结合旋量理论和代数方法的六自由度机械臂逆运动学求解算法

针对六自由度且具有相互平行的3个相邻关节轴的串联式机械臂逆运动学问题,提出一种结合旋量理论与代数方法的逆运动学求解方法。首先,通过旋量理论建立运动学模型,利用Paden-Kahan第1类子问题求解第1关节角度;其次,采用欧拉角理论,通过代数方法求解第5、6关节角度;最后,再次利用Paden-Kahan第1类子问题求解第2、3、4关节角度。以UR5协作机械臂为例,计算逆运动学得出8组解,其中逆解的最大位姿误差为10~(-15)数量级,证明了提出的逆运动学求解算法的准确性。

Inverse Kinematic Solution Algorithm of 6R Robot Arm With Combination of Screw Theory and Algebraic Methods

According to the inverse kinematic problem of a 6 degrees of freedom serial manipulator with three consecutive revolute joint axes parallel each other, a method combining screw theory and algebra method is proposed. Firstly, the kinematics model is established by screw theory, and the first joint angle is solved by the first type of Paden-Kahan subproblem; Then, the Euler angle theory is used to solve the fifth and sixth joint angles by algebraic method; Finally, the first type of Paden-Kahan subproblem is again used to solve the second, third, and fourth joint angles. Taking the UR5 collaborative manipulator as an example, eight groups of solutions are obtained by calculating the inverse kinematics. The maximum pose error of the inverse solution is 10^(-15) orders of magnitude, which proves the accuracy of the inverse kinematics solving algorithm proposed in this paper.