The first stage in developing a task planning language for redundant m
anipulators 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 provid
e an initial joint configuration and periodically to correct for any j
oint errors that may have accumulated. Here, it is assumed that there
is complete correlation and coherence of solutions between these analy
ses, otherwise problems, such as a lack of repeatability may occur. Th
is may be accomplished by modelling the manipulator as an elastic syst
em which permits the development of a task planning method by using an
alyses which are all mutually coherent. In this paper, the method is d
eveloped and demonstrated using a redundant manipulator that simultane
ously avoids obstables, singularities and joint motion limitations. Th
e task planning method and associated analyses are applicable to the g
eneral serial redundant manipulator with an arbitrary degree of redund
ancy.