Hostname: page-component-75d7c8f48-q7pjp Total loading time: 0 Render date: 2026-03-21T14:50:15.640Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-objective optimal trajectory planning for robot manipulator attention to end-effector path limitation

Published online by Cambridge University Press:  17 April 2024

Jintao Ye Open the ORCID record for Jintao Ye [Opens in a new window] ,
Lina Hao  and
Hongtai Cheng
Jintao Ye
Affiliation:
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
Lina Hao*
Affiliation:
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
Hongtai Cheng
Affiliation:
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
*
Corresponding author: Lina Hao; Email: haolina@me.neu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In the process of trajectory optimization for robot manipulator, the path that is generated may deviate from the intended path because of the adjustment of trajectory parameters, if there is limitation of end-effector path in Cartesian space for specific tasks, this phenomenon is dangerous. This paper proposes a methodology that is based on the Pareto front to address this issue, and the methodology takes into account both the multi-objective optimization of robotic arm and the quality of end-effector path. Based on dung beetle optimizer, this research proposes improved non-dominated sorting dung beetle optimizer. This paper interpolates manipulator trajectory with quintic B-spline curves, achieves multi-objective trajectory optimization that simultaneously optimizes traveling time, energy consumption, and mean jerk, proposes a trajectory selection strategy that is based on Pareto solution set by introducing the concept of Fréchet distance, and the strategy enables the end-effector to approach the desired path in Cartesian space. Simulation and experimental results validate the effectiveness and practicability of the proposed methodology on the Sawyer robot manipulator.

Keywords

robot manipulatormulti-objectivetrajectory optimizationB-spline curvesFréchet distance

Information

Type
Research Article
Information
Robotica , Volume 42 , Issue 6 , June 2024 , pp. 1761 - 1780
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Yu, X., Dong, M. and Yin, W., “Time-optimal trajectory planning of manipulator with simultaneously searching the optimal path,” Comp Commun 181, 446–453 (2022). doi: 10.1016/j.comcom.2021.10.005.CrossRefGoogle Scholar
Marauli, T., Gattringer, H. and Müller, A., “Time-optimal path following for non-redundant serial manipulators using an adaptive path-discretization,” Robotica 41(6), 1856–1871 (2023). doi: 10.1017/S026357472300022X.CrossRefGoogle Scholar
Li, X., Lan, Y., Jiang, P., Cao, H. and Zhou, J., “An efficient computation for energy optimization of robot trajectory,” IEEE Trans Ind Electron 69(11), 11436–11446 (2021). doi: 10.1109/TIE.2021.3118367.CrossRefGoogle Scholar
Liu, Z., Huang, Y., Liu, D., Guo, X., Wang, K. and Tan, J., “Trajectory planning of large redundant manipulator considering kinematic constraints and energy efficiency,” Robotica 41(11), 3524–3540 (2023). doi: 10.1017/S0263574723001157.CrossRefGoogle Scholar
Kyriakopoulos, K. J. and Saridis, G. N., “Minimum Jerk Path Generation,” In: Proceedings. 1988 IEEE International Conference on Robotics and Automation, (1988) pp. 364–369. doi: 10.1109/ROBOT.1988.12075.CrossRefGoogle Scholar
Shrivastava, A. and Dalla, V. K., “Jerk optimized motion planning of redundant space robot based on grey-wolf optimization approach,” Arab J Sci Eng 48(3), 2687–2699 (2023). doi: 10.1007/s13369-022-07002-1.CrossRefGoogle Scholar
Huang, J., Hu, P., Wu, K. and Zeng, M., “Optimal time-jerk trajectory planning for industrial robots,” Mech Mach Theory 121, 530–544 (2018). doi: 10.1016/j.mechmachtheory.2017.11.006.CrossRefGoogle Scholar
Zhang, X. and Shi, G., “Multi-objective optimal trajectory planning for manipulators in the presence of obstacles,” Robotica 40(4), 888–906 (2022). doi: 10.1017/S0263574721000886.CrossRefGoogle Scholar
Ekrem, Özge and Aksoy, B., “Trajectory planning for a 6-axis robotic arm with particle swarm optimization algorithm,” Eng Appl Artif Intel 122, 106099 (2023). doi: 10.1016/j.engappai.2023.106099.CrossRefGoogle Scholar
Zhang, S., Dai, S. and Zhao, Y., “Continuous trajectory planning based on learning optimization in high dimensional input space for serial manipulators,” Eng Optimiz 54(10), 1724–1742 (2022). doi: 10.1080/0305215X.2021.1958210.CrossRefGoogle Scholar
Wang, M., Luo, J., Zheng, L., Yuan, J. and Walter, U., “Generate optimal grasping trajectories to the end-effector using an improved genetic algorithm,” Adv Space Res 66(7), 1803–1817 (2020). doi: 10.1016/j.asr.2020.06.022.CrossRefGoogle Scholar
Li, Y., Huang, T. and Chetwynd, D. G., “An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines,” Mech Mach Theory 126, 479–490 (2018). doi: 10.1016/j.mechmachtheory.2018.04.026.CrossRefGoogle Scholar
Chen, D., Li, S., Wang, J. F., Feng, Y. and Liu, Y., “A multi-objective trajectory planning method based on the improved immune clonal selection algorithm,” Rob Comp-Integr manufact 59, 431–442 (2019). doi: 10.1016/j.rcim.2019.04.016.CrossRefGoogle Scholar
Li, G., Liu, H., Liu, S. and Xiao, J., “A general ${C}^2$ continuous toolpath corner smoothing method for a 5-DOF hybrid robot,” Mech Mach Theory 169, 104640 (2022). doi: 10.1016/j.mechmachtheory.2021.104640.CrossRefGoogle Scholar
Yu, L., Zhou, S. and Huang, S., “Trajectory optimization of the redundant manipulator with local variable period under multi-machine coordination,” Robotica 41(1), 292–305 (2023). doi: 10.1017/S0263574722001291.CrossRefGoogle Scholar
Skrobek, D. and Cekus, D., “Optimization of the operation of the anthropomorphic manipulator in a three-dimensional working space,” Eng Optimiz 51(11), 1997–2010 (2019). doi: 10.1080/0305215X.2018.1564919.CrossRefGoogle Scholar
He, Y., Mei, J., Fang, Z., Zhang, F. and Zhao, Y., “Minimum energy trajectory optimization for driving systems of palletizing robot joints,” Math Probl Eng 2018(11), 1–26 (2018). doi: 10.1155/2018/7247093.Google Scholar
Jin, R., Rocco, P. and Geng, Y., “Cartesian trajectory planning of space robots using a multi-objective optimization,” Aerosp Sci Technol 108, 106360 (2021). doi: 10.1016/j.ast.2020.106360.CrossRefGoogle Scholar
Singh, G. and Banga, V. K., “Combinations of novel hybrid optimization algorithms-based trajectory planning analysis for an industrial robotic manipulators,” J Field Robot 39(5), 650–674 (2022). doi: 10.1002/rob.22069.CrossRefGoogle Scholar
Huang, Y. and Fei, M., “Motion planning of robot manipulator based on improved NSGA-II,” International Journal of Control, Automation and Systems. 16(4), 1878–1886 (2018). doi: 10.1007/s12555-016-0693-3.CrossRefGoogle Scholar
Wang, Z., Li, Y., Shuai, K., Zhu, W., Chen, B. and Chen, K., “Multi-objective trajectory planning method based on the improved elitist non-dominated sorting genetic algorithm,” Chin J Mech Eng 35(1), 1–15 (2022). doi: 10.1186/s10033-021-00669-x.CrossRefGoogle Scholar
Xidias, E. K., “Time-optimal trajectory planning for hyper-redundant manipulators in 3D workspaces,” Rob Comp-Integra Manufact 50, 286–298 (2018). doi: 10.1016/j.rcim.2017.10.005.CrossRefGoogle Scholar
Yang, Y., Xu, H.-Z., Li, S.-H., Zhang, L.-L. and Yao, X.-M., “Time-optimal trajectory optimization of serial robotic manipulator with kinematic and dynamic limits based on improved particle swarm optimization,” Int J Adv Manufact Tech 120(1-2), 1253–1264 (2022). doi: 10.1007/s00170-022-08796-y.CrossRefGoogle Scholar
Liu, Y., Jin, Z. and Teng, L., “PSO-based time optimal rapid orientation for micronano space robot,” IEEE Trans Aero Elec Sys 59(2), 1921–1934 (2022). doi: 10.1109/TAES.2022.3207124.Google Scholar
Zhang, X., Xiao, F., Tong, X. L., Yun, J., Liu, Y., Sun, Y., Tao, B., Kong, J., Xu, M. and Chen, B., “Time optimal trajectory planing based on improved sparrow search algorithm,” Front Bioengin Biotech 10, 852408 (2022). doi: 10.3389/fbioe.2022.852408.CrossRefGoogle ScholarPubMed
Petrone, V., Ferrentino, E. and Chiacchio, P., “Time-optimal trajectory planning with interaction with the environment,” IEEE Rob Auto Lett 7(4), 10399–10405 (2022). doi: 10.1109/LRA.2022.3191813.CrossRefGoogle Scholar
Kucuk, S., “Optimal trajectory generation algorithm for serial and parallel manipulators,” Rob Comp-Integr Manufact 48, 219–232 (2017). doi: 10.1016/j.rcim.2017.04.006.CrossRefGoogle Scholar
Ma, J.-W., Gao, S., Yan, H.-T., Lv, Q. and Hu, G.-Q., “A new approach to time-optimal trajectory planning with torque and jerk limits for robot,” Robot Auton Syst 140, 103744 (2021). doi: 10.1016/j.robot.2021.103744.CrossRefGoogle Scholar
Vivas, A. V., Cherubini, A., Garabini, M., Salaris, P. and Bicchi, A., “Minimizing energy consumption of elastic robots in repetitive tasks,” IEEE Trans Syst, Man, Cybernet 53(8), 5006–5018 (2023). doi: 10.1109/TSMC.2023.3260644.CrossRefGoogle Scholar
Bonami, P., Olivares, A. and Staffetti, E., “Energy-optimal multi-goal motion planning for planar robot manipulators,” J Optim Theory Appl 163(1), 80–104 (2014). doi: 10.1007/s10957-013-0516-0.CrossRefGoogle Scholar
Lu, S., Ding, B. and Li, Y., “Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation,” Adv Mech Eng 12(3), 1687814020913667 (2020). doi: 10.1177/1687814020913667.CrossRefGoogle Scholar
Wang, Z., Li, Y., Sun, P., Luo, Y., Chen, B. and Zhu, W., “A multi-objective approach for the trajectory planning of a 7-DOF serial-parallel hybrid humanoid arm,” Mech Mach Theory 165, 104423 (2021). doi: 10.1016/j.mechmachtheory.2021.104423.CrossRefGoogle Scholar
Cheng, Q., Hao, X., Wang, Y., Xu, W. and Li, S., “Trajectory planning of transcranial magnetic stimulation manipulator based on time-safety collision optimization,” Robot Auton Syst 152, 104039 (2022). doi: 10.1016/j.robot.2022.104039.CrossRefGoogle Scholar
Gasparetto, A., Lanzutti, A., Vidoni, R. and Zanotto, V., “Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning,” Robot Com-Integr Manuf 28(2), 164–181 (2012). doi: 10.1016/j.rcim.2011.08.003.CrossRefGoogle Scholar
Ren, Z., Hu, B., Wang, Z., Sun, L. and Zhu, Q., “Knowledge database-based multiobjective trajectory planning of 7-DOF manipulator with rapid and continuous response to uncertain fast-flying objects,” IEEE Trans Robot 39(2), 1012–1028 (2023). doi: 10.1109/TRO.2022.3207616.CrossRefGoogle Scholar
Li, X., Gu, Y., Wu, L., Sun, Q. and Song, T., “Time and energy optimal trajectory planning of wheeled mobile dual-arm robot based on tip-over stability constraint,” Appl Sci 13(6), 3780 (2023). doi: 10.3390/app13063780.CrossRefGoogle Scholar
Halinga, M. S., Nyobuya, H. J. and Uchiyama, N., “Generation and experimental verification of time and energy optimal coverage motion for industrial machines using a modified S-curve trajectory,” Int J Adv Manufact Tech 125(7-8), 3593–3605 (2023). doi: 10.1007/s00170-023-10912-5.CrossRefGoogle Scholar
Liu, J., Wang, H., Li, X., Chen, K. and Li, C., “Robotic arm trajectory optimization based on multiverse algorithm,” Math Biosci Eng 20(2), 2776–2792 (2023). doi: 10.3934/mbe.2023130.CrossRefGoogle ScholarPubMed
Cao, X., Yan, H., Huang, Z., Ai, S., Xu, Y., Fu, R. and Zou, X., “A multi-objective particle swarm optimization for trajectory planning of fruit picking manipulator,” Agronomy 11(11), 2286 (2021). doi: 10.3390/agronomy11112286.CrossRefGoogle Scholar
Added, E., Gritli, H.ène and Belghith, S., “Trajectory tracking-based control of the chaotic behavior in the passive bipedal compass-type robot,” European Phys J Spec Top 231(5), 1071–1084 (2022). doi: 10.1140/epjs/s11734-022-00471-3.CrossRefGoogle Scholar
Fazel, R., Shafei, A. M. and Nekoo, S. R., “A new method for finding the proper initial conditions in passive locomotion of bipedal robotic systems,” Commun Nonlinear Sci 130, 107693 (2024). doi: 10.1016/j.cnsns.2023.107693.CrossRefGoogle Scholar
Park, J., Haan, J. and Park, F. C., “Convex optimization algorithms for active balancing of humanoid robots,” IEEE Trans Robot 23(4), 817–822 (2007). doi: 10.1109/TRO.2007.900639.CrossRefGoogle Scholar
Xue, J. and Shen, B., “Dung beetle optimizer: A new meta-heuristic algorithm for global optimization,” J Supercomp 79(7), 7305–7336 (2023). doi: 10.1007/s11227-022-04959-6.CrossRefGoogle Scholar
Zhu, F., Li, G., Tang, H., Li, Y., Lv, X. and Wang, X., “Dung beetle optimization algorithm based on quantum computing and multi-strategy fusion for solving engineering problems,” Exp Syst Appl 236, 121219 (2023). doi: 10.1016/j.eswa.2023.121219.CrossRefGoogle Scholar
He, T., Zhang, Y., Sun, F. and Shi, X., “Immune Optimization Based Multi-Objective Six-DOF Trajectory Planning for Industrial Robot Manipulators,” In: 2016 12th World Congress on Intelligent Control and Automation (WCICA, 66, (2016) pp. 2945–2950. doi: 10.1109/WCICA.2016.7578610.CrossRefGoogle Scholar
Riazi, S., Wigström, O., Bengtsson, K. and Lennartson, B., “Energy and peak power optimization of time-bounded robot trajectories,” IEEE Trans Autom Sci Eng 14(2), 646–657 (2017). doi: 10.1109/TASE.2016.2641743.CrossRefGoogle Scholar
Elnagar, A. and Hussein, A., “On optimal constrained trajectory planning in 3D environments,” Robot Auton Syst 33(4), 195–206 (2000). doi: 10.1016/S0921-8890(00)00095-6.CrossRefGoogle Scholar
Tian, Y., Lu, C., Zhang, X., Cheng, F. and Jin, Y., “A pattern mining-based evolutionary algorithm for large-scale sparse multiobjective optimization problems,” IEEE Trans Cybernet 52(7), 6784–6797 (2022). doi: 10.1109/TCYB.2020.3041325.CrossRefGoogle ScholarPubMed
Viswanathan, G. M., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P. and Stanley, H. E., “Optimizing the success of random searches,” Nature 401(6756), 911–914 (1999). doi: 10.1038/44831.CrossRefGoogle ScholarPubMed
Heidari, A. A. and Pahlavani, P., “An efficient modified grey wolf optimizer with Lévy flight for optimization tasks,” Appl Soft Comp 60, 115–134 (2017). doi: 10.1016/j.asoc.2017.06.044.CrossRefGoogle Scholar
Houssein, E. H., Saad, M. R., Hashim, F. A., Shaban, H. and Hassaballah, M., “Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems,” Eng Appl Artif Intel 94, 103731 (2020). doi: 10.1016/j.engappai.2020.103731.CrossRefGoogle Scholar
Iacca, G., dos Santos, J., Celso, V., de, M. and Veloso, V., “An improved jaya optimization algorithm with Lévy flight,” Expert Syst Appl 165, 113902 (2021). doi: 10.1016/j.eswa.2020.113902.CrossRefGoogle Scholar
Ni, S., Chen, W., Ju, H. and Chen, T., “Coordinated trajectory planning of a dual-arm space robot with multiple avoidance constraints,” Acta Astrona 195, 379–391 (2022). doi: 10.1016/j.actaastro.2022.03.024.CrossRefGoogle Scholar
Alt, H. and Godau, M., “Computing the Fréchet distance between two polygonal curves,” Int J Comp Geo Appl 5(01n02), 75–91 (1995). doi: 10.1142/S0218195995000064.CrossRefGoogle Scholar
Gudmundsson, J., van Renssen, A., Saeidi, Z. and Wong, S., “Translation invariant Fréchet distance queries,” Algorithmica 83(11), 3514–3533 (2021). doi: 10.1007/s00453-021-00865-0.CrossRefGoogle Scholar