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Multi-objective trajectory planning for industrial robots using a hybrid optimization approach
Published online by Cambridge University Press: 10 May 2024
Abstract
In this paper, a hybrid approach organized in four phases is proposed to solve the multi-objective trajectory planning problem for industrial robots. In the first phase, a transcription of the original problem into a standard multi-objective parametric optimization problem is achieved by adopting an adequate parametrization scheme for the continuous robot configuration variables. Then, in the second phase, a global search is performed using a population-based search metaheuristic in order to build a first approximation of the Pareto front (PF). In the third phase, a local search is applied in the neighborhood of each solution of the PF approximation using a deterministic algorithm in order to generate new solutions. Finally, in the fourth phase, results of the global and local searches are gathered and postprocessed using a multi-objective direct search method to enhance the quality of compromise solutions and to converge toward the true optimal PF. By combining different optimization techniques, we intend not only to improve the overall search mechanism of the optimization strategy but also the resulting hybrid algorithm should keep the robustness of the population-based algorithm while enjoying the theoretical properties of convergence of the deterministic component. Also, the proposed approach is modular and flexible, and it can be implemented in different ways according to the applied techniques in the different phases. In this paper, we illustrate the efficiency of the hybrid framework by considering different techniques available in various numerical optimization libraries which are combined judiciously and tested on various case studies.
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References
Craig, J. J.. Introduction to Robotics: Mechanics and Control 4th edn, (Pearson Education Limited, 2022).Google Scholar
Kahn, M., The near-minimum time control of open-loop articulated kinematic linkages Tech. Rep. AIM-106, (1969). Stanford University.Google Scholar
Kahn, M. E. and Roth, B., “The near minimum time control of open loop articulated kinematic chains,” ASME J Dyn Sys Meas Cont 11(3), 164–172 (1971).CrossRefGoogle Scholar
Bobrow, J. E., Dubowsky, S. and Gibson, J. S., “Time-optimal control of robotic manipulators,” Int J Robot Res 4(3), 3–17 (1985).CrossRefGoogle Scholar
Betts, J. T., “Survey of numerical methods for trajectory optimization,” J Guid Cont Dyn 21(2), 193–207 (1998).CrossRefGoogle Scholar
Bruce, A. C., “A survey of methods available for the numerical optimization of continuous dynamic systems,” J Optim Theory Appl 152, 271–306 (2012).Google Scholar
von Stryk, O. and Bulirsch, R., “Direct and indirect methods for trajectory optimization,” Ann Oper Res 37(1), 357–373 (1993).CrossRefGoogle Scholar
Stryk, O. V. and Schlemmer, M., “Optimal Control of the Industrial Robot Manutec r3,” In: Computational Optimal Control International Series of Numerical Mathematics (Bulirshn, R. and Kraft, D., eds.) (Basel: Birkhäuser, 1994) pp. 367–382.CrossRefGoogle Scholar
Fotouhi, C. R. and Szyszkowski, W., “An algorithm for time-optimal control problems,” J Dyn Syst Meas Cont 120(3), 414–418 (1998). doi: 10.1115/1.2805419
CrossRefGoogle Scholar
Ghasemi, M. H., Kashiri, N. and Dardel, M., “Time-optimal trajectory planning of robot manipulators in point-to-point motion using an indirect method,” Proceed Inst Mech Eng Part C: J Mech Eng Sci 226(2), 473–484 (2012).https://doi:10
CrossRefGoogle Scholar
Massaro, M., Lovato, S., Bottin, M. and Rosati, G., “An optimal control approach to the minimum-time trajectory planning of robotic manipulators,” Robotics 12(3), 64 (2023). doi: 10.3390/robotics12030064.CrossRefGoogle Scholar
Chettibi, T., Lehtihet, H. E., Haddad, M. and Hanchi, S., “Minimum cost trajectory planning for industrial robots,” European J Mech-A/Soli 23(4), 703–715 (2004).CrossRefGoogle Scholar
Chettibi, T. and Lehtihet, H. E., “A New Approach for Point-to-Point Optimal Motion Planning Problems of Robotic Manipulators,” In: Proc. of 6th Biennial Conf. on Engineering System Design and Analysis, APM10, (2002).Google Scholar
Chettibi, T., Haddad, M., Rebai, S. and Hentout, A., “A Stochastic off Line Planner of Optimal Dynamic Motions for Robotic Manipulators,” In: Proceedings of 1st International Conference on Informatics, in Control, Automation and Robotics, (2004).Google Scholar
Rana, A. S. and Zalazala, A. M. S., “Near time optimal collision free motion planning of robotic manipulators using an evolutionary algorithm,” Robotica 14, 621–632 (1996).CrossRefGoogle Scholar
Latombe, J. C., “Motion planning: A journey of, molecules, digital actors and other artefacts,” Int J Robot Res 18(11), 1119–1128 (1999).CrossRefGoogle Scholar
Gasparetto, A., Boscariol, P., Lanzutti, A. and Vidoni, R., “Path Planning and Trajectory Planning Algorithms: A General Overview,Path Planning and Trajectory Planning Algorithms: A General Overview,” In: Motion and Operation Planning of Robotic Systems, (Springer, 2015) pp. 3–27.CrossRefGoogle Scholar
Marler, R. T. and Arora, J. S., “Survey of multi-objective optimization methods for engineering,” struct Multidisc Optim 26(6), 369–395 (2004). doi: 10.1007/s00158-003-0368-6.CrossRefGoogle Scholar
Deb, K., “Multi-Objective Optimisation Using Evolutionary Algorithms: An Introduction,” In: Multi-Objective Evolutionary Optimisation for Product Design and Manufacturing, (Springer Verlag, (2011). doi: 10.1007/978-0-85729-652-8_1
Google Scholar
Pereira, J. L. J., Oliver, G. A., Francisco, M. B., Cunha, S. S. and Gomes, G. F., “A review of multi‐objective optimization: Methods and algorithms in mechanical engineering problems,” Arch Comput Method E 29(4), 2285–2308 (2022). doi: 10.1007/s11831-021-09663-x.CrossRefGoogle Scholar
Logist, F., Houska, B., Diehl, M. and Van Impe, J., “Fast pareto set generation for nonlinear optimal control problems with multiple objectives,” Struct Multidisc Optim 42(4), 591–603 (2010). doi: 10.1007/s00158-010-0506-x
CrossRefGoogle Scholar
Gasparetto, A. and Zanotto, V., “Optimal trajectory planning for industrial robots,” Adv Eng Softw 41(4), 548–556 (2010). doi: 10.1016/j.advengsoft.2009.11.001.CrossRefGoogle Scholar
Yang, X.-S.. Optimization techniques and applications with examples (JohnWiley & Sons Inc., 2018). ISBN: 9781119490609.CrossRefGoogle Scholar
Emmerich, M. T. M. and Deutz, A. H., “A tutorial on multiobjective optimization: Fundamentals and evolutionary methods,” Nat Comput 17(3), 585–609 (2018). doi: 10.1007/s11047-018-9685-y
CrossRefGoogle ScholarPubMed
Saravanan, R., Ramabalan, S. and Balamurugan, C., “Evolutionary optimal trajectory planning for industrial robot with payload constraints,” Int J Adv Manuf Technol 38, 1213–1226 (2008). doi: 10.1007/s00170-007-
CrossRefGoogle Scholar
Saravanan, R., Ramabalan, S. and Balamurugan, C., “Evolutionary multi-criteria trajectory modeling of industrial robots in the presence of obstacles,” Eng Appl Artif Intell 22, 329–342 (2009). doi: 10.1016/j.engappai.20
CrossRefGoogle Scholar
Xu, Z., Li, S., Chen, Q. and Hou, B.. MOPSO Based Multi-Objective Trajectory Planning for Robot Manipulators. In: 2nd International Conference on Information Science and Control Engineering, (2015) pp. 824–828.Google Scholar
Shi, X., Fang, H. and Guo, L., “Multi-Objective Optimal Trajectory Planning of Manipulators Based on Quintic NURBS,” In: 2016 IEEE International Conference on Mechatronics and Automation, (2016) pp. 759–765. doi:, 10.1109/ICMA.2016.7558658
Google Scholar
Abu-Dakka, F. J., Valero, F. J., Suner, J. L. and Mata, V., “A direct approach to solving trajectory planning problems using genetic algorithms with dynamics considerations in complex environments,” Robotica 33(3), 669–683 (2018).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).CrossRefGoogle Scholar
Rout, A., Mahanta, G. B., Bbvl, D. and Biswal, B. B., “Kinematic and dynamic optimal trajectory planning of industrial robot using improved multi-objective ant lion optimizer,” J Inst Eng India Ser:C 101(3), 559–569 (2020).CrossRefGoogle Scholar
Lan, J., Xie, Y., Liu, G. and Cao, M., “A multi-objective trajectory planning method for collaborative robot,” Electronics 9(5), 859 (2020). doi: 10.3390/electronics9050859.CrossRefGoogle Scholar
Wu, G., Zhao, W. and Zhang, X., “Optimum time-energy-jerk trajectory planning for serial robotic manipulators by reparameterized quintic NURBS curves,” Proceed Inst Mech Eng Part C: J Mech Eng Sci 235(19), 4382–4393 (2021). doi: 10.1177/0954406220969734.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 Cambridge University PressCrossRefGoogle 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).CrossRefGoogle Scholar
Shi, Q., Wang, Z., Ke, X., Zheng, Z., Zhou, Z., Wang, Z., Fan, Y., Lei, B. and Wu, P., “Trajectory optimization of wall-building robots using response surface and non-dominated sorting genetic algorithm III,” Automat Constr 155, 105035 (2023). doi: 10.1016/j.autcon.2023.105035.CrossRefGoogle Scholar
Tian, Y., Cheng, R., Zhang, X. and Jin, Y., “PlatEMO: A MATLAB platform for evolutionary multi-objective optimization,” IEEE Comput Intell Mag 12(4), 73–87 (2017). doi: 10.1109/MCI.2017.2742868.CrossRefGoogle Scholar
Blank, J. and Deb, K., “Pymoo: multi-objective optimization in python, “IEEE Access 8, 89497–89509 (2020). doi: 10.1109/ACCESS.2020.2990567.CrossRefGoogle Scholar
Coello, C., “Recent Trends in Evolutionary Multiobjective Optimization,” In: Evolutionary Multiobjective Optimization, Abraham, A., Jain, L. and Goldberg, R.eds.) (Springer, 2005) pp. 7–32.CrossRefGoogle Scholar
Zitzler, E., Deb, K. and Thiele, L., “Comparison of multiobjective evolutionary algorithms: Empirical results,” Evol Comput 8(2), 173–195 (2000).CrossRefGoogle ScholarPubMed
Sindhya, K., Miettinen, K. and Deb, K., “A hybrid framework for evolutionary multi-objective optimization,” IEEE Trans Evolu Comput 17(4), 495–511 (2013).CrossRefGoogle Scholar
Talbi, E.-G., “Hybrid metaheuristics for multi-objective optimization,” J Algor Comp Technol 9(1), 41–63 (2015).CrossRefGoogle Scholar
Alotto, P. and Capasso, G., “A deterministic multiobjective optimizer,” COMPEL-J Comput Math Electr Electron Eng 34(5), 1351–1363 (2015). doi: 10.1108/COMPEL-03-2015-0117.CrossRefGoogle Scholar
Berger, R., Bruns, M., Ehrmann, A., Haldar, A., Hafele, J., Hofmeister, B., Hübler, C. and Rolfes, R., “EngiO – object-oriented framework for engineering optimization,” Adv Eng Softw 153, 102959 (2021). doi: 10.1016/j.advengsoft.2020.102959.CrossRefGoogle Scholar
Tian, Y., Zhu, W., Zhang, X. and Jin, Y., “A practical tutorial on solving optimization problems via PlatEMO,” Neurocomputing 518, 190–205 (2023). doi: 10.1016/j.neucom.2022.10.075.CrossRefGoogle Scholar
Jaszkiewicz, A., “Genetic local search for multi-objective combinatorial optimization,” European J Oper Res 137(1), 50–71 (2002).CrossRefGoogle Scholar
Sindhya, K., Deb, K. and Miettinen, K., “A Local Search Based Evolutionary Multi-Objective Approach for Fast and Accurate Convergence,” In: Proc. 10th Parallel Problem Solving From Nature, (2008) pp. 815–824.Google Scholar
Sharma, S. and Kumar, V., “A comprehensive review on multi‐objective optimization techniques: Past, present and future,” Arch Comput Method E 29(7), 5605–5633 (2022). doi: 10.1007/s11831-022-09778-9.CrossRefGoogle Scholar
Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans Evolu Comput 6(2), 182–197 (2002). doi: 10.1109/4235.996017.CrossRefGoogle Scholar
Jain, H. and Deb, K., “An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach,” IEEE Trans Evolu Comput 18(4), 602–622 (2014). doi: 10.1109/TEVC.2013.2281534.CrossRefGoogle Scholar
Tian, Y., Zhang, T., Xiao, J., Zhang, X. and Jin, Y., “A coevolutionary framework for constrained multiobjective optimization problems,” IEEE Trans Evolu Comput 25(1), 102–116 (2021). doi: 10.1109/TEVC.2020.3004012.CrossRefGoogle Scholar
Sun, R., Zou, J., Liu, Y., Yang, S. and Zheng, J., “A multistage algorithm for solving multi-objective optimization problems with multi-constraints,” IEEE Trans Evolut Comput 27(5), 1207–1219 (2023). doi: 10.1109/TEVC.2022.3224600.CrossRefGoogle Scholar
Rao, S. S., “Engineering Optimization: Theory and Practice, 4th edn. (John Wiley & Sons, Inc., 2009).CrossRefGoogle Scholar
Messac, A.. Optimization in Practice with MATLAB® for Engineering Students and Professionals (Cambrdige University Press, 2015).CrossRefGoogle Scholar
Eichfelder, G.. Adaptive Scalarization Methods in Multiobjective Optimization (Springer-Verlag, 2008).CrossRefGoogle Scholar
Martins, J. R. R. A. and Ning, A.. Engineering Design Optimization (Cambrdige University Press, 2021).CrossRefGoogle Scholar
Custòdio, A. L., Madeira, J. F. A., Vaz, A. I. F. and Vicente, L. N., “Direct multisearch for multiobjective optimization,” SIAM J Optim 21(3), 1109–1140 (2011). doi: 10.1137/10079731X.CrossRefGoogle Scholar
Hooke, R. and Jeeves, T. A., “`` Direct Search” solution of numerical and statistical problems,” J ACM 8(2), 212–229 (1961). doi: 10.1145/321062.321069.CrossRefGoogle Scholar
Corke, P., Roboitics Vision and Control Fundamental Algorithms in MATLAB (Springer Tracts in Advanced Robotics 2nd edn, Springer, 2017).Google Scholar