Often it is desirable to guarantee that a manipulator will remain stable when contacting any member of some set of environments. Coupled stability criteria based on passivity may be used to provide such a guarantee, but may be arbitrarily conservative depending on the environment set. In this paper, two techniques for reducing conservativeness are introduced. The first is based on a canonical coordinate transformation which enables an environment set viewed in the frequency domain to be conformally mapped to the interior of the unit circle. A stability criterion is then derived via the small gain theorem. The second technique uses logical combinations of such criteria to reduce conservativeness further. Both techniques are illustrated with nontrivial examples.
Coordinate Transformations and Logical Operations for Minimizing Conservativeness in Coupled Stability Criteria
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Colgate, J. E. (December 1, 1994). "Coordinate Transformations and Logical Operations for Minimizing Conservativeness in Coupled Stability Criteria." ASME. J. Dyn. Sys., Meas., Control. December 1994; 116(4): 643–649. https://doi.org/10.1115/1.2899263
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