Closed form solutions for inverse kinematics approximation of general 6R manipulators

This paper presents an original use of Evolutionary Algorithms in order to approximate by a closed form the inverse kinematic model (IKM) of analytical, non-analytical and general (i.e. with an arbitrary geometry) manipulators. The objective is to provide a fast and general solution to the inverse kinematic problem when it is extensively evaluated as in design processes of manipulators. A mathematical function is evolved through Genetic Programming according to the known direct kinematic model to determine an analytical expression which approximates the joint variable solution for a given end-effector configuration. As an illustration of this evolutionary symbolic regression process, the inverse kinematic models of the PUMA and the GMF Arc Mate are approximated before to apply the algorithm to general 6R manipulators.