A Computational Technique for Solving Robot End-Effector Trajectories into Joint Trajectories

Abstract

where t is the time variable, x is the (m x 1) vector of task coordinates, q is the (n x 1) vector of joint coordinates, and f is a nonlinear vectorial function, whose structure and parameters are known. It is well known that the solution of the inverse kinematic problem, i.e. solving eq. (1), is of fundamental importance for robot control. A typical robot task is specified as a trajectory assigned to the end-effector, say ^(t), R(t), x(t). This must .be solved into a joint trajectory, say 4(t), q(t), q(t), which constitutes the reference input to the joint control servos. The most popular approach to the problem relies on the possibility of finding a closed-form analytical solution to the robot kinematic equation. It is recognized that this is true only for robots having simple geometries [21, such as the spherical wrist, the elbow manipulator etc. Further, the analytical solution is usually non-unique and sequential, and requires the computation of Atan2 functions. Besides eq. (1), the other direct kinematic relation is