| Abstract: | An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated. |
