Chinese Journal of Mechanical Engineering >

2022 , Vol. 35 >Issue 1: 7 - 7

DOI: https://doi.org/10.1186/s10033-021-00669-x

Mechanism and Robotics

Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

  • Zesheng Wang ,
  • Yanbiao Li ,
  • Kun Shuai ,
  • Wentao Zhu ,
  • Bo Chen ,
  • Ke Chen
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  • 1. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310023, China;
    2. Key Laboratory of E & M, Ministry of Education & Zhejiang Province, Zhejiang University of Technology, Hangzhou, 310032, China

收稿日期: 2020-11-27

  修回日期: 2021-10-10

  网络出版日期: 2022-06-30

基金资助

Supported by the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists (Grant No. LR18E050003); the National Natural Science Foundation of China (Grant Nos. 51975523, 51905481); Natural Science Foundation of Zhejiang Province (Grant No. LY22E050012); the Students in Zhejiang Province Science and Technology Innovation Plan (Xinmiao Talents Program) (Grant No. 2020R403054); and the China Postdoctoral Science Foundation (Grant No. 2020M671784)

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Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

  • Zesheng Wang ,
  • Yanbiao Li ,
  • Kun Shuai ,
  • Wentao Zhu ,
  • Bo Chen ,
  • Ke Chen
Expand
  • 1. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310023, China;
    2. Key Laboratory of E & M, Ministry of Education & Zhejiang Province, Zhejiang University of Technology, Hangzhou, 310032, China

Received date: 2020-11-27

  Revised date: 2021-10-10

  Online published: 2022-06-30

Supported by

Supported by the Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists (Grant No. LR18E050003); the National Natural Science Foundation of China (Grant Nos. 51975523, 51905481); Natural Science Foundation of Zhejiang Province (Grant No. LY22E050012); the Students in Zhejiang Province Science and Technology Innovation Plan (Xinmiao Talents Program) (Grant No. 2020R403054); and the China Postdoctoral Science Foundation (Grant No. 2020M671784)

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摘要

Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult to find a better desired trajectory. In this paper, a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) is proposed. Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves. Then, an INSGA-II, by introducing three genetic operators: ranking group selection (RGS), direction-based crossover (DBX) and adaptive precision-controllable mutation (APCM), is developed to optimize travelling time and torque fluctuation. Inverted generational distance, hypervolume and optimizer overhead are selected to evaluate the convergence, diversity and computational effort of algorithms. The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory. Taking a serial-parallel hybrid manipulator as instance, the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method. The effectiveness and practicability of the proposed method are verified by simulation results. This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

关键词： Hybrid manipulator; Bezier curve; Improved optimization algorithm; Trajectory planning; Multi-objective optimization

本文引用格式

Zesheng Wang , Yanbiao Li , Kun Shuai , Wentao Zhu , Bo Chen , Ke Chen . Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm[J]. Chinese Journal of Mechanical Engineering, 2022 , 35(1) : 7 -7 . DOI: 10.1186/s10033-021-00669-x

Abstract

Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult to find a better desired trajectory. In this paper, a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) is proposed. Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves. Then, an INSGA-II, by introducing three genetic operators: ranking group selection (RGS), direction-based crossover (DBX) and adaptive precision-controllable mutation (APCM), is developed to optimize travelling time and torque fluctuation. Inverted generational distance, hypervolume and optimizer overhead are selected to evaluate the convergence, diversity and computational effort of algorithms. The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory. Taking a serial-parallel hybrid manipulator as instance, the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method. The effectiveness and practicability of the proposed method are verified by simulation results. This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Key words： Hybrid manipulator; Bezier curve; Improved optimization algorithm; Trajectory planning; Multi-objective optimization

参考文献

[1] J J Kim, J J Lee. Trajectory optimization with particle swarm optimization for manipulator motion planning. IEEE Transactions on Industrial Informatics, 2015, 11(3):620-631.
[2] H Wang, H Wang, J Huang, et al. Smooth point-to-point trajectory planning for industrial robots with kinematical constraints based on high-order polynomial curve. Mechanism and Machine Theory, 2019, 139:284-293.
[3] H Liu, X Lai, W Wu. Time-optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints. Robotics and Computer-Integrated Manufacturing, 2013, 29(2):309-317.
[4] X Shi, H Fang, L Guo. Multi-objective optimal trajectory planning of manipulators based on quintic NURBS. 2016 IEEE International Conference on Mechatronics and Automation. Harbin, China, August, 2016:759-765.
[5] Ü Dinçer, M Çevik. Improved trajectory planning of an industrial parallel mechanism by a composite polynomial consisting of Bezier curves and cubic polynomials. Mechanism and Machine Theory, 2019, 132:248-263.
[6] A Gasparetto, V Zanotto. A new method for smooth trajectory planning of robot manipulators. Mechanism and Machine Theory, 2007, 42 (4):455-471.
[7] K X Ba, Y H Song, B Yu, et al. Kinematics correction algorithm for the LHDS of a legged robot with semi-cylindrical foot end based on V-DOF. Mechanical Systems and Signal Processing, 167, 2022:108566.
[8] B Chen, D R Gao, Y B Li, et al. Investigation of the droplet characteristics and size distribution during the collaborative atomization process of a twin-fluid nozzle. The International Journal of Advanced Manufacturing Technology, 2020, 107(3-4):1625-1639.
[9] L F Tian, C Curtis. An effective robot trajectory planning method using a genetic algorithm. Mechatronics, 2004, 14(5):455-470.
[10] H I Lin. A fast and unified method to find a minimum-jerk robot joint trajectory using particle swarm optimization. Journal of Intelligent & Robotic Systems, 2014, 75 (3-4):379-392.
[11] J S Huang, P F Hu, K Y Zeng, et al. Optimal time-jerk trajectory planning for industrial robots. Mechanism and Machine Theory, 2018, 121:530-544.
[12] P Huang, G Liu, J Yuan, et al. Multi-objective optimal trajectory planning of space robot using particle swarm optimization. International Symposium on Neural Networks. Berlin, Heidelberg, 2008:171-179.
[13] M da Graça Marcos, J T Machado, T P Azevedo-Perdicoúlis. A multi-objective approach for the motion planning of redundant manipulators. Applied Soft Computing, 2012, 12(2):589-599.
[14] R Saravanan, S Ramabalan, C Balamurugan, et al. Evolutionary trajectory planning for an industrial robot. International Journal of Automation and Computing, 2010, 7(2):190-198.
[15] D Chen, S Li, J Wang, et al. A multi-objective trajectory planning method based on the improved immune clonal selection algorithm. Robotics and Computer-Integrated Manufacturing, 2019, 59:431-442.
[16] S F Saramago, V S Junior. Optimal trajectory planning of robot manipulators in the presence of moving obstacles. Mechanism and Machine Theory, 2000, 35(8):1079-1094.
[17] M Benzaoui, H Chekireb, M Tadjine, et al. Trajectory tracking with obstacle avoidance of redundant manipulator based on fuzzy inference systems. Neurocomputing, 2016, 196:23-30.
[18] J Garrido, W Yu, X O Li. Robot trajectory generation using modified hidden Markov model and Lloyd's algorithm in joint space. Engineering Applications of Artificial Intelligence, 2016, 53:32-40.
[19] A Reiter, A Müller, H Gattringer. On higher order inverse kinematics methods in time-optimal trajectory planning for kinematically redundant manipulators. IEEE Transactions on Industrial Informatics, 2018, 14(4):1681-1690.
[20] Y Fang, J Hu, W Liu, et al. Smooth and time-optimal S-curve trajectory planning for automated robots and machines. Mechanism and Machine Theory, 2019, 137:127-153.
[21] Y B Li, L Wang, B Chen, et al. Optimization of dynamic load distribution of a serial-parallel hybrid humanoid arm. Mechanism and Machine Theory, 2020, 149:103792.
[22] Y B Li, Z S Wang, P Sun, et al. Dynamic load distribution optimization for a 4-DOF redundant and series-parallel hybrid humanoid arm. Journal of Mechanical Engineering, 2020, 56(9):45-54. (in Chinese)
[23] N Srinivasan, K Deb. Multi-objective function optimisation using non-dominated sorting genetic algorithm. Evolutionary Compution, 1994, 2(3):221-248.
[24] K Deb, A Pratap, S Agarwal, et al. A fast and elitist multiobjective genetic algorithm:NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[25] K Deb, H Jain. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I:solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 2013, 18(4):577-601.
[26] Y Song, F Wang, X Chen. An improved genetic algorithm for numerical function optimization. Applied Intelligence, 2019, 49(5):1880-1902.
[27] K Zhang, Z W Xu, S L Xie, et al. Evolution strategy-based many-objective evolutionary algorithm through vector equilibrium. IEEE Transactions on Cybernetics, 2021, 51(11):5455-5467.
[28] X Cai, Y Xiao, M Li, et al. A grid-based inverted generational distance for multi/many-objective optimization. IEEE Transactions on Evolutionary Computation, 2020, 25(1):21-34.
[29] L H Wu, Y N Wang, X F Yuan, et al. Environmental/economic power dispatch problem using multi-objective differential evolution algorithm. Electric Power Systems Research, 2010, 80(9):1171-1181.
[30] M Asafuddoula, T Ray, R Sarker. A decomposition-based evolutionary algorithm for many objective optimization. IEEE Transactions on Evolutionary Computation, 2015, 19(3):445-460.
[31] Z S Wang, Y B Li, Y Q Luo, et al. Dynamic analysis of a 7-DOF redundant and hybrid mechanical arm. Journal of Zhejiang University, 2020, 54(8):1505-1515. (in Chinese)
[32] Z S Wang, Y B Li, P Sun, et al. A multi-objective approach for the trajectory planning of a 7-DOF serial-parallel hybrid humanoid arm. Mechanism and Machine Theory, 2021, 165:104423.
[33] Z Wang, Z Wang, W Liu, et al. A study on workspace, boundary workspace analysis and workpiece positioning for parallel machine tools. Mechanism and Machine Theory, 2001, 36(5):605-622.
[34] K Deb, H Jain. Handling many-objective problems using an improved NSGA-II procedure. Proceedings of the IEEE Congress on Evolutionary Computation, 2012:1-8.
[35] N Panagant, S Bureerat, K Tai. A novel self-adaptive hybrid multi-objective meta-heuristic for reliability design of trusses with simultaneous topology, shape and sizing optimisation design variables. Structural and Multidisciplinary Optimization, 2019, 60(5):1937-1955.
[36] S J Tsai, T Y Sun, C C Liu, et al. An improved multi-objective particle swarm optimizer for multi-objective problems. Expert Systems with Applications, 2010, 37(8):5872-5886.
[37] L R Farias, A F Araújol. Many-objective evolutionary algorithm based on decomposition with random and adaptive weights. 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC). IEEE, 2019:3746-3751.
[38] W Gong, Z Cai. An improved multiobjective differential evolution based on Pareto-adaptive ε-dominance and orthogonal design. European Journal of Operational Research, 2009, 198(2):576-601.
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