A novel closed-form solution for the inverse kinematics of redundant manipulators through workspace analysis

This work addresses the inverse kinematic problem for redundant serial manipulators. Its importance relies on its effect in the programming and control of redundant robots. Besides, no general closed-form techniques have been developed so far. In this paper, redundant manipulators are reduced to non-redundant ones by selecting a set of joints, denoted redundant joints, and parametrizing its joint variables. This selection is made through a workspace analysis which also provides an upper bound for the number of different closed-form solutions for a given pose. Once these joints have been identified several closed-form methods developed for non-redundant manipulators can be applied for obtaining the analytical solutions. Finally, particular instances for the parametrized joints variables are determined depending on the task to be executed. Different criteria and optimization functions can be defined for that purpose.