Kinematic Inversion of Robotic Manipulators in the Presence of Redundancies

A general algorithm for the solution of the inverse kinematic problem of robotic manipulators in the presence of redundan cies is presented in this article. Redundancies are handled using a constrained nonlinear least-square minimization approach in which a positive definite performance index is minimized subject to the associated kinematic closure equa tions. The arising nonlinear problem is solved as a sequence of linear quadratic programs. The algorithm is aimed at providing an efficient and general solution that avoids the production of undesirable effects such as non-conservative joint motions. Numerical stability of the procedure is en hanced by use of the Newton-Gauss method. Examples are given using the six-axis PUMA and seven-axis CYBOTECH P-15, each performing a task for which five degrees of free dom are required to orient and position an axially-symmetric peg through a continuous path.