A closed-form inverse kinematic modelling of a 7R anthropomorphic upper limb based on a joint parametrization

The problem of the redundancy control of 7R anthropomorphic arms is addressed by looking for an inverse kinematic model of the augmented wrist location. The classical notion of "arm angle" as a privileged additional scalar parameter is studied: its direct expression is given in the case of a zero-offset 7R anthropomorphic arm, but its inverse expression in closed-form appears to be too difficult to obtain. To overcome this difficulty we propose using a joint variable as a redundancy parameter and we show that the choice of the abduction arm angle allows the indirect, but efficient, control of the "arm angle". A simple and complete closed-form inverse kinematic model of a typical 7R anthropomorphic robot-arm can then be exhibited. Simulations show the relevance of the approach to controlling, in a simple way, both hand and elbow location