Pith. sign in

REVIEW 4 major objections 6 minor 30 references

A QAOA-based planner maps each drone route segment to a qubit and finds collision-free paths with circuit depth linear in segment count.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

The proposed QUAV framework maps a segmented drone path to a linear-cost QAOA, but the mapping lacks a defined way to turn the quantum result into a collision-free trajectory.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection The paper is readable and includes a real hardware run, but the described algorithm cannot generate the plotted paths: straight-line segmentation, a linear cost Hamiltonian, and no decoding rule make the central empirical claim unsupported. the 4 major comments →

arxiv 2508.21361 v1 pith:2AA3XT2J submitted 2025-08-29 quant-ph

QUAV: Quantum-Assisted Path Planning and Optimization for UAV Navigation with Obstacle Avoidance

Nouhaila Innan , Muhammad Kashif , Alberto Marchisio , Yung-Sze Gan , Frederic Barbaresco , Muhammad Shafique This is my paper
classification quant-ph
keywords quantum approximate optimization algorithmQAOAUAV path planningobstacle avoidancetrajectory optimizationquantum optimizationnear-term quantum hardwarepath planning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 proposes QUAV, a drone path planner that treats routing as a quantum optimization problem. It encodes each straight segment of a candidate route as a qubit and uses QAOA—a variational quantum algorithm—to search for low-cost combinations that avoid obstacles and stay near the direct line. The authors claim this is among the first uses of QAOA for drone trajectory planning, and they report that circuit depth grows linearly with the number of route segments, in contrast to the exponential worst case of some classical search methods. If the approach holds, near-term quantum hardware could take over part of the combinatorial planning load in urban drone navigation, complementing classical planners such as A* and RRT.

Core claim

The paper's central claim is that a QAOA circuit with one qubit per path segment can serve as the optimization engine of a drone path planner. The cost Hamiltonian adds a distance term and an obstacle-proximity penalty for every segment; the mixer lets the state explore different segment choices; after k alternating layers, measurement produces bitstrings that represent candidate trajectories. The authors test this on six start/end scenarios, comparing against A* and RRT, and report QUAV paths that are shorter than RRT's and close to A*'s, while keeping complexity O(S·|E|) under fixed shot and layer budgets. They also run the circuit on a real 20-qubit quantum processor and report convergenc

What carries the argument

The central object is the QAOA circuit with cost Hamiltonian HC = Σ C(ei) Zi and mixer Hamiltonian HB = Σ Xi. Each edge of a segmented route is assigned one qubit; C(ei) is the segment's Euclidean length plus an exponential obstacle-buffer penalty. Alternating the cost and mixer unitaries for k layers, with the angles γ and β tuned by a classical optimizer, produces a low-energy bitstring that the paper treats as the optimized path. The workhorse complexity claim is that, with k and the number of measurement shots fixed, the circuit's resource cost scales linearly with the number of edges, |E|.

Load-bearing premise

The load-bearing premise is that assigning one qubit to each straight-line piece of the route and adding up per-piece penalties really captures the path-planning problem, so that the bitstring output by the circuit can be decoded into one continuous collision-free trajectory.

What would settle it

Run the QUAV circuit under the paper's settings on the same simulator and real backend, record the measured samples, and try to reconstruct the plotted paths from those samples alone; if the high-probability bitstrings do not form connected start-to-end routes that respect the obstacle buffers, the central claim fails. A second check: remove the obstacle penalty from the cost Hamiltonian and see whether paths still avoid obstacles; if they do, obstacle avoidance is happening outside the quantum objective.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • QAOA-based planning would give a route optimizer whose quantum circuit depth scales linearly in the number of path segments, avoiding the exponential worst-case search of A*.
  • Obstacle avoidance can be folded directly into the objective as a buffer penalty, so no separate collision-checking loop is needed during the quantum optimization phase.
  • The planner can run end-to-end on current noisy quantum hardware and still converge, suggesting near-term viability for small problem instances.
  • Compared with RRT, the approach produces shorter paths on the tested scenarios; compared with A*, it trades a little path length for better asymptotic scaling.
  • Because each segment maps to one qubit, adding more segments only adds qubits and gates linearly, making the formulation a candidate for larger maps as quantum hardware grows.

Where Pith is reading between the lines

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

  • Because the cost Hamiltonian contains no term coupling one segment to another, the QAOA objective factorizes: the optimal bitstring minimizes each segment independently, and the connected routes shown in the figures likely arise from the classical enumeration and segmentation part of the pipeline rather than from quantum correlations. Reconstructing the plotted paths from raw measurement samples w
  • A direct test: add two-qubit ZZ penalties linking consecutive segments (or enforcing a single connected path constraint) and check whether path quality and connectivity improve; that would turn the current independent-segment encoding into a genuinely combinatorial QAOA planning problem.
  • The paper's complexity bound treats the number of classical optimization steps S as a fixed constant, but for larger maps S may need to grow; the practical scaling story stands or falls on how S depends on map size, which the paper does not address.
  • The same qubit-per-segment idea extends naturally to three dimensions and to time-indexed dynamic obstacles, where the linear-in-edges circuit scaling would be even more valuable.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes QUAV, a QAOA-based framework for UAV path planning with obstacle avoidance. The methodology comprises spatial preprocessing (GPS-to-UTM conversion and obstacle buffering), path finding on a grid, path segmentation into segments, assignment of a cost to each segment, and QAOA optimization over a Hamiltonian whose single-qubit terms are the segment costs. The authors report simulations and an execution on IBM's ibm_kyiv backend, compare path lengths to A* and RRT, and claim linear scaling in circuit depth with respect to the number of edges. The central claims are that QUAV is one of the first QAOA applications for drone trajectory optimization and that it generates feasible, efficient, collision-free trajectories.

Significance. If the method worked as described, it would provide a concrete QAOA formulation for a practical path-planning problem, with a real-hardware demonstration and a complexity analysis. The paper includes useful elements: a clearly stated Algorithm 1, benchmarking against A* and RRT, and an experiment on ibm_kyiv. However, the significance is undermined by a fundamental disconnect between the algorithm description and the results: the segmentation constructs a straight-line path, the cost Hamiltonian is a sum of single-qubit terms with no couplings, and no decoding rule is provided from the measured bitstring to the plotted trajectories. As written, the QAOA optimization cannot produce the obstacle-avoiding curves in Fig. 4, and the path-finding phase is not used. These issues affect the core claim of the paper rather than being presentation concerns.

major comments (4)
  1. [§IV-C, §IV-D, Algorithm 1 (lines 10-15)] The segmentation loop sets P_next = P_current + v_dir * Δs, where v_dir always points directly from P_current to P_end. Therefore every waypoint lies on the straight line between start and end. The cost Hamiltonian H_C = Σ_i C(e_i) Z_i is a sum of single-qubit terms with no coupling terms, so QAOA optimizes each segment independently. No decoding procedure from the measured bitstring to a continuous trajectory is defined anywhere in Sections IV-D through V-C. Consequently, the curved obstacle-avoiding paths shown in Fig. 4 cannot be produced by Algorithm 1 as stated. This missing link is load-bearing for the claim that QUAV generates feasible, efficient trajectories.
  2. [§IV-D, Algorithm 1 step 19] Because H_C is a linear combination of Z_i operators, the objective is separable: the optimal value of each qubit is determined solely by the sign of the corresponding C(e_i). With the hand-set coefficients (10^6 obstacle penalty, −10^3 start bias, and the buffer penalty), the measured bitstring is essentially predetermined by the cost assignment. The QAOA parameters γ and β cannot introduce coupling or enforce path continuity. Thus the statement that the optimizer 'balances path length and safety' (Sec. V-B) is not supported by the model. This is a circularity issue: the cost coefficients fully determine the outcome, so the experiments do not validate QAOA as a path planner.
  3. [§IV-B/§IV-C, Algorithm 1 steps 4-15] The path-finding phase constructs a grid, enumerates candidate paths, and computes their lengths and smoothness (steps 4-7). The path segmentation phase (steps 10-15) ignores these candidates entirely and produces a single straight-line path from P_start to P_end. The enumerated candidate paths therefore play no role in the subsequent optimization. This internal inconsistency contradicts the paper's description of 'efficient exploration of multiple paths' and makes the comparison with A* and RRT in Table II inappropriate: A* and RRT plan on the grid, while QUAV's path is a straight line plus unspecified post-processing.
  4. [§V, Table II and Fig. 4] The reported QUAV path distances cannot be reconciled with the straight-line segmentation of Sec. IV-C. If all waypoints are collinear, the path length is approximately the Euclidean distance between start and end; the extra lengths and curved shapes in Fig. 4 must come from an unstated procedure. Either the decoding/reconstruction algorithm must be provided and analyzed, or the figures and distance tables are not reproducible from the described method. This is a reproducibility defect in the main results.
minor comments (6)
  1. [Abstract and §II-B] The claim 'one of the first applications of QAOA for drone trajectory optimization' is inconsistent with Reference [20], which is described as a QAOA-based formulation of multi-UAV path planning. Please reconcile the novelty statement.
  2. [§IV-D] The notation 'HC = PN i=1 C(ei)Zi' is ambiguous; it should be H_C = Σ_i C(e_i) Z_i. Also, the described gate implementation ('sequence of CNOT gates...') is inconsistent with a purely single-qubit diagonal Hamiltonian; if interactions are intended, the Hamiltonian must be written explicitly.
  3. [§IV-D and Algorithm 1 step 19] The buffer penalty C(e_i) = C(e_i) + λ·exp(−d_i/d_s) is introduced after the final cost formula in Algorithm 1. It should be clarified whether this term is included in the simulations and hardware runs, and how λ and d_s are set.
  4. [§V-C] The explanation of zigzag patterns as due to 'the probabilistic nature of QAOA' is not supported by a linear cost model with no couplings. If the observed zigzags arise from post-processing, that should be stated; otherwise the explanation is misleading.
  5. [Fig. 4] The caption says the path is a dashed black line, but the figure does not clearly show this in the text version. The plotted path appears continuous, while the described method yields 20 discrete collinear segments. Please clarify the rendering and the relationship between qubits/segments and the drawn curve.
  6. [§IV-E] The phrase 'linear scaling in circuit depth' is used imprecisely. With a single-qubit cost Hamiltonian, each QAOA layer has constant depth if single-qubit gates are applied in parallel; the stated O(S·|E|) complexity is for gate count, not circuit depth. The text should distinguish gate complexity from circuit depth.

Circularity Check

1 steps flagged

QAOA 'optimization' reduces to sign-thresholding the hand-assigned per-edge costs because the cost Hamiltonian has no coupling terms; the claimed obstacle-avoiding trajectories are not derived from the stated method.

specific steps
  1. self definitional [Sec. IV-D (Quantum-Assisted Optimization), H_C equation; supported by Sec. IV-C path segmentation]
    "The cost Hamiltonian is designed to encode the optimization problem, incorporating penalties for inefficient paths and obstacle proximity: HC = Σ_{i=1}^{N} C(e_i) Zi, where C(e_i) represents the cost associated with path segment ei, and Zi is the Pauli-Z operator acting on qubit i. ... the resulting bitstrings represent candidate paths."

    Because HC is a sum of single-qubit Z terms with no ZZ couplings or path-continuity constraints, minimizing its expectation separates into N independent decisions: each qubit's optimal state is fixed solely by the sign of the input scalar C(e_i). Thus the 'quantum-optimized path' is, by construction, exactly the bitstring threshold of the hand-assigned costs (start bias -10^3, obstacle penalty 10^6, buffer/length terms). No new geometric or combinatorial information can emerge from QAOA; the claimed obstacle avoidance is merely a restatement of the penalty coefficients already put into C(e_i). Moreover, Sec. IV-C defines every Pnext on the straight line from Pstart to Pend, so any subset of kept segments is also collinear; the curved paths plotted in Fig. 4 cannot be generated by the descr

full rationale

The paper's central derivation chain is not self-citation-based; it compares against A* and RRT and presents its own experiments. However, the core 'optimization' step is circular in the technical sense: the QAOA cost Hamiltonian H_C = Σ C(e_i) Z_i is diagonal and fully separable, so the optimum bitstring is a per-qubit sign decision on the hand-coded C(e_i) values. The output path is therefore equivalent to the input cost coefficients by construction, not an independent prediction of a feasible trajectory. The path-segmentation step further restricts all candidate waypoints to the straight line from start to end, making the curved obstacle-avoiding paths in Fig. 4 impossible to obtain from the stated Algorithm 1 without an unspecified decoding/smoothing stage. These are load-bearing gaps: the abstract's claim that 'results demonstrate that QUAV generates feasible, efficient trajectories' and the claimed linear-scaling advantage rest on this reduction. The complexity bound is simply gate counting and is not circular. Overall score 6: one or more predictions reduce by construction, though the paper does contain independent experimental comparisons and does not rely on self-citation.

Axiom & Free-Parameter Ledger

6 free parameters · 4 axioms · 0 invented entities

The central claim depends on hand-chosen cost coefficients that fully determine the solution, and on an undefined bitstring-to-path reconstruction. No independent benchmarks or external predictions are provided.

free parameters (6)
  • Obstacle penalty = 1e6
    Assigned to segments intersecting an obstacle; hand-set and dominates the cost.
  • Start segment bias = -1000
    Negative cost to anchor start; hand-set.
  • Obstacle buffer = 5 meters
    Safety margin used in penalty; chosen per scenario.
  • Buffer penalty scale lambda = not reported
    Scales the exponential penalty exp(-di/ds); no value given in the paper.
  • Segment count N = 20
    Number of segments equals qubit count; chosen to match hardware resources.
  • Scaling factors (sx, sy) = not reported
    Safety buffer scaling around obstacles; no numeric values given.
axioms (4)
  • domain assumption The straight-line segmentation between start and end, divided into N segments, represents all relevant candidate paths.
    Used in Sec. IV-C; ignores the candidate paths enumerated in Sec. IV-B and restricts to a single straight corridor.
  • ad hoc to paper QAOA with a linear cost Hamiltonian and X mixer can solve the path-selection problem.
    The cost Hamiltonian HC = sum C(ei) Zi has no two-body terms, so QAOA separates into independent single-qubit rotations; no combinatorial optimization occurs.
  • domain assumption The measured bitstring can be interpreted as a continuous collision-free path.
    The paper never defines the reconstruction rule; this assumption is load-bearing for the obstacle-avoidance results.
  • domain assumption IBM ibm_kyiv noise can be treated as a mild perturbation of the optimization.
    Used in Sec. V-F; hardware results are interpreted as convergence despite noise, but no hardware trajectory is shown.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of QUAV: Quantum-Assisted Path Planning and Optimization for UAV Navigation with Obstacle Avoidance." pith.science (2026). https://pith.science/paper/2AA3XT2J

@misc{pith2026250821361,
  author       = {Pith},
  title        = {Pith review of: QUAV: Quantum-Assisted Path Planning and Optimization for UAV Navigation with Obstacle Avoidance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2AA3XT2J}},
  note         = {Machine review of arXiv:2508.21361}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The growing demand for drone navigation in urban and restricted airspaces requires real-time path planning that is both safe and scalable. Classical methods often struggle with the computational load of high-dimensional optimization under dynamic constraints like obstacle avoidance and no-fly zones. This work introduces QUAV, a quantum-assisted UAV path planning framework based on the Quantum Approximate Optimization Algorithm (QAOA), to the best of our knowledge, this is one of the first applications of QAOA for drone trajectory optimization. QUAV models pathfinding as a quantum optimization problem, allowing efficient exploration of multiple paths while incorporating obstacle constraints and geospatial accuracy through UTM coordinate transformation. A theoretical analysis shows that QUAV achieves linear scaling in circuit depth relative to the number of edges, under fixed optimization settings. Extensive simulations and a real-hardware implementation on IBM's ibm_kyiv backend validate its performance and robustness under noise. Despite hardware constraints, results demonstrate that QUAV generates feasible, efficient trajectories, highlighting the promise of quantum approaches for future drone navigation systems.

Figures

Figures reproduced from arXiv: 2508.21361 by Alberto Marchisio, Frederic Barbaresco, Muhammad Kashif, Muhammad Shafique, Nouhaila Innan, Yung-Sze Gan.

Figure 1
Figure 1. Figure 1: Overview of the proposed quantum-assisted path planning framework. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Quantum circuit representation of the QAOA. The circuit consists of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Cost function convergence during the optimization process using default [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Obstacle avoidance performance across six scenarios using QUAV. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Obstacle avoidance performance across six scenarios using RRT. The [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Obstacle avoidance performance across six scenarios using A*. The [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Cost function convergence during the optimization process using the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Qubit connectivity map of the IBM ibm_kyiv QPU. Each node represents a physical qubit, and edges show available couplings. VI. DISCUSSION QUAV demonstrates a balance between computational efficiency and path quality, adapting well to constrained environments. Its convergence behavior, characterized by initial fluctuations followed by stabilization, reflects QAOA’s probabilistic nature, enabling the flexibl… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

30 extracted references · 27 canonical work pages

  1. [1]

    A review on graph search algorithms for optimal energy efficient path planning for an unmanned air vehicle,

    S. K. Debnath et al., “A review on graph search algorithms for optimal energy efficient path planning for an unmanned air vehicle,” Indonesian Journal of Electrical Engineering and Computer Science , 2019

    work page 2019

  2. [2]

    A review on quantum approximate optimization algorithm and its variants,

    K. Blekos et al. , “A review on quantum approximate optimization algorithm and its variants,” Physics Reports, 2024

    work page 2024

  3. [3]

    Sampling-based robot motion planning: A review,

    M. Elbanhawi and M. Simic, “Sampling-based robot motion planning: A review,” Ieee access, 2014

    work page 2014

  4. [4]

    Motion planning for robotics: A review for sampling- based planners,

    L. Zhang et al., “Motion planning for robotics: A review for sampling- based planners,” Biomimetic Intelligence and Robotics , 2025

    work page 2025

  5. [5]

    An overview of nature-inspired, conventional, and hybrid methods of autonomous vehicle path planning,

    B. B. K. Ayawli et al., “An overview of nature-inspired, conventional, and hybrid methods of autonomous vehicle path planning,” Journal of Advanced Transportation, p. 8269698, 2018

    work page 2018

  6. [6]

    Evolutionary computation for unmanned aerial vehicle path planning: A survey,

    Y . Jianget al., “Evolutionary computation for unmanned aerial vehicle path planning: A survey,” Artificial Intelligence Review , 2024

    work page 2024

  7. [7]

    Recent progress, challenges and future prospects of applied deep reinforcement learning: A practical perspective in path planning,

    Y . Zhang et al. , “Recent progress, challenges and future prospects of applied deep reinforcement learning: A practical perspective in path planning,” Neurocomputing, 2024

    work page 2024

  8. [8]

    Path planning algorithms in the autonomous driving system: A comprehensive review,

    M. Reda, A. Onsy, A. Y . Haikal, and A. Ghanbari, “Path planning algorithms in the autonomous driving system: A comprehensive review,” Robotics and Autonomous Systems , 2024

    work page 2024

  9. [9]

    Uav path planning based on random obstacle training and linear soft update of drl in dense urban environment,

    Y . Zhuet al., “Uav path planning based on random obstacle training and linear soft update of drl in dense urban environment,” Energies, 2024

    work page 2024

  10. [10]

    Optimal path planning for drones based on swarm intelligence algorithm,

    R. A. o. Saeed, “Optimal path planning for drones based on swarm intelligence algorithm,” Neural Computing and Applications , 2022

    work page 2022

  11. [11]

    An obstacle avoidance approach for uav path planning,

    N. Bashir et al., “An obstacle avoidance approach for uav path planning,” Simulation modelling practice and theory , 2023

    work page 2023

  12. [12]

    3d jps path optimization algorithm and dynamic-obstacle avoidance design based on near-ground search drone,

    Y . Luoet al., “3d jps path optimization algorithm and dynamic-obstacle avoidance design based on near-ground search drone,” Applied Sciences, 2022

    work page 2022

  13. [13]

    Multidepot drone path planning with collision avoidance,

    K. Shen et al., “Multidepot drone path planning with collision avoidance,” IEEE Internet of Things Journal , 2022

    work page 2022

  14. [14]

    Dynamic step opposition-based learning sparrow search algorithm for uav path planning,

    Y . He and M. Wang, “Dynamic step opposition-based learning sparrow search algorithm for uav path planning,” Cluster Computing, 2025

    work page 2025

  15. [15]

    Uav path planning method in dynamic environments: an ant colony algorithm-based optimization study,

    J. Zhang et al., “Uav path planning method in dynamic environments: an ant colony algorithm-based optimization study,” in International Conference on Remote Sensing and Digital Earth (RSDE 2024) . SPIE, 2025

    work page 2024

  16. [16]

    Research on application of improved quantum optimization algorithm in path planning,

    Z. Du and H. Li, “Research on application of improved quantum optimization algorithm in path planning,” Applied Sciences, 2024

    work page 2024

  17. [17]

    Quantum algorithms using infeasible solution constraints for collision-avoidance route planning,

    Q. Li et al., “Quantum algorithms using infeasible solution constraints for collision-avoidance route planning,” IEEE Transactions on Consumer Electronics, 2024

    work page 2024

  18. [18]

    Enhancing automobile motion planning algorithms using quantum computing: A systematic review,

    M. Ramasamy et al., “Enhancing automobile motion planning algorithms using quantum computing: A systematic review,” in 2024 10th Interna- tional Conference on Communication and Signal Processing (ICCSP) . IEEE, 2024

    work page 2024

  19. [19]

    Quantum annealing solutions for drone route planning problems,

    R. Hua et al., “Quantum annealing solutions for drone route planning problems,” in 2024 IEEE International Conference on Quantum Com- puting and Engineering (QCE) . IEEE, 2024

    work page 2024

  20. [20]

    Quantum algorithms for drone mission planning,

    E. Davies and P. Kalidindi, “Quantum algorithms for drone mission planning,” in Quantum Technologies for Defence and Security . SPIE, 2024

    work page 2024

  21. [21]

    Pennylane: Automatic differentiation of hybrid quantum-classical computations,

    V . Bergholm et al. , “Pennylane: Automatic differentiation of hybrid quantum-classical computations,” arXiv preprint arXiv:1811.04968, 2018

    Pith/arXiv arXiv 2018

  22. [22]

    Quantum computing with qiskit,

    A. Javadi-Abhari et al., “Quantum computing with qiskit,” arXiv preprint arXiv:2405.08810, 2024

    Pith/arXiv arXiv 2024

  23. [23]

    Python interface to proj

    “Python interface to proj.” [Online]. Available: https://pypi.org/project/ pyproj/

    work page

  24. [24]

    A formal basis for the heuristic determination of minimum cost paths,

    P. E. Hart, N. J. Nilsson, and B. Raphael, “A formal basis for the heuristic determination of minimum cost paths,” IEEE transactions on Systems Science and Cybernetics , 1968

    work page 1968

  25. [25]

    Recent advances in rapidly-exploring random tree: A review,

    T. Xu, “Recent advances in rapidly-exploring random tree: A review,” Heliyon, 2024

    work page 2024

  26. [26]

    Rapidly-exploring random trees: A new tool for path planning,

    S. LaValle, “Rapidly-exploring random trees: A new tool for path planning,” Research Report 9811 , 1998

    1998

  27. [27]

    Artificial intelligence: a modern approach,

    R. Stuartl and N. Peter, “Artificial intelligence: a modern approach,” Artificial Intelligence: A Modern Approach , 2021

    work page 2021

  28. [28]

    Pathfinding in procedurally generated mazes,

    M. Kupre ˇsak, ˇC. Livada, T. Galba, and A. Baumgartner, “Pathfinding in procedurally generated mazes,” in 2024 International Conference on Smart Systems and Technologies (SST) . IEEE, 2024, pp. 145–151

    work page 2024

  29. [29]

    Sampling-based algorithms for optimal motion planning,

    S. Karaman and E. Frazzoli, “Sampling-based algorithms for optimal motion planning,” The international journal of robotics research , 2011

    work page 2011

  30. [30]

    A fast quantum mechanical algorithm for database search,

    L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 1996

    work page 1996

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.