Kinematically redundant manipulators: The hyperbolic behavior of the singularly perturbed necessary conditions

An examination is made of the nature of continuation methods associated with integral optimal redundancy resolution. The goal is to reduce the computational requirements for the solution of the problem as well as to study the convergence behavior afforded by a continuation method. A differential equation describing the variation in the solution with ε is obtained. It is shown that under relatively mild conditions the continued solution exists for parameter values near the starting point of the method, but that the differential equations determining the curve are stiff and as such may be difficult to integrate numerically. Using the theory of exponential dichotomies, a transformation that permits the stable numerical integration of an approximation to these equations in the vicinity of ε=0 is obtained