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基于唯一域方法的機(jī)器人逆向運(yùn)動(dòng)學(xué)求解
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國(guó)家自然科學(xué)基金項(xiàng)目(11602082)和湖南省自然科學(xué)基金項(xiàng)目(2018JJ4079)


Solution of Inverse Kinematics of Robots Based on Unique Domain Method
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    摘要:

    針對(duì)機(jī)器人的逆運(yùn)動(dòng)學(xué)多解問(wèn)題,,提出一種基于唯一域求解的新方法,。利用機(jī)器人的雅可比矩陣行列式等于0確定的邊界,將機(jī)器人的關(guān)節(jié)空間劃分為與逆運(yùn)動(dòng)學(xué)多解數(shù)目一致的唯一域;各唯一域的邊界作為約束條件,,將唯一域內(nèi)的逆運(yùn)動(dòng)學(xué)求解轉(zhuǎn)換為CMA-ES算法的有約束尋優(yōu);利用佳點(diǎn)集均勻分布性的特點(diǎn),,優(yōu)化唯一域中CMA-ES算法求解的初始均值點(diǎn),。通過(guò)求6R工業(yè)機(jī)器人的逆運(yùn)動(dòng)學(xué)多解,闡述了該方法的應(yīng)用,,并以機(jī)械臂逆解數(shù)值法為參照,,在錢(qián)江一號(hào)6R工業(yè)機(jī)器人和KUKA仿人機(jī)械臂上進(jìn)行了2個(gè)仿真實(shí)驗(yàn)對(duì)比。仿真結(jié)果表明,,本文所提方法在滿足精度要求的前提下,,平均求解時(shí)間更短。實(shí)驗(yàn)1中,,CMA-ES算法求解一組逆解的平均速度約為5.1ms/次,,數(shù)值法求解的平均速度約為7.5ms/次;實(shí)驗(yàn)2中,一組逆解的求解平均速度約為18.9ms/次,,數(shù)值法求解的平均速度約為54.8ms/次,;CMA-ES算法對(duì)兩款機(jī)器人的位置跟蹤精度均穩(wěn)定在10-6mm數(shù)量級(jí)。

    Abstract:

    The inverse robot kinematics problem has been extensively studied by many workers, but still some problems related to the complexity and strong nonlinear of the inverse kinematics process need suitable heuristic and adhoc techniques and simplifications. A novel method based on uniqueness domains notion was proposed. With using the boundary confirmed by robot’s Jacobian matrix determinant equal to zero, the joint space of the robot was divided into uniqueness domains with the same number of solutions as the inverse kinematics, and the boundary of each uniqueness domain was used as a constraint condition. Then the inverse kinematics solution in the uniqueness domain was transformed into the constrained optimization of the CMA-ES algorithm, the initial mean points of the CMA-ES algorithm in the uniqueness domain were optimized by using the characteristics of the uniform distribution of the good point set. The application of the presented method was described in detail by solving the inverse kinematics multiple solution of the 6R industrial robot, and comparing with the numerical method on Qianjiang No.1 industrial robot and the KUKA humanoid manipulator. The simulation results showed that under the precondition of accuracy requirement, the proposed method had a faster solution speed. For the industrial 6R robot, the average solution time of CMA-ES algorithm was about 5.1ms/time, and that of numerical method was about 7.5ms/time, and KUKA humanoid manipulator, the average solution time of inverse solutions was about 18.9ms/time, and the average solution time of numerical method was about 54.8ms/time. The presented CMA-ES algorithm stabilized the position tracking accuracy of both robots at 10-6mm level.

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李光,肖帆,楊加超,章曉峰,馬祺杰.基于唯一域方法的機(jī)器人逆向運(yùn)動(dòng)學(xué)求解[J].農(nóng)業(yè)機(jī)械學(xué)報(bào),2019,50(10):386-394. LI Guang, XIAO Fan, YANG Jiachao, ZHANG Xiaofeng, MA Qijie. Solution of Inverse Kinematics of Robots Based on Unique Domain Method[J]. Transactions of the Chinese Society for Agricultural Machinery,2019,50(10):386-394.

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  • 收稿日期:2019-03-19
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  • 在線發(fā)布日期: 2019-10-10
  • 出版日期: 2019-10-10
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