基于MATLAB Robotics Toolbox的四足机器人轨迹仿真与优化

doi:10.16180/j.cnki.issn1007-7820.2020.09.006

摘要/Abstract

摘要：

仿生四足机器人的足端轨迹对其运动状况具有重要作用。MATLAB Robotics Toolbox可用于机器人的建模、求正反解、末端轨迹规划等仿真与分析工作。四足机器人末端只有3个自由度的结构,通过MATLAB Robotics Toolbox来求解与仿真存在一定的缺陷。文中通过研究该工具箱的底层函数,发现出问题的原因是其中的“ikine”函数不适用。文中通过改用反解公式来代替"ikine"函数,对该工具箱进行有针对性的二次开发。同时,增加优化算法对逆向运动学的多解问题按照角度变化最小原则进行优选。对设定轨迹的实时动态仿真结果显示其行走的过程自然平缓,关节转动特性曲线在合理范围内,证明了该优化算法的有效性与合理性。

关键词: 仿生, 四足机器人, 仿真, 轨迹优化, 运动学, 机器人工具箱

Abstract:

The foot end trajectory of the bionic quadruped robot plays an important role in its movement. MATLAB Robotics Toolbox has been used for modeling, solving the forward and reverse solutions and trajectory planning. For a structure such as a quadruped robot with only 3 DOF at the end, there are certain defects in the solution and simulation by this tool. In this study, by exploring the underlying function of the toolbox, the reason for the problem is that the “ikine” function was not applicable. The toolbox is targeted for secondary development by replacing the "ikine" function with the inverse solution formula. At the same time, the problem of increasing the multi-solution of the inverse kinematics of the optimization algorithm is optimized according to the principle of minimum angle change. The real-time dynamic simulation results of the set trajectory shows that the walking process is naturally smooth, and the joint rotation characteristic curve is within a reasonable range, which verifies the effectiveness and rationality of the optimization algorithm.

Key words: bionic, quadruped robot, simulation, trajectory optimization, kinematics, robotics toolbox

中图分类号:

U461

陈明方,张凯翔,陈久朋,熊彬洲,李奇,姚国一,李鹏宇. 基于MATLAB Robotics Toolbox的四足机器人轨迹仿真与优化[J]. 电子科技, 2020, 33(9): 31-37.

CHEN Mingfang,ZHANG Kaixiang,CHEN Jiupeng,XIONG Bingzhou,LI Qi,YAO Guoyi,LI Pengyu. Simulation and Optimization of Quadruped Robot Trajectory Based on MATLAB Robotics Toolbox[J]. Electronic Science and Technology, 2020, 33(9): 31-37.

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参考文献 19

[1]	丁良宏. BigDog四足机器人关键技术分析[J]. 机械工程学报, 2015,51(7):1-23.
	Ding Hongliang. Key technology analysis of BigDog quadruped robot[J]. Journal of Mechanical Engineering, 2015,51(7):1-23.
[2]	Li Z, Ge Q, Ye W, et al. Dynamic balance optimization and control of quadruped robot systems with flexible joints[J]. IEEE Transactions on Systems,Manand Cybernetics:Systems, 2015(7):1-14.
[3]	Lei J, Yu H, Wang T. Dynamic bending of bionic flexible body driven by Pneumatic Artificial Muscles (PAMs) for spinning gait of quadruped robot[J]. Journal of Mechanical Engineering, 2016,29(1):11-20.
[4]	周坤. 面向未知复杂地形的四足机器人运动规划方法研究[D]. 杭州:浙江大学, 2017.
	Zhou Kun. Research on motion planning method for quadratic robots walking on unknown rough terrain[D]. Hangzhou:Zhejiang University, 2017.
[5]	李宏凯, 李志, 郭朝龙, 等. 基于四足机器人稳定性的对角步态规划[J]. 机械设计, 2016(1):64-69.
	Li Hongkai, Li Zhi, Guo Chaolong, et al. Gait planning of trotting based on quadruped robot's stability[J]. Journal of Machine Design, 2016(1):64-69.
[6]	Raibert M, Blankespoor K, Nelson G, et al. Bigdog, the rough-terrain quadruped robot[C]. Seoul:The Seventeenth International Federation of Automatic Control World Congress, 2008.
[7]	Wooden D, Malchano M, Blankespoor K, et al. Autonomous navigation for BigDog[C]. Anchorage:IEEE International Conference on Robotics and Automation, 2010.
[8]	Semini C, Tsagarakis N G, Guglielmino E, et al. Design of HyQ-a hydraulically and electrically actuated quadruped robot[J]. Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering, 2011,225(6):831-849. doi: 10.1177/0959651811402275
[9]	Fukui T, Fujisawa H, Otaka K, et al. Autonomous gait transition and galloping over unperceived obstacles of a quadruped robot with CPG modulated by vestibular feedback[J]. Robotics and Autonomous Systems, 2019,11(1):1-19. doi: 10.1016/0921-8890(93)90002-T
[10]	王立鹏, 王军政, 汪首坤, 等. 基于足端轨迹规划算法的液压四足机器人步态控制策略[J]. 机械工程学报, 2013,49(1):39-44.
	Wang Lipeng, Wang Junzheng, Wang Shoukun, et al. Strategy of foot trajectory generation for hydraulic quadruped robots gait planning[J]. Journal of Mechanical Engineering, 2013,49(1):39-44.
[11]	John J Craig. 机器人学导论[M].3版.贠超,译. 北京: 机械工业出版社, 2006.
	John J Craig. Introduction to robotics[M].3rd Edition.Translated by Yuan Chao. Beijing: Mechanical Industry Press, 2006.
[12]	高艺, 马国庆, 于正林, 等. 一种六自由度工业机器人运动学分析及三维可视化仿真[J]. 中国机械工程, 2016,27(13):1726-1731.
	Gao Yi, Ma Guoqing, Yu Zhenglin, et al. Kinematicsanalysis of an 6-DOF industrial robot and its 3D visualization simulation[J]. China Mechanical Engineering, 2016,27(13):1726-1731.
[13]	谢斌, 蔡自兴. 基于MATLAB Robotics Toolbox的机器人学仿真实验教学[J]. 计算机教育, 2010,19(10):140-143.
	Xie Bin, Cai Zixing. Simulation experimental teaching of robotics based on MATLAB Robotics Toolbox[J]. Computer Education, 2010,19(10):140-143.
[14]	Kulić D, Croft E A. Real-time safety for human-robot interaction[J]. Robotics and Autonomous Systems, 2006,54(1):1-12. doi: 10.1016/j.robot.2005.10.005
[15]	陆佳皓, 平雪良, 李朝阳. 基于MATLAB Robotic Toolbox的关节型机器人运动仿真研究[J]. 机床与液压, 2017,45(17):60-62.
	Lu Jiahao, Ping Xueliang, Li Zhaoyang. Research on simulation of revolute robot motion based on MATLAB Robotics Toolbox[J]. Machine Tool & Hydraulics, 2017,45(17):60-62.
[16]	李瑞峰, 马国庆. 基于MATLAB仿人机器人双臂运动特性分析[J]. 华中科技大学学报(自然科学版), 2013,41(z1) : 343-347.
	Li Ruifeng, Ma Guoqing. Dual-arm kinematic characteristics analysis of humanoid robot based on MATLAB[J]. Journal of Huazhong University of Science and Technology(Natural Science Edition), 2013,41(z1):343-347.
[17]	Chen Jiupeng, San Hongjun, Wu Xing, et al. Structural design and characteristic analysis for a 4-degree-of-freedom parallel manipulator[J]. Advances in Mechanical Engineering, 2019,11(5):1-12.
[18]	宋修洋, 陈劲杰, 余洁. 基于D-H方法建立抛光机器人的运动学模型[J]. 电子科技, 2017,30(6):50-53.
	Song Xiuyang, Chen Jinjie, Yu Jie. Polishing robot kinematics model based on the D-H method[J]. Electronic Science and Technology, 2017,30(6):50-53.
[19]	于凌涛, 王文杰, 王正雨, 等. 一类不满足 Pieper 准则的机器人逆运动学解析解获取方法[J]. 机器人, 2016,38(4):486-494. doi: 10.13973/j.cnki.robot.2016.0486
	Yu Lingtao, Wang Wenjie, Wang Zhengyu, et al. Acquisition method of inverse kinematics analytical solutions for a class of robots dissatisfying the Pieper criterion[J]. Robot, 2016,38(4):486-494. doi: 10.13973/j.cnki.robot.2016.0486

轨迹点	θ₂/rad	换算角度/(°)	θ₃/rad	换算角度/(°)
点1	-175.348 3	33.282 5	582.640 2	82.824 4
点2	-169.070 6	32.968 2	563.813 4	84.128 3
点3	-31.949 0	-30.542 9	208.954 5	92.211 0
点4	-63.332 7	-28.696 4	347.092 7	86.946 8
点5	0.529 8	30.355 3	36.281 6	98.782 6

轨迹点	θ₂ /rad	换算角度/(°)	θ₃/rad	换算角度/(°)
点1	-0.562 7	-32.240 3	1.696 0	97.173 6
点2	-0.557 4	-31.936 7	1.673 3	95.873 0
点3	0.567 9	32.538 3	-0.508 5	-29.134 9
点4	-0.500 9	-28.699 5	1.517 5	86.946 3
点5	-0.465 4	-26.665 5	1.417 5	81.216 8

轨迹点	θ₂ /rad	换算角度/(°)	θ₃/rad	换算角度/(°)
点1	-0.562 7	-32.240 3	1.696 0	97.173 6
点2	-0.557 4	-31.936 7	1.673 3	95.873 0
点3	-0.533 0	-30.538 7	1.609 4	92.211 8
点4	-0.500 9	-28.699 5	1.517 5	86.946 3
点5	-0.465 4	-26.665 5	1.417 5	81.216 8