基于旋量理论和代数消元6R机器人逆解算法  

Inverse kinematic solution algorithm of 6R robots based on screw theory and algebraic elimination

作　　者：赵荣波 施智平[1] 关永[1] 邵振洲 王国辉[1] 吴立峰 ZHAO Rong-bo;SHI Zhi-ping;GUAN Yong;SHAO Zhen-zhou;WANG Guo-hui;WU Li-feng(College of Information Engineering,Capital Normal University,Beijing 100048,China)

机构地区：[1]首都师范大学信息工程学院,北京100048

出　　处：《传感器与微系统》2018年第12期114-117,121,共5页Transducer and Microsystem Technologies

基　　金：国家自然科学基金资助项目(61572331;61472468;61602325;61373034);国家科技支撑计划资助项目(2015BAF13B01);北京市科委项目(LJ201607);北京市教委科研基地建设项目(TJSHG201510028010);北京市属高等学校创新团队建设与教师职业发展计划资助项目(IDHT20150507);国际科技合作计划资助项目(2011DFG13000)

摘　　要：为了解决6自由度后3关节轴线相交于一点的串联机器人逆运动学问题,采用指数积(POE)方法建立运动学模型,并采用几何、代数方法和Paden-Kahan子问题进行逆运动学求解。几何方法获得前3关节运动轨迹的交点,将求解转换成已知的Paden-Kahan子问题,使几何意义更加清晰、直观,且大大简化了计算。采用代数消元法MATLAB求解第4,5关节,减少了人工计算,有效避免了由复杂计算产生的错误。最终,得到了1组封闭的逆运动学的解。通过实验计算出逆解最大位姿误差为10-12数量级,证明了提出的算法具有很高的精度,验证了算法的正确性。To solve the inverse kinematic problem of the serial robots with 6 degrees of freedom (DOF)whose axes of the last three joints intersect at a point,a solution algorithm is proposed.This algorithm adopts the product of exponentials (POE)method to establish the kinematic model,and the inverse kinematics are solved by adopting geometric and algebraic methods combined with the Paden-Kahan sub-problem.The application of geometric method is to obtain the points of intersection of motion trajectory of the first three joints,and then the solution is converted into the known Paden-Kahan sub-problem,which makes the geometric significance more clearer,more intuitive and greatly simplifies the calculation.Algebraic elimination method is used to cope with the fourth and fifth joints,which reduces the manual calculation by employing MATLAB and effectively avoids the error caused by complex calculations.Finally,a closed-form solution of inverse kinematics is determined.Correctness of proposed algorithm is validated by experiment the maximum pose error is calculated in the order of 10^-12 magnitude,which is demonstrated to possess an extremely high precision.

关 键 词：旋量理论 指数积 Paden—Kahan子问题 逆运动学 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]