基于调整步长牛顿法的Stewart并联机构位置正解

强红宾; 王力航; 姜雪

doi:10.3788/OPE.20182612.2982

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基于调整步长牛顿法的Stewart并联机构位置正解

微纳技术与精密机械 | 更新时间：2020-07-05

- 基于调整步长牛顿法的Stewart并联机构位置正解
- Forward kinematics of Stewart parallel manipulator based on step-adjusting Newton method
- 光学精密工程 2018年26卷第12期页码：2982-2990
- 作者机构：
  
  1.燕山大学河北省重型机械流体动力传输与控制重点实验室, 河北秦皇岛 066004
  2.燕山大学先进锻压成形技术与科学教育部重点实验室, 河北秦皇岛 066004
- 作者简介：
  
  [ "强红宾(1991-), 男, 河北石家庄人, 博士研究生, 2014年于燕山大学获得学士学位, 主要从事并联机构优化及协同控制的研究。E-mail:hbqiang927@163.com" ]
- 基金信息：
  
  国家自然科学基金资助项目(No.51875499)
- DOI：10.3788/OPE.20182612.2982
  中图分类号： TP242
- 收稿日期：2018-04-23，
  
  录用日期：2018-6-14，
  
  纸质出版日期：2018-12-25
- 稿件说明：
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强红宾, 王力航, 姜雪. 基于调整步长牛顿法的Stewart并联机构位置正解[J]. 光学精密工程, 2018,26(12):2982-2990.

Hong-bin QIANG, Li-hang WANG, Xue JIANG. Forward kinematics of Stewart parallel manipulator based on step-adjusting Newton method[J]. Optics and precision engineering, 2018, 26(12): 2982-2990.
强红宾, 王力航, 姜雪. 基于调整步长牛顿法的Stewart并联机构位置正解[J]. 光学精密工程, 2018,26(12):2982-2990. DOI： 10.3788/OPE.20182612.2982.

Hong-bin QIANG, Li-hang WANG, Xue JIANG. Forward kinematics of Stewart parallel manipulator based on step-adjusting Newton method[J]. Optics and precision engineering, 2018, 26(12): 2982-2990. DOI： 10.3788/OPE.20182612.2982.

摘要

针对采用牛顿或拟牛顿迭代算法求解Stewart并联机构接近奇异位姿的位置正解时存在计算结果不收敛以及采用牛顿下山迭代算法求解时间较长的问题，提出了将调整步长牛顿法应用于并联机构位置正解。首先设计基于调整步长牛顿法的Stewart并联机构位置正解流程；然后，采用遗传算法以步长矩阵初值及等比参数为变量，以Stewart并联机构64种极限位姿正解所需迭代步数为目标，得到步长矩阵初值及等比参数最优值。通过数值算例，设置机构杆长绝对误差为0.01 mm，对64种极限位姿进行正解，牛顿法与拟牛顿法共6种位姿正解不收敛；牛顿下山法10种位姿正解时间大于2.0 ms；调整步长牛顿法正解时间均小于2.0 ms。调整步长牛顿法为Stewart并联机构位置正解的实时应用提供了理论指导。

Abstract

Forward kinematics of the near singular position of the Stewart parallel manipulator based on the Newton method or quasi-Newton method are not converge; Newton downhill method is time-consuming

sometimes. To resolve the situation

a method of applying the step-adjusting Newton method to a parallel manipulator is proposed. Firstly

the process of forward kinematics of the Stewart parallel manipulator based on the step-adjusting Newton method was designed. Then

the fewest iterative steps in the forward kinematics of sixty-four kinds of utmost poses was used as the objective function. The initial values of the step matrix and geometric parameters were taken as design variables by genetic algorithm to obtain the optimal values. Numerical examples show that when the absolute error of the rod length was set as 0.01 mm

in solving the forward kinematics of sixty-four kinds of utmost poses

the Newton method or quasi-Newton method did not converge on six kinds of utmost poses. The Newton downhill method takes longer than 2.0 ms on ten kinds of utmost poses

while the time taken by the step-adjusting Newton method was less than 2.0 ms. The step-adjusting Newton method provides theoretical guidance for the forward kinematics of the Stewart parallel manipulator in real-time occasions.

关键词

Keywords

references

黄真, 赵永生, 赵铁石.高等空间机构学[M].北京:高等教育出版社, 2006.

HUANG ZH, ZHAO Y SH, ZHAO T SH.Advanced Spatial Mechanism[M].Beijing:High Education Press, 2006.(in Chinese)

HUANG X, LIAO Q, WEI S.Closed-form forward kinematics for a symmetrical 6-6 Stewart platform using algebraic elimination[J].Mechanism and Machine Theory, 2010, 45(2):327-334.

胡鹏浩, 李松原.3-PSS并联机构正解及其在坐标测量机中的应用[J].光学精密工程, 2012, 20(4):782-788.

HU P H, LI S Y.Kinematic solution of 3-PSS parallel mechanism and its application in parallel CMM[J].Opt.Precision Eng., 2012, 20(4):782-788.(in Chinese)

赵磊, 梁超, 张德福, 等.基于3-RRR结构的光学元件柔顺微动调整机构的位姿正解[J].光学精密工程, 2016, 24(6):1373-1381.

ZHAO L, LIANG CH, ZHANG D F, et al..forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment[J].Opt.Precision Eng., 2016, 24(6):1373-1381.(in Chinese)

刘得军, 刘彩平, 韦荣方.基于粒子群算法的6-DOF并联坐标测量机的测量建模[J].光学精密工程, 2008, 16(1):76-81.

LIU D J, LIU C P, WEI R F.Measurement modeling for 6-DOF parallel-link coordinate measuring machine based on particle swarm optimization[J].Opt.Precision Eng., 2008, 16(1):76-81.(in Chinese)

吴小勇, 谢志江, 宋代平, 等.基于改进蚁群算法的3-PPR并联机构位置正解研究[J].农业机械学报, 2015, 46(7):339-344.

WU X Y, XIE ZH J, SONG D P, et al..Forward kinematics of 3-PPR parallel mechanism based on improved ant colony algorithm[J].Transaction of the Chinese Society for Agricultural Machinery, 2015, 46(7):339-344.(in Chinese)

毛冰滟, 谢志江, 吴小勇, 等.基于引导人工蜂群算法的3-RPS并联机构正解优化[J].农业机械学报, 2017, 48(1):339-345.

MAO B Y, XIE ZH J, WU X Y, et al..Forward kinematics optimization of 3-RPS parallel manipulator based on global-best artificial bee colony algorithm[J].Transaction of the Chinese Society for Agricultural Machinery, 2017, 48(1):339-345.(in Chinese)

董彦良, 吴盛林.一种实用的6-6 Stewart平台的实时位置正解法[J].哈尔滨工业大学学报, 2002, 34(1):116-119.

DONG Y L, WU SH L.A hybrid method to solve forward kinematics of general 6-6 stewart platform[J].Journal of Harbin Institute of Technology, 2002, 34(1):116-119.(in Chinese)

MAHMOODI A, SAYADI A, MENHAJ M B.Solution of forward kinematics in Stewart platform using six rotary sensors on joints of three legs[J].Advanced Robotics, 2013, 28(1):27-37.

刘艳梨, 程世利, 蒋素荣, 等.带位移传感器的6-UPS并联机构运动学正解[J].机械工程学报, 2018, 54(5):1-7.

LIU Y L, CHENG SH L, JIANG S R, et al..Forward kinematics of 6-UPS parallel manipulators with one displacement sensor[J].Journal of Mechanical Engineering, 2018, 54(5):1-7.(in Chinese)

NGUYEN C C, ZHOU Z L, ANTRAZI S S, et al..Efficient computation of forward kinematics and Jacobian matrix of a Stewart platform-based manipulator[J].IEEE Proceedings of IEEE, 2002(2):869-874.

卢启鹏, 李勇军, 彭忠琦, 等.六杆并联机构运动学正解研究及其在同步辐射光束线中的应用[J].光学精密工程, 2008, 16(10):1874-1879.

LU Q P, LI Y J, PENG ZH Q, et al..Forward kinematics of six-bar parallel mechanism and its applications in synchrotron radiation beam-line[J].Opt.Precision Eng., 2008, 674(10):8-14.(in Chinese)

贺新升, 高春甫, 王彬, 等.太阳自动跟踪机构的设计和位姿分析[J].光学精密工程, 2012, 20(5):1048-1054.

SHENG H X, GAO CH, WANG B, et al..Design and positional posture analysis of parallel sun auto-tracking mechanism[J].Opt.Precision Eng., 2012, 20(5):1048-1054.(in Chinese)

耿明超, 赵铁石, 王唱, 等.基于拟Newton法的并联机构位置正解[J].机械工程学报, 2015, 51(9):28-36.

GENG M CH, ZHAO T SH, WANG CH, et al..Direct position analysis of parallel mechanism based on quasi-newton method[J].Journal of Mechanical Engineering, 2015, 51(9):28-36.(in Chinese)

刘停战, 刘伟, 何颖.调整步长牛顿法[J].中国传媒大学学报(自然科学版), 2012, 19(1):8-10.

LIU T ZH, LIU W, HE Y.Step-adjusting newton method[J].Journal of Communication University of China:Natural Science Version, 2012, 19(1):8-10.(in Chinese)

马建明.飞行模拟器液压Stewart平台奇异位形分析及其解决方法研究[D].哈尔滨: 哈尔滨工业大学, 2010.

MA J M. Analysis of Singular Configuration and Research of Its Solving Method of the Hydraulic Stewart Platform of Flight Simulator [D].Harbin: Harbin Institute of Technology, 2010(in Chinese)

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