The workspace of a redundant manipulator can be partitioned into afinite number of invertible subsets such that the inverse image of eachsubset has trivial fiber bundle topology, with the manifolds ofmanipulator self-motion as the fibers. As a consequence we show that acanonical representation of the self-motion manifolds is possible overthese well-defined subsets. The canonical representation parameterizes afamily of inverse functions over the work space subsets. Thisparameterization can be used to approximate a continuous inversekinematic function over each workspace subset. Setting appropriatevalves of the parameters yields particular inverse functions whichprovide access to all solution branches and to the full range of theredundant degrees of freedom in order to satisfy any side constraintswhich may be imposed during operation
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