Three necessary conditions derived from classical geometry are proposed to evaluate formulations for the simultaneous twist and wrench control of rigid bodies, and for any theory to be meaningful it must be invariant with respect to (1) Euclidean Collineations, (2) Change of Unit Length, and (3) Change of Basis. It is demonstrated in this paper that a previously established theory of hybrid control for robot manipulators (see for example [1–3]) is in fact based on noninvariant principles and is noninvariant with respect to (1) and (2). A new alternative invariant formulation based on screw theory is presented. An example of insertion is included which illustrates both invariant and noninvariant methods.
KeywordsVirtual Work Robotic Manipulator Hybrid Control Projective Relation Screw Theory
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