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REVIEW 3 major objections 5 minor 30 references

Simulation-based planning of Motion Sequences for Automated Procedure Optimization in Multi-Robot Assembly Cells

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read Splitting each assembly step into fixed core operations and flexible connecting moves, then coordinating only the collision-prone parts, cuts simulated multi-robot assembly duration by 10-20% relative to an earlier decentralized method.

desk verdict A genuinely useful decomposition-based planner for multi-robot assembly scheduling, but the headline 10-20% improvement over the prior baseline is not fully established because the baseline numbers are not re-run in the identical setup. read the letter →

arxiv 2507.23270 v3 pith:JRAPG5QB submitted 2025-07-31 cs.RO cs.SYeess.SY

classification cs.ROcs.SYeess.SY
keywords multi-robotassemblydurationoptimizationtaskandmotionplanningschedulingMonteCarloTreeSearchgradient-freeprobabilisticroadmapsreconfigurablemanufacturingcells
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

Multi-robot assembly cells are attractive because several robots can work in parallel, but the real bottleneck is generating the coordinated motion sequence that gets the job done fastest. This paper argues that the key to that problem is a clean split: each assembly step consists of a fixed 'core' manipulation (gripping, placing, fastening, with known duration) and a flexible 'traverse' move that carries the robot between cores. The paper proposes to schedule the fixed core operations optimally and then plan the flexible traverse motions only in the narrow time-and-space windows where robots would collide, leaving everywhere else on individually planned paths. In simulation experiments with two, three, and four robots assembling a seven-part box, the resulting collision-free procedures are roughly 10-20% faster than the earlier decentralized-motion baseline, with assembly duration dropping from 41.2s to the low-to-mid 30s. The practical interest is that reconfigurable cells could be re-planned automatically for each new product without giving up speed.

What carries the argument

The load-bearing object is the decomposition of every assembly step into a core operation (a fixed-duration, preplanned manipulation such as gripping or placing) and a traverse operation (a single motion action connecting the end of one core to the start of the next). On top of this, the method builds a schedule represented as a vector of core start times and uses motion hypotheses from individual time-optimal paths as a lower bound on traverse duration. When the relaxed schedule is fixed, a cross-sectional roadmap in the combined configuration space of all robots is built at each problem-area boundary: sample collision-free joint configurations at boundary times, connect them with edges that respect velocity and acceleration limits, find a guide path, then refine each edge with sampling-based planners such as probabilistic roadmaps and RRT-Connect. Failure counts from unsolvable roadmaps and guide paths are fed back into the schedulers as penalties, which closes the loop between scheduling and motion planning.

What would settle it

Run the proposed pipeline and the baseline method from [2] on the same cell description, with the same seven-component box task, the same two-, three-, and four-robot configurations, the same time discretization, and the same CPU and time budget, then compare the resulting procedure durations. If the new method is not consistently faster than the baseline under matched conditions, the central 10-20% reduction claim is refuted.

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Extended reading notes

Core claim

Treating every assembly step as an alternating chain of a fixed core operation and a connecting traverse operation turns procedure generation into two coupled subproblems: choose the start time of each core operation (scheduling), and plan collision-free traverse motions for the gaps (motion planning). The paper's central claim is that this decomposition, with the traverse motions coordinated only inside 'problem areas' where the individually planned paths collide, reaches assembly durations of roughly 33-37 seconds for the two- and three-robot configurations and a similar improvement for four robots, versus 41.2s and 41.6s reported for the previous method [2]. The speedup comes from allowing robots to move during each other's traverse windows in a coordinated way rather than independently with conservative separation. The claim is demonstrated in simulation across five runs per method, several schedulers (sampling heuristic, simulated annealing, particle swarm, evolutionary algorithm, and Monte Carlo Tree Search variants), and two-, three-, and four-robot cells; no single scheduler dominates, but at least one variant from each successful family beats the baseline.

Load-bearing premise

The 10-20% improvement claim stands or falls on whether the earlier method's published durations (41.2s and 41.6s) were measured under the same assembly task, robot models, tools, simulation stack, and computational budget as the new experiments.

Editorial extensions

If this is right

  • If the 10-20% speedup holds, reconfigurable assembly cells can be re-planned automatically for new products without sacrificing cycle time, because the same pipeline takes a precedence graph and robot assignment and outputs an optimized procedure.
  • The decomposition means only traverse operations need coordinated planning; core operations can be reused as preplanned building blocks, so adding a robot or swapping a tool only invalidates the affected portions of the procedure.
  • The failure-feedback mechanism turns motion-planning dead ends into quantitative penalties, so schedule optimizers can steer away from configurations that are fast in theory but unsolvable in practice.
  • The method applies to any assembly task whose core operations have known durations and time-dependent collision geometries, including tasks with more than four robots, though computation time scales nonlinearly with robot count.
  • The evaluation found no single scheduler uniformly superior, so in practice the fixed compute budget is better spent running several schedulers and keeping the best result.

Reading between the lines

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

  • Editorial inference: if the fixed core-operation assumption were relaxed, for example by allowing alternative approach poses or variable gripper timing, the optimization space would widen beyond traverse moves and could yield further gains than the reported 10-20%.
  • Editorial inference: the problem-area identification could be reused as a bottleneck diagnostic, letting a cell designer see which robot-pair overlaps force the slowest coordinated passes and reposition tools or stations accordingly.
  • Editorial inference: because the output is a timed geometric path that is not immediately executable on physical robots, the practical speedup depends on the downstream trajectory-execution layer, and a physical demonstration would be needed to confirm the simulated gain in production.
  • Editorial inference: the reported computation times, which rise nonlinearly with robot count, mean the method is suited to offline replanning per product change rather than online adaptation during a running cell.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper addresses the automated optimization of multi-robot assembly procedures in reconfigurable cells with a fixed structural configuration and fixed assignment of assembly steps to robots. The approach decomposes each assembly step into predetermined core operations and connecting traverse operations, then optimizes the schedule of core operations using a sampling heuristic, gradient-free optimizers (SA, PSO, EA), and MCTS variants. Traverse motions are planned by identifying collision-prone 'problem areas' in the schedule and solving them with cross-sectional roadmaps, guide paths, and centralized path planners, with motion-planning failures fed back into the scheduling objective. Experiments in PyBullet on two-, three-, and four-robot configurations of a seven-component box assembly task report assembly durations approximately 10-20% lower than the authors' earlier method [2].

Significance. If the quantitative claim holds, the paper makes a useful contribution to automated procedure optimization for multi-robot assembly cells. Its strengths include a detailed algorithmic description, a clean separation of scheduling and motion planning, an explicit feedback mechanism for motion-planning failures, and an honest presentation of limitations, including the absence of physical execution and the nonlinear scaling of computation time. However, the headline 10-20% improvement is not yet established: it is based on two scalar baseline values from a prior paper with no variance, no evidence of experiment comparability, no statistical tests, and a hard duration bound d_max=40s that lies below the quoted baseline durations. The significance of the contribution is therefore conditional on a corrected, more rigorous evaluation and on clear specification of which scheduling method defines 'the proposed approach.'

major comments (3)
  1. [Section IV-C] The central 10-20% reduction claim is compared against only two scalar values (41.2s and 41.6s) from [2], with no variance, no sample size, and no statement that the assembly task, robot models, tools, PyBullet setup, timing conventions, or computational budget were identical in the two experiments. Since [2] is the authors' own prior work and the paper does not re-run the baseline, the comparability of the results is not established. The new results are boxplots over five runs, and no statistical test or overlap measure is provided. This concern is load-bearing because the claimed improvement is the main quantitative contribution. Please re-run the baseline in the identical setup, or otherwise provide direct evidence of comparability, before the 10-20% claim can be accepted.
  2. [Section IV-B] The maximum assembly duration is set to d_max=40s, which lies below the quoted baseline durations of 41.2s (two/three robots) and 41.6s (four robots). Since every successful candidate schedule must satisfy d(theta) <= d_max, any feasible solution is constrained to be at least about 1.2-1.6s (about 3%) shorter than the baseline, independent of the algorithmic contribution. The observed 10-20% reduction is not implied by this bound, but the experimental protocol conflates the method's optimization ability with an externally imposed feasibility margin. Please either set d_max equal to the baseline, or use the same duration constraint for both methods and report how often each method finds a feasible schedule within it.
  3. [Section IV-A and IV-C] Several scheduling methods fail completely in the two- and three-robot experiments (MCTS and MCTS-G with light playouts, EA with random initialization), and only three methods are applied to the four-robot configuration. The paper does not define a selection rule for the result used in the headline comparison, so 'the proposed approach' is not a single well-specified system, and the reported improvement may depend on post-hoc selection of successful runs. Please specify the evaluation protocol (e.g., best-of-five per method, median, or a fixed default method) and report success rates and the distribution of motion-planning failures over all runs.
minor comments (5)
  1. [Figure 8] The sample counts above the boxplots are useful, but the text should clarify whether these counts include only solved guide-path subproblems or also roadmap-construction failures; otherwise the runtime distributions are hard to interpret.
  2. [Section III-C.4] The notation A_P and A_R is introduced in the text after the objective function is extended; define these quantities before the first occurrence in an equation for readability.
  3. [Section IV-B] The many free parameters (mu_1..mu_4, lambda_1..lambda_3, PSO and EA parameters, T_max, L0) are given without sensitivity analysis; a short paragraph on robustness, or a supplementary experiment varying one or two key parameters, would increase confidence in the method.
  4. [General] No code, data, or detailed experiment configuration is released, which makes it difficult to reproduce the reported baseline comparison; please provide at least an artifact appendix or a public repository.
  5. [Section V] The conclusion correctly lists the absence of physical execution and the nonlinear scaling of computation time as limitations; however, the abstract's phrase 'collision-free multi-robot assembly procedures' should be qualified as 'simulated' to avoid overstatement.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the planning pipeline is an optimization procedure, and the 10-20% improvement claim is an empirical comparison; the only circularity-adjacent issue is reliance on the authors' own prior baseline [2] without re-verifying comparability, which is a validity concern rather than a circular derivation.

full rationale

The method decomposes assembly steps into fixed-duration core operations and traverse operations, optimizes core-operation start times via sampling, gradient-free search, or MCTS, and then plans collision-free traverse motions with a decomposition-based roadmap method. Each quantity in the pipeline is either an input (precedence graph, core-operation durations, robot assignment), an optimized decision variable (start times), or an evaluated outcome (assembly duration, computation time). No predicted result is defined as a fitted parameter, and no equation reduces the claimed improvement to its own inputs. The central quantitative claim in Section IV-C compares against baseline durations from [2], the authors' prior work; the paper does not re-run that baseline in the identical setup nor provide uncertainty for the 41.2s/41.6s reference values, and the hard time cap d_max=40s lies below those references. These are legitimate experimental-comparability concerns (and a self-citation in the benchmark), but they do not make the derivation circular: the reported durations are measured outcomes of the new pipeline, not quantities derived from [2]. Section V honestly lists limitations (fixed core-operation motions, no uniformly superior scheduler, high computation times, non-executable geometric paths), and none of these indicate a definitional or statistical equivalence between inputs and outputs. Hence no circular step is present; the score reflects only the minor self-citation in the baseline comparison.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claim rests on a set of domain assumptions about core-operation fixedness, the availability of components, reachability, and the validity of standard probabilistic planners, plus a large set of hand-chosen hyperparameters that control the scheduling and motion-planning pipeline.

free parameters (8)
  • d_max: maximum assembly duration = 40 s
    Sets the scheduling horizon and the duration penalty threshold in objectives (6) and reward (7).
  • Time discretization for scheduling = 0.2 s
    Converts continuous start times into 200 discrete steps; controls schedule granularity.
  • Penalty weights mu_1, mu_2, mu_3, mu_4 in objective (6) = 30, 900, 10, 1
    Hand-chosen to balance collision count, duration overshoot, and motion-planning failure magnitudes; central to gradient-free optimization.
  • MCTS reward weights lambda_1, lambda_2, lambda_3 and exploration constant c = 0.01, 1, 0.1, sqrt(2)
    Shape the reward function (7) and the exploration-exploitation trade-off in MCTS variants.
  • Sampling heuristic probability distribution f_q(x)=1/(x+2)^2 = quadratic decline
    Biases sampled start times toward the beginning of feasible intervals; chosen by hand in Section IV-B.1.
  • PSO parameters w_p, c_soc, c_cog, N_p, v_min, v_max = 0.9, 2, 1, 15, -20, 20
    Standard PSO settings from [30], not tuned per task.
  • EA parameters = population 15, 5-point crossover, 7 best produce 14 descendants, Gaussian sigma=3, 20% mutation
    Chosen by hand with no ablation or sensitivity analysis.
  • Motion-planning limits L0, T_max, guide-path time limit = 10 samples, 30*n_r seconds, 15 minutes
    Limit computation time and directly affect which problem areas are solvable; failure magnitudes feed back into scheduling.
assumptions (6)
  • domain assumption Assembly steps can be partitioned into fixed-duration core operations and single-motion traverse operations.
    Section III-A introduces this decomposition, and it is foundational to the scheduling/motion-planning split; if core operation durations are not fixed, the scheduling formulation collapses.
  • domain assumption All required components and tools are available with known initial and goal locations; assigned robots can reach all relevant locations and no handovers are needed.
    Stated as assumptions 1-3 in Section III; these simplify the problem and are not guaranteed in general reconfigurable cells.
  • domain assumption Each robot has a collision-free escape configuration.
    Assumption 4 in Section III; needed for resetting schedules and for feasible boundary configurations in problem areas.
  • domain assumption Core operations have known durations and time-dependent collision geometries.
    Section V states the method's applicability is broad provided that core operations have known durations and time-dependent collision geometries; this is a precondition for the whole approach.
  • standard math PRM and RRT-Connect are valid subproblem solvers for the combined space-time X-space.
    Section III-C.3 relies on these planners; their probabilistic completeness is standard background, but time limits and sampling limits mean solutions are not guaranteed.
  • domain assumption The initial motion hypotheses provide a valid lower bound on traverse duration.
    Section III-B uses individual-robot paths with time-optimal parametrization as a lower bound for scheduling; this is reasonable if a coordinated plan cannot be faster than a single-robot path between the same endpoints, but the bound ignores inter-robot coupling effects.

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Cite this review

Pith. "Pith review of Simulation-based planning of Motion Sequences for Automated Procedure Optimization in Multi-Robot Assembly Cells." pith.science (2026). https://pith.science/paper/JRAPG5QB

@misc{pith2026250723270,
  author       = {Pith},
  title        = {Pith review of: Simulation-based planning of Motion Sequences for Automated Procedure Optimization in Multi-Robot Assembly Cells},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRAPG5QB}},
  note         = {Machine review of arXiv:2507.23270}
}
read the original abstract

Reconfigurable multi-robot cells offer a promising approach to meet fluctuating assembly demands. However, the recurrent planning of their configurations introduces new challenges, particularly in generating optimized, coordinated multi-robot motion sequences that minimize the assembly duration. This work presents a simulation-based method for generating such optimized sequences. The approach separates assembly steps into task-related core operations and connecting traverse operations. While core operations are constrained and predetermined, traverse operations offer substantial optimization potential. Scheduling the core operations is formulated as an optimization problem, requiring feasible traverse operations to be integrated using a decomposition-based motion planning strategy. Several solution techniques are explored, including a sampling heuristic, tree-based search and gradient-free optimization. For motion planning, a decomposition method is proposed that identifies specific areas in the schedule, which can be solved independently with modified centralized path planning algorithms. The proposed method generates efficient and collision-free multi-robot assembly procedures that outperform a baseline relying on decentralized, robot-individual motion planning. Its effectiveness is demonstrated through simulation experiments.

Figures

Figures reproduced from arXiv: 2507.23270 by the authors.

Figure 1
Figure 1. Overview of our approach. For an assembly task [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Identification of problem areas in a schedule based on collisions of traverse operations. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Exploration of the decision tree by MCTS-G. (a) The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: A cross-sectional roadmap with a guide path. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Structural configurations with two (a), three (b) and four (c) robots. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Optimized solutions after five experiments. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Optimized solutions in a structural configuration with [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Computation time for successful motion planning. [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

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Reference graph

Works this paper leans on

30 extracted references · 26 canonical work pages

  1. [2]

    Assembly procedure generation for reconfigurable robot cells considering operation concur- rency and geometrical constraints,

    M. Ungen, E. Huber, D. Kampert, and O. Riedel, “Assembly procedure generation for reconfigurable robot cells considering operation concur- rency and geometrical constraints,” in2024 IEEE 20th International Conference on Automation Science and Engineering (CASE), Bari, Italy, September 2024, pp. 981–987

  2. [1]

    H. A. ElMaraghy and H.-P. Wiendahl,Changeable and Reconfigurable Manufacturing Systems, H. A. ElMaraghy, Ed. Springer London, 2009

  3. [3]

    Bandit based monte-carlo planning,

    L. Kocsis and C. Szepesv ´ari, “Bandit based monte-carlo planning,” inMachine Learning: ECML 2006, vol. 4212. Berlin/Heidelberg, Germany: Springer Berlin Heidelberg, September 2006, pp. 282–293

  4. [4]

    Toward efficient trajectory planning: The path-velocity decomposition,

    K. Kant and S. W. Zucker, “Toward efficient trajectory planning: The path-velocity decomposition,”The International Journal of Robotics Research, vol. 5, no. 3, pp. 72–89, September 1986

  5. [5]

    A new approach to time-optimal path parameterization based on reachability analysis,

    H. Pham and Q.-C. Pham, “A new approach to time-optimal path parameterization based on reachability analysis,”IEEE Transactions on Robotics, vol. 34, no. 3, pp. 645–659, 2018

  6. [6]

    Time-based RRT algorithm for rendezvous planning of two dynamic systems,

    A. Sintov and A. Shapiro, “Time-based RRT algorithm for rendezvous planning of two dynamic systems,” in2014 IEEE International Con- ference on Robotics and Automation (ICRA), Hong Kong, China, June 2014, pp. 6745–6750

  7. [7]

    St-rrt*: Asymptotically-optimal bidirectional motion planning through space- time,

    F. Grothe, V . N. Hartmann, A. Orthey, and M. Toussaint, “St-rrt*: Asymptotically-optimal bidirectional motion planning through space- time,” in2022 International Conference on Robotics and Automation (ICRA), Philadelphia, PA, USA, May 2022, pp. 3314–3320

  8. [8]

    On multiple moving objects,

    M. Erdmann and T. Lozano-Perez, “On multiple moving objects,” Algorithmica, vol. 2, pp. 477 – 521, January 1987

Show all 30 references
  1. [9]

    Path planning in 1000+ dimensions us- ing a task-space voronoi bias,

    A. Shkolnik and R. Tedrake, “Path planning in 1000+ dimensions us- ing a task-space voronoi bias,” in2009 IEEE International Conference on Robotics and Automation (ICRA). Kobe, Japan: IEEE, May 2009, pp. 2061–2067

  2. [10]

    Multilevel motion planning: A fiber bundle formulation,

    A. Orthey, S. Akbar, and M. Toussaint, “Multilevel motion planning: A fiber bundle formulation,”The International Journal of Robotics Research, vol. 43, no. 1, pp. 3–33, 2024

  3. [11]

    Centralized path planning for multiple robots: Optimal decoupling into sequential plans,

    J. van den Berg, J. Snoeyink, M. Lin, and D. Manocha, “Centralized path planning for multiple robots: Optimal decoupling into sequential plans,” inProceedings of Robotics: Science and Systems, Seattle, USA, June 2009

  4. [12]

    Multi-modal motion planning in non- expansive spaces,

    K. Hauser and J.-C. Latombe, “Multi-modal motion planning in non- expansive spaces,”International Journal of Robotics Research, vol. 29, pp. 897 – 915, 2010

  5. [13]

    Randomized multi-modal motion planning for a humanoid robot manipulation task,

    K. Hauser and V . Ng-Thow-Hing, “Randomized multi-modal motion planning for a humanoid robot manipulation task,”The International Journal of Robotics Research, vol. 30, no. 6, pp. 678–698, 2011

  6. [14]

    Integrated task and motion planning,

    C. R. Garrett, R. Chitnis, R. Holladay, B. Kim, T. Silver, L. P. Kael- bling, and T. Lozano-P ´erez, “Integrated task and motion planning,” Annual Review of Control, Robotics, and Autonomous Systems, vol. 4, no. 1, pp. 265–293, 2021

  7. [15]

    Long-horizon multi-robot rearrangement planning for construction assembly,

    V . N. Hartmann, A. Orthey, D. Driess, O. S. Oguz, and M. Toussaint, “Long-horizon multi-robot rearrangement planning for construction assembly,”IEEE Transactions on Robotics, vol. 39, no. 1, pp. 239– 252, February 2023

  8. [16]

    Cooperative task and motion planning for multi-arm assembly systems,

    J. Chen, J. Li, Y . Huang, C. Garrett, D. Sun, C. Fan, A. Hofmann, C. Mueller, S. Koenig, and B. C. Williams, “Cooperative task and motion planning for multi-arm assembly systems,” arXiv preprint arXiv:2203.02475, 2022

  9. [17]

    Multi-robot geometric task-and-motion planning for collaborative manipulation tasks,

    H. Zhang, S.-H. Chan, J. Zhong, J. Li, P. Kolapo, S. Koenig, Z. Agioutantis, S. Schafrik, and S. Nikolaidis, “Multi-robot geometric task-and-motion planning for collaborative manipulation tasks,”Au- tonomous Robots, vol. 47, no. 8, pp. 1537–1558, December 2023

  10. [18]

    Multi- arm trajectory planning for optimal collision-free pick-and-place op- erations,

    D. Mateu-Gomez, F. J. Mart ´ınez-Peral, and C. Perez-Vidal, “Multi- arm trajectory planning for optimal collision-free pick-and-place op- erations,”Technologies, vol. 12, no. 1, p. 12, January 2024

  11. [19]

    Optimization by simulated annealing,

    S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,”Science, vol. 220, no. 4598, pp. 671–680, May 1983

  12. [20]

    Statistical cooling: A general approach to combinatorial optimization problems,

    E. H. L. Aarts and P. J. M. Van Laarhoven, “Statistical cooling: A general approach to combinatorial optimization problems,”Philips Journal of Research, vol. 40, no. 4, pp. 193–226, 1985

  13. [21]

    Multi-robot task scheduling in micro-manufacturing,

    K. Doring and H. Gordon Petersen, “Multi-robot task scheduling in micro-manufacturing,” inThe 6th IEEE International Symposium on Assembly and Task Planning: From Nano to Macro Assembly and Manufacturing (ISATP). Montreal, Quebec, Canada: IEEE, July 2005, pp. 125–131

  14. [22]

    A new optimizer using particle swarm theory,

    R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” inMHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, October 1995, pp. 39–43

  15. [23]

    A note on two problems in connexion with graphs,

    E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, December 1959

  16. [24]

    Probabilistic roadmaps for path planning in high-dimensional configuration spaces,

    L. Kavraki, P. Svestka, J.-C. Latombe, and M. Overmars, “Probabilistic roadmaps for path planning in high-dimensional configuration spaces,” IEEE Transactions on Robotics and Automation, vol. 12, no. 4, pp. 566–580, 1996

  17. [25]

    Rrt-connect: An efficient approach to single-query path planning,

    J. Kuffner and S. LaValle, “Rrt-connect: An efficient approach to single-query path planning,” inProceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Au- tomation. Symposia Proceedings (Cat. No.00CH37065), vol. 2, San Francisco, CA, USA, ...

  18. [26]

    SANDROS: a dynamic graph search al- gorithm for motion planning,

    P. Chen and Y . Hwang, “SANDROS: a dynamic graph search al- gorithm for motion planning,”IEEE Transactions on Robotics and Automation, vol. 14, no. 3, pp. 390–403, June 1998

  19. [27]

    Creating high-quality paths for motion planning,

    R. Geraerts and M. H. Overmars, “Creating high-quality paths for motion planning,”The International Journal of Robotics Research, vol. 26, no. 8, pp. 845–863, 2007

  20. [28]

    Pybullet, a python module for physics sim- ulation for games, robotics and machine learning,

    E. Coumans and Y . Bai, “Pybullet, a python module for physics sim- ulation for games, robotics and machine learning,” http://pybullet.org, 2016–2023

  21. [29]

    The Open Motion Planning Library,

    I. A. S ¸ucan, M. Moll, and L. E. Kavraki, “The Open Motion Planning Library,”IEEE Robotics & Automation Magazine, vol. 19, no. 4, pp. 72–82, December 2012, https://ompl.kavrakilab.org

  22. [30]

    A modified particle swarm optimizer,

    Y . Shi and R. Eberhart, “A modified particle swarm optimizer,” in 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), Anchorage, AK, USA, May 1998, pp. 69–73

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