Inverse kinematics of robot manipulators with offset wrist

摘要

The inverse kinematics for a robot manipulator with offset wrist is formulated as a minimization problem in this paper to reduce its complexity and accelerate the computation speed. A specific type of robot such as Yaskawa MA1400, which has an offset between the last two axes, is chosen for analysis. Given an initial guess angle of last joint, all the 6 joint angles can be easily found through analytical solution. The output value is compared with the initial guess. An error function with only one variable is then defined and Newton-Raphson method is applied to search for the solution where the error goes to zero. To check the validity of the algorithm, forward kinematics is first computed and the position and orientation of end-effector are then applied in the inverse kinematics to solve the joint angles back. The computation converges within 5 iterations in cases when the angle θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> is far away from zero and the accuracy is within 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-10</sup> degree. When θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> approaches zero, searching direction is slightly modified to achieve convergence for the algorithm. The number of iterations increases for the same accuracy. The results show that the approach presented in this paper greatly reduces the computation time and is suitable for real time application.