FEEDBACK SYSTEM FOR INVERSE KINEMATICS.

The transformation from the joint coordinates of a robot to cartesian coordinates is a vector-valued nonlinear function called the forward kinematic solution. The inverse kinematic problem in robotics is to invert this nonlinear function to obtain a transformation from cartesian to joint coordinates. Under this transformation, a trajectory in cartesian coordinates maps to a trajectory in joint coordinates, and the first and second derivatives of this joint trajectory are also required by modern robotic control algorithms. In this paper, a nonlinear feedback system is presented which, when driven by a desired cartesian trajectory, has as outputs the corresponding joint angles, velocities and accelerations. It is shown that the nonlinear system is related to a linear system which can be used to compute precise performance bounds. Simulation results for a Reis 625 manipulator are given