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Stochastic Models, Information Theory, and Lie Groups, Volume 2 pp 187–228Cite as

Parts Entropy and the Principal Kinematic Formula

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Automated (robotic) assembly systems that are able to function in the presence of uncertainties in the positions and orientations of feed parts are, by definition, more robust than those that are not able to do so. This can be quantified with the concept of “parts entropy,” which is a statistical measure of the ensemble of all possible positions and orientations of a single part confined to move in a finite domain. In this chapter the concept of parts entropy is extended to the case of multiple interacting parts. Various issues associated with computing the entropy of ensembles of configurations of parts with excluded-volume constraints are explored. The rapid computation of excluded-volume effects using the “principal kinematic formula” from the field of Integral Geometry is illustrated as a way to potentially avoid the massive computations associated with brute-force calculation of parts entropy when many interacting parts are present.

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  1. Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD, 21218-2682, USA

    Gregory S. Chirikjian

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Chirikjian, G.S. (2012). Parts Entropy and the Principal Kinematic Formula. In: Stochastic Models, Information Theory, and Lie Groups, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4944-9_6

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