The first stage in developing a task planning language for redundant manipulators is that of constructing an algorithm to produce a schedule of joint displacements for the specified task. This algorithm may be based upon the use of an inverse infinitesimal kinematic analysis for the majority of the path with a finite inverse analysis used to provide an initial joint configuration and periodically to correct for any joint errors that may have accumulated. Here, it is assumed that there is complete correlation and coherence of solutions between these analyses, otherwise problems, such as a lack of repeatability may occur. This may be accomplished by modelling the manipulator as an elastic system which permits the development of a task planning method by using analyses which are all mutually coherent. In this paper, the method is developed and demonstrated using a redundant manipulator that simultaneously avoids obstables, singularities and joint motion limitations. The task planning method and associated analyses are applicable to the general serial redundant manipulator with an arbitrary degree of redundancy.