Using finite element methods to approximate kinematic solutions of robot manipulators when closed form solutions are unobtainable

The following paper demonstrates how finite element methods can be applied to approximating inverse kinematic solutions of robot, manipulators. The method demonstrated in this paper is unique to previous work on this subject in that it requires computation of only the forward solution and not the inverse. This is significant when the robot geometry is too complex to yield an easily obtainable inverse solution. After computation of the approximating solution, the actual kinematic solution of the robot is obtained by interpolating across an element, as in typical finite element problems. In this case element node values represent joint configurations rather than the more common elastic displacement or stress. The approximation is obtained by dividing the workspace into an element grid, and minimizing a potential function to obtain the best fit node values of joint configuration. An example is included.