ABSTRACT
A solution of the inverse kinematics problem in robotics is presented. The usual difficulty of inversion or non-invertability of robot kinematics is circumvented by linearization of the forward kinematics and the design of an appropriate energy function, which then is minimized by linear dynamic networks. The results of the dynamic optimization process are the ‘best’ joint angle rates which minimize the manipulator’s position error. We call the class of networks used Linear Hopfield Networks, due to it’s similarities with the original Continuous Hopfield Network. A convergence proof for the dynamics of the synchronous Linear Hopfield Network is given. The development of an explicit upper bound on the step size is presented which guarantees convergence and whose values at or near the upper bound provide fast convergence. The simulated tracking control of a trajectory in 3-D Cartesian space with a three-joint robot manipulator demonstrates the performance of this approach.
