, but the plots in Figures 5-7 should be described as construction checks rather than independent evidence of formation-keeping behavior.
[Table 1] The 'Max cost' column is identical (248.28) for all four algorithms, which is suspicious and likely a formatting or reporting error. Please clarify what this column represents and why the maximum values coincide exactly.
[Figure 2 and Eq. (13)] The pseudo-code contains several unclear or corrupted expressions, notably 'while rand < 1˘ξ/ξmax' on line 15 and the comment '/* using (12) */' in the teaching-phase mutation loop, where Eq. (13) appears to be the intended update. The update rule around Eq. (13) and the elite replacement in Eq. (17) should be stated unambiguously in pseudo-code.
[Equation (7)] The typeset formula for the path-length cost is garbled; the norm of the segment vector is missing in the rendered text. The equation should be rewritten in a standard vector form so that the cost definition is unambiguous.

Circularity Check

1 steps flagged · score 1.0 of 10

Formation-maintenance claim is definitional, but the optimization comparison is self-contained.

self definitional [Section 2.1 (Eq. 4), Section 5.1, Section 5.2 (Figure 5)]
"By substituting (4) into (2) and (3) and solving the resulting equations, we obtain the value of ∆Pn. Using this, the position of each UA V in the formation can be determined for each corresponding value of PF. ... ∆P1 = [0, 0, 2] m, ∆P2 = [3, 0,−1] m, and ∆P3 = [−3, 0,−1] m. ... Figure 5 shows that the triangular shape of the UA Vs is maintained at every waypoint."

Individual UAV paths are constructed as P_n = P_F + ∆P_n with fixed offsets (Eq. 4 and Section 5.1). The triangular formation is therefore guaranteed by construction for any centroid path; reporting it as an observed outcome in Section 5.2 is a definitional consequence, not an independent prediction. This is a benign self-definitional property of the problem formulation rather than a hidden reuse of the optimization result, and it does not bear on the convergence comparison.

full rationale

The paper's central quantitative claim is that FTLBO converges to the lowest fitness value among GA, TLBO, and θ-PSO (Table 1, Figure 8). That comparison is self-contained: all algorithms minimize the same defined fitness function under the same experimental setup, and the result is not derived from the paper's own prior conclusions. The enhancements to TLBO—mutation, elite selection, and multi-subject learning—are described with explicit equations and cite independent sources [15,16], not merely the authors' own work. Self-citations [13,14] are used only to state that TLBO was previously applied to single-UAV path planning; no load-bearing theorem or fitted value is imported from them. The formation-maintenance statement is a definitional consequence of Eq. (4) and is flagged as a self-definitional step, but it is a property of the path parameterization rather than a circular derivation of the objective. The safety gap identified by the skeptic (obstacle cost evaluated only on the centroid path while individual UAVs are offset by up to 3 m) is a correctness risk, not a circularity: the fitness function simply may not encode the actual safety condition. Overall, the paper does not exhibit a load-bearing circular argument, so the circularity score is low.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The method reuses standard optimizer constructs and a kinematic formation model. The main unstated inputs are the fitness weights, the formation offsets, and the obstacle model, all of which are free parameters or domain assumptions.

free parameters (3)

Fitness weight coefficients α, β, γ = not reported
Used to combine path length, safety, and task costs in Eq. (5); the balance among objectives strongly affects the resulting path, but no values or sensitivity analysis are given.
Initial formation offsets ΔP1, ΔP2, ΔP3 = [0,0,2], [3,0,-1], [-3,0,-1] m
Hand-chosen offsets define the triangular formation geometry and indirectly the individual UAV paths; no derivation or optimization is provided for them.
TLBO hyperparameters (class size N, waypoint count, iterations L) = N=100, 10 waypoints, L=150
Chosen for the experiment without a sensitivity study; they influence solution quality and runtime.

assumptions (4)

domain assumption Obstacles can be accurately represented by upright cylinders with known center and radius (Eq. (8)).
The satellite-image based modeling in Section 4 treats trees and buildings as cylinders; errors in radius or position would invalidate the collision-cost computation.
domain assumption The minimum of the weighted sum of path length, obstacle cost, and altitude cost is a good proxy for an optimal and safe flight path.
The fitness function in Eq. (5) is the only optimization criterion; dynamic feasibility, wind, and real obstacle geometry are not included.
domain assumption TLBO and its enhancements converge to a useful suboptimal solution within L=150 iterations for this problem instance.
Convergence is asserted from Figure 8 for one run; no proof or multi-run statistics are provided.
domain assumption Each UAV can track the planned waypoint path without deviating into obstacles.
The planner is kinematic; there is no dynamic model or controller analysis, only a qualitative statement in Section 5.3 that paths are smooth enough.

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Cite this review

Pith. "Pith review of Path Planning for a UAV Swarm Using Formation Teaching-Learning-Based Optimization." pith.science (2026). https://pith.science/paper/A4VLG2BP

@misc{pith2026250109357,
  author       = {Pith},
  title        = {Pith review of: Path Planning for a UAV Swarm Using Formation Teaching-Learning-Based Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A4VLG2BP}},
  note         = {Machine review of arXiv:2501.09357}
}

read the original abstract

This work addresses the path planning problem for a group of unmanned aerial vehicles (UAVs) to maintain a desired formation during operation. Our approach formulates the problem as an optimization task by defining a set of fitness functions that not only ensure the formation but also include constraints for optimal and safe UAV operation. To optimize the fitness function and obtain a suboptimal path, we employ the teaching-learning-based optimization algorithm and then further enhance it with mechanisms such as mutation, elite strategy, and multi-subject combination. A number of simulations and experiments have been conducted to evaluate the proposed method. The results demonstrate that the algorithm successfully generates valid paths for the UAVs to fly in a triangular formation for an inspection task.

Figures

Figures reproduced from arXiv: 2501.09357 by the authors.

**Figure 1.** Inertial and formation frames in UAV formation paths for the UAVs to flight when conducting a surveying task. The structure of the paper is as follows: Section 2 introduces the formation model and the multi-objective path planning problem. Section 3 details the proposed algorithm. Section 4 discusses the implementation of the path planning algorithm for the UAV formation and individual UAVs. Simulation and experim… view at source ↗

**Figure 3.** Working area with the obstacles identified [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Generated path for the formation’s centroid the farm and its working conditions based on satellite images. The experimental area is a rectangular defined by two opposite vertices Γ1 = {12.2335526, 109.1144313}, Γ2 = {112.2331044, 109.1152252}. The maximum and minimum altitudes are set to hmax = 7 m and hmin = 2 m, respectively. With these settings, a number of obstacles are identified, each with a different radius… view at source ↗

Figures from the paper (4 more)

**Figure 2.** Figure 2: Pseudo code of the FTLBO for formation path planning. 5 Experiments A number of experiments have been conducted to evaluate the performance of the proposed algorithm with details as follows. 5.1 Experimental setup In the experiment, the task is to survey an area of in…

**Figure 5.** Figure 5: Generated paths for three UAVs [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 7.** Figure 7: Projected paths on vertical (y-z and x-z) planes [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

**Figure 8.** Figure 8: Convergence comparison [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Y . Yang, X. Xiong, Y . Yan, Uav formation trajectory planning algorithms: A review, Drones 7, 62 (2023)

work page 2023

[2] [2]

López, J

B. López, J. Muñoz, F. Quevedo, C.A. Monje, S. Garrido, L.E. Moreno, Path planning and collision risk management strategy for multi-uav systems in 3d environments, Sensors 21, 4414 (2021)

work page 2021

[3] [3]

D’Amato, M

E. D’Amato, M. Mattei, I. Notaro, Bi-level flight path planning of uav formations with collision avoid- ance, Journal of Intelligent & Robotic Systems 93, 193 (2019). https: //doi.org/10.1007/s10846-014- 0077-y

work page doi:10.1007/s10846-014- 2019

[4] [4]

Huang, W

J. Huang, W. Sun, A method of feasible trajectory planning for uav formation based on bi-directional fast search tree, Optik 221, 165213 (2020)

work page 2020

[5] [5]

Z. Pan, C. Zhang, Y . Xia, H. Xiong, X. Shao, An im- proved artificial potential field method for path plan- ning and formation control of the multi-uav systems, IEEE Transactions on Circuits and Systems II: Ex- press Briefs 69, 1129 (2021)

work page 2021

[6] [6]

Roberge, M

V . Roberge, M. Tarbouchi, G. Labonté, Fast ge- netic algorithm path planner for fixed-wing military uav using gpu, IEEE Transactions on Aerospace and Electronic Systems 54, 2105 (2018)

work page 2018

[7] [7]

H. Song, M. Jia, Y . Lian, Y . Fan, K. Liang, Uav path planning based on an improved ant colony algorithm, Journal of Electronic Research and Application6, 10 (2022)

work page 2022

[8] [8]

Hoang, M.D

V .T. Hoang, M.D. Phung, H.D. Tran, Q.P. Ha, Angle- Encoded Swarm Optimization for UA V Formation Path Planning, in Intelligent Robots and Systems (IROS), 2018 IEEE/RSJ International Conference on (IEEE, 2018), pp. 5239–5244

work page 2018