Comparative Analysis of Quasi-Differential Approaches in Inverse Kinematics

In general, i.e. when the kinematic construction of a redundant robot arm does not meet special requirements, the inverse kinematic task has only differential solutions that do not exist in the kinematically singular points and suffer from large angular velocity components in the vicinity of the singularities. Recently it has been pointed out that these problems are caused by the use of some generalized matrix inverses, and they can be evaded by the application of a quasi-differential approach that transforms the task into a Fixed Point Problem and solves it with a convergent iteration without the use of any matrix inversion. In this paper it is shown that further possibilities are available in the quasi-differential approach that differ from each other in the use of the elements of the Null Space of the Jacobian. It is concluded that for maintaining the continuity of the solutions the use of the elements of this null space are practically important. This conclusion is illustrated via simulations for an irregularly extended PUMA-type robot arm, that is an 8 Degree of Freedom system.