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A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm


  • Received: 16 November 2023 Revised: 16 January 2024 Accepted: 19 January 2024 Published: 04 February 2024
  • In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.

    Citation: Chengjun Wang, Xingyu Yao, Fan Ding, Zhipeng Yu. A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 3364-3390. doi: 10.3934/mbe.2024149

    Related Papers:

  • In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.



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    [1] Y. Chen, L. Li, Collision-free trajectory planning for dual-robot systems using B-splines, Int. J. Adv. Rob. Syst., 14 (2017). https://doi.org/10.1177/1729881417728021 doi: 10.1177/1729881417728021
    [2] R. Marco, C. Fabio, S. Marco, A. Alessandra, A new framework for joint trajectory planning based on time-parameterized B-splines, Comput.-Aided Des., 154 (2023), 103421. https://doi.org/10.1016/j.cad.2022.103421 doi: 10.1016/j.cad.2022.103421
    [3] Y. Li, H. Tian, D. G. Chetwynd, An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines, Mech. Mach. Theory, 126 (2018), 479–490. https://doi.org/10.1016/j.mechmachtheory.2018.04.026 doi: 10.1016/j.mechmachtheory.2018.04.026
    [4] H. Wang, W. Heng, J. Huang, B. Zhao, L. Quan, Smooth point-to-point trajectory planning for industrial robots with kinematical constraints based on high-order polynomial curve, Mech. Mach. Theory, 139 (2019), 284–293. https://doi.org/10.1016/j.mechmachtheory.2019.05.002 doi: 10.1016/j.mechmachtheory.2019.05.002
    [5] H. Wang, Q. Zhao, H. Li, R. Zhao, Polynomial-based smooth trajectory planning for fruit-picking robot manipulator, Inf. Process. Agric., 9 (2022), 112–122. https://doi.org/10.1016/j.inpa.2021.08.001 doi: 10.1016/j.inpa.2021.08.001
    [6] X. Li, H. Lv, D. Zeng, Q. Zhang, An improved multi-objective trajectory planning algorithm for kiwifruit harvesting manipulator, IEEE Access, 11 (2023), 65689–65699. https://doi.org/10.1109/ACCESS.2023.3289207 doi: 10.1109/ACCESS.2023.3289207
    [7] Ü. Dinçer, M. Çevik, Improved trajectory planning of an industrial parallel mechanism by a composite polynomial consisting of Bézier curves and cubic polynomials, Mech. Mach. Theory, 132 (2019), 248–263. https://doi.org/10.1016/j.mechmachtheory.2018.11.009 doi: 10.1016/j.mechmachtheory.2018.11.009
    [8] F. Lin, L. Shen, C. Yuan, Z. Mi, Certified space curve fitting and trajectory planning for CNC machining with cubic B-splines, Comput.-Aided Des., 106 (2019), 13–29. https://doi.org/10.1016/j.cad.2018.08.001 doi: 10.1016/j.cad.2018.08.001
    [9] S. Lu, B. Ding, Y. Li, Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation, Adv. Mech. Eng., 12 (2020). https://doi.org/10.1177/1687814020913667 doi: 10.1177/1687814020913667
    [10] X. Zhao, M. Wang, N. Liu, Y. Tang, Trajectory planning for 6-DOF robotic arm based on quintic polynormial, in Proceedings of the 2017 2nd International Conference on Control, Automation and Artificial Intelligence (CAAI 2017), 2017. https://doi.org/10.2991/CAAI-17.2017.23
    [11] G. Wu, S. Zhang, Real-time jerk-minimization trajectory planning of robotic arm based on polynomial curve optimization, Proc. Inst. Mech. Eng., Part C: J. Mech., 236 (2022), 10852–10864. https://doi.org/10.1177/09544062221106632 doi: 10.1177/09544062221106632
    [12] M. Dupac, Smooth trajectory generation for rotating extensible manipulators, Math. Methods Appl. Sci., 41 (2018), 2281–2286. https://doi.org/10.1002/mma.4210 doi: 10.1002/mma.4210
    [13] P. Boscariol, D. Richiedei, Energy-efficient design of multipoint trajectories for Cartesian robots, Int. J. Adv. Manuf. Technol., 102 (2019), 1853–1870. https://doi.org/10.1007/s00170-018-03234-4 doi: 10.1007/s00170-018-03234-4
    [14] A. E. Ezugwu, A. K. Shukla, R. Nath, A. A. Akinyelu, J. O. Agushaka, H. Chiroma, Metaheuristics: a comprehensive overview and classification along with bibliometric analysis, Artif. Intell. Rev., 54 (2021), 4237–4316. https://doi.org/10.1007/s10462-020-09952-0 doi: 10.1007/s10462-020-09952-0
    [15] J. Zhang, Q. Meng, X. Feng, H. Shen, A 6-DOF robot-time optimal trajectory planning based on an improved genetic algorithm, Rob. Biomimetics, 5 (2018), 3. https://doi.org/10.1186/s40638-018-0085-7 doi: 10.1186/s40638-018-0085-7
    [16] K. Shi, Z. Wu, B. Jiang, H. R. Karimi, Dynamic path planning of mobile robot based on improved simulated annealing algorithm, J. Franklin Inst., 360 (2023), 4378–4398. https://doi.org/10.1016/j.jfranklin.2023.01.033 doi: 10.1016/j.jfranklin.2023.01.033
    [17] X. Zhang, F. Xiao, X. Tong, J. Yun, Y. Liu, Y. Sun, et al., Time optimal trajectory planing based on improved sparrow search algorithm, Front. Bioeng. Biotechnol., 10 (2022), 852408. https://doi.org/10.3389/fbioe.2022.852408 doi: 10.3389/fbioe.2022.852408
    [18] T. Wang, Z. Xin, H. Miao, H. Zhang, Z. Chen, Y. Du, Optimal trajectory planning of grinding robot based on improved whale optimization algorithm, Math. Probl. Eng., 2020 (2020), 3424313. https://doi.org/10.1155/2020/3424313 doi: 10.1155/2020/3424313
    [19] I. Carvajal, E. A. Martínez-García, R. Lavrenov, E. Magid, Robot arm planning and control by τ-Jerk theory and vision-based recurrent ANN observer, in 2021 International Siberian Conference on Control and Communications (SIBCON), (2021), 1–6. https://doi.org/10.1109/SIBCON50419.2021.9438857
    [20] E. Ö zge, A. Bekir, Trajectory planning for a 6-axis robotic arm with particle swarm optimization algorithm, Eng. Appl. Artif. Intell., 122 (2023), 106099. https://doi.org/10.1016/j.engappai.2023.106099 doi: 10.1016/j.engappai.2023.106099
    [21] G. Chen, W. Peng, Z. Wang, J. Tu, H. Hu, D. Wang, et al., Modeling of swimming posture dynamics for a beaver-like robot, Ocean Eng., 279 (2023), 114550. https://doi.org/10.1016/j.oceaneng.2023.114550 doi: 10.1016/j.oceaneng.2023.114550
    [22] G. Chen, Y. Xu, C. Yang, X. Yang, H. Hu, X. Chai, et al., Design and control of a novel bionic mantis shrimp robot, IEEE/ASME Trans. Mechatron., 28 (2023), 3376–3385. https://doi.org/10.1109/TMECH.2023.3266778 doi: 10.1109/TMECH.2023.3266778
    [23] K. Wu, L. Chen, K. Wang, M. Wu, W. Pedrycz, K. Hirota, Robotic arm trajectory generation based on emotion and kinematic feature, in 2022 International Power Electronics Conference (IPEC-Himeji 2022-ECCE Asia), (2022), 1332–1336. https://doi.org/10.23919/IPEC-Himeji2022-ECCE53331.2022.9807205
    [24] G. Hu, Y. Guo, G. Wei, L. Abualigah, Genghis Khan shark optimizer: a novel nature-inspired algorithm for engineering optimization, Adv. Eng. Inf., 58 (2023), 102210. https://doi.org/10.1016/j.aei.2023.102210 doi: 10.1016/j.aei.2023.102210
    [25] R. V. Ram, P. M. Pathak, S. J. Junco, Inverse kinematics of mobile manipulator using bidirectional particle swarm optimization by manipulator decoupling, Mech. Mach. Theory, 131 (2019), 385–405. https://doi.org/10.1016/j.mechmachtheory.2018.09.022 doi: 10.1016/j.mechmachtheory.2018.09.022
    [26] P. Golla, S. Ramesh, S. Bandyopadhyay, Kinematics of the Hybrid 6-Axis (H6A) manipulator, Robotica, 41 (2023), 2251–2282. https://doi.org/10.1017/S0263574723000334 doi: 10.1017/S0263574723000334
    [27] A. V. Antonov, A. S. Fomin, Inverse kinematics of a 5-DOF hybrid manipulator, Autom. Remote Control, 84 (2023), 281–293. https://doi.org/10.1134/S0005117923030037 doi: 10.1134/S0005117923030037
    [28] J. Q. Gan, E. Oyama, E. Rosales, H. Hu, A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm, Robotica, 23 (2005), 123–129. https://doi.org/10.1017/S0263574704000529 doi: 10.1017/S0263574704000529
    [29] G. Zhong, B. Peng, W. Dou, Kinematics analysis and trajectory planning of a continuum manipulator, Int. J. Mech. Sci., 222 (2022), 107206. https://doi.org/10.1016/j.ijmecsci.2022.107206 doi: 10.1016/j.ijmecsci.2022.107206
    [30] C. Wang, F. Ding, L. Ling, S. Li, Design of a teat cup attachment robot for automatic milking systems, Agriculture, 13 (2023), 1273. https://doi.org/10.3390/agriculture13061273 doi: 10.3390/agriculture13061273
    [31] A. Messaoudi, R. Sadaka, H. Sadok, Matrix recursive polynomial interpolation algorithm: An algorithm for computing the interpolation polynomials, J. Comput. Appl. Math., 373 (2020), 112471. https://doi.org/10.1016/j.cam.2019.112471 doi: 10.1016/j.cam.2019.112471
    [32] M. Ivan, V. Neagos, A representation of the interpolation polynomial, Numerical Algorithms, 88 (2021), 1215–1231. https://doi.org/10.1007/s11075-021-01072-2 doi: 10.1007/s11075-021-01072-2
    [33] X. Liu, G. Lin, W. Wei, Adaptive transition gait planning of snake robot based on polynomial interpolation method, Actuators, 11 (2022), 222. https://doi.org/10.3390/act11080222 doi: 10.3390/act11080222
    [34] A. Shrivastava, V. K. Dalla, Multi-segment trajectory tracking of the redundant space robot for smooth motion planning based on interpolation of linear polynomials with parabolic blend, Proc. Inst. Mech. Eng., Part C: J. Mech., 236 (2022), 9255–9269. https://doi.org/10.1177/09544062221088723 doi: 10.1177/09544062221088723
    [35] D. Wang, D. Tan, L. Liu, Particle swarm optimization algorithm: an overview, Soft Comput., 22 (2017), 387–408. https://doi.org/10.1007/s00500-016-2474-6 doi: 10.1007/s00500-016-2474-6
    [36] V. Trivedi, P. Varshney, M. Ramteke, A simplified multi-objective particle swarm optimization algorithm, Swarm Intell., 14 (2020), 83–116. https://doi.org/10.1007/s11721-019-00170-1 doi: 10.1007/s11721-019-00170-1
    [37] Y. Zhang, X. Liu, F. Bao, J. Chi, C. Zhang, P. Liu, Particle swarm optimization with adaptive learning strategy, Knowledge-Based Syst., 196 (2020), 105789. https://doi.org/10.1016/j.knosys.2020.105789 doi: 10.1016/j.knosys.2020.105789
    [38] A. G. Gad, Particle swarm optimization algorithm and its applications: a systematic review, Arch. Comput. Methods Eng., 29 (2022), 2531–2561. https://doi.org/10.1007/s11831-021-09694-4 doi: 10.1007/s11831-021-09694-4
    [39] J. Zheng, Y. Gao, H. Zhang, Y. Lei, J. Zhang, OTSU multi-threshold image segmentation based on improved particle swarm algorithm, Appl. Sci., 12 (2022), 11514. https://doi.org/10.3390/app122211514 doi: 10.3390/app122211514
    [40] L. Yu, Y. Han, L. Mu, Improved quantum evolutionary particle swarm optimization for band selection of hyperspectral image, Remote Sens. Lett., 11 (2020), 866–875. https://doi.org/10.1080/2150704X.2020.1782501 doi: 10.1080/2150704X.2020.1782501
    [41] S. Obukhov, A. Ibrahim, A. A. Z. Diab, A. S. Al-Sumaitim, R. Aboelsaud, Optimal performance of dynamic particle swarm optimization based maximum power trackers for stand-alone PV system under partial shading conditions, IEEE Access, 8 (2020), 20770–20785. https://doi.org/10.1109/ACCESS.2020.2966430 doi: 10.1109/ACCESS.2020.2966430
    [42] X. Li, B. Tian, S. Hou, X. Li, Y. Li, C. Liu, et al., Path planning for mount robot based on improved particle swarm optimization algorithm, Electronics, 12 (2023), 3289. https://doi.org/10.3390/electronics12153289 doi: 10.3390/electronics12153289
    [43] P. Qu, F. Du, Improved particle swarm optimization for laser cutting path planning, IEEE Access, 11 (2023), 4574–4588. https://doi.org/10.1109/ACCESS.2023.3236006 doi: 10.1109/ACCESS.2023.3236006
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