Closed form inverse kinematics solution for a redundant anthropomorphic robot arm

An inverse kinematics solution of a redundant 7R serial chain that mimics the human arm is presented. Such manipulators are composed of two spherical wrists with one revolute joint in between. In the case of non-redundant manipulators the inverse kinematics yields a discrete set of solutions for the joint axes to reach a given end effector position and orientation. For redundant arms, however, the solution consists of a one parameter set. In contrast to other solutions to this problem herein a closed form solution is given without the need of specifying the design, task nor the redundant parameter in the solution process. That gives the possibility to use the degree of freedom provided by the additional joint for different applications, such as avoiding singularities, joint limits and collisions or to apply an optimization algorithm to achieve, for example, minimal joint velocities or joint movements.