The workspace of a redundant manipulator can be partitioned into a finite number of invertible subsets such that the inverse image of each subset has trivial fiber bundle topology, with the manifolds of manipulator self-motion as the fibers. As a consequence we show that a canonical representation of the self-motion manifolds is possible over these well-defined subsets. The canonical representation parameterizes a family of inverse functions over the work space subsets. This parameterization can be used to approximate a continuous inverse kinematic function over each workspace subset. Setting appropriate valves of the parameters yields particular inverse functions which provide access to all solution branches and to the full range of the redundant degrees of freedom in order to satisfy any side constraints which may be imposed during operation.
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