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This paper revisits the concept of controlled reduction, a symmetry-based method of decomposing the control of mechanical systems into lower-dimensional problems. Founded on a geometric property of serial kinematic chains termed recursive cyclicity, the present work extends this property to branched chains by defining the minimal irreducible tree structure. We then generalize the subrobot theorem...
This paper develops the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We introduce a geometric property of general serial-chain robots termed recursive cyclicity, leading to our presentation of the subrobot theorem. This shows that reduction-based control can arbitrarily reduce the dimensionality of any serial-chain...
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