A global modeling methodology based on Koopman operator theory for the dynamics of rigid bodies that make and break contact is presented. Traditionally, robotic systems that contact with their environment are represented as a system comprised of multiple dynamic equations that are switched depending on the contact state. This switching of governing dynamics has been a challenge in both task planning and control. Here, a Koopman lifting linearization approach is presented to subsume multiple dynamics such that no explicit switching is required for examining the dynamic behaviors across diverse contact states. First, it is shown that contact/noncontact transitions are continuous at a microscopic level. This allows for the application of Koopman operator theory to the class of robotic systems that repeat contact/non-contact transitions. Second, an effective method for finding Koopman operator observables for capturing rapid changes to contact forces is presented. The method is applied to the modeling of dynamic peg insertion where a peg collides against and bounces on the chamfer of the hole. Furthermore, the method is applied to the dynamic modeling of a sliding object subject to complex friction and damping properties. Segmented dynamic equations are unified with the Koopman modeling method.
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A Plate-Like Sensor for the Identification of Sample Viscoelastic Properties Using Contact Resonance Atomic Force Microscopy
Abstract In this article, we present a new contact resonance atomic force microscopy-based method utilizing a square, plate-like microsensor to accurately estimate viscoelastic sample properties. A theoretical derivation, based on Rayleigh–Ritz method and on an “unconventional” generalized eigenvalue problem, is presented and a numerical experiment is devised to verify the method. We present an updated sensitivity criterion that allows users, given a set of measured in-contact eigenfrequencies and modal damping ratios, to select the best eigenfrequency for accurate data estimation. The verification results are then presented and discussed. Results show that the proposed method performs extremely well in the identification of viscoelastic properties over broad ranges of nondimensional sample stiffness and damping values.
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- PAR ID:
- 10211411
- Date Published:
- Journal Name:
- ASME Letters in Dynamic Systems and Control
- Volume:
- 1
- Issue:
- 3
- ISSN:
- 2689-6117
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A global modeling methodology based on Koopman operator theory for the dynamics of rigid bodies that make and break contact is presented. Traditionally, robotic systems that contact with their environment are represented as a system comprised of multiple dynamic equations that are switched depending on the contact state. This switching of governing dynamics has been a challenge in both task planning and control. Here, a Koopman lifting linearization approach is presented to subsume multiple dynamics such that no explicit switching is required for examining the dynamic behaviors across diverse contact states. First, it is shown that contact/noncontact transitions are continuous at a microscopic level. This allows for the application of Koopman operator theory to the class of robotic systems that repeat contact/non-contact transitions. Second, an effective method for finding Koopman operator observables for capturing rapid changes to contact forces is presented. The method is applied to the modeling of dynamic peg insertion where a peg collides against and bounces on the chamfer of the hole. Furthermore, the method is applied to the dynamic modeling of a sliding object subject to complex friction and damping properties. Segmented dynamic equations are unified with the Koopman modeling method.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4049538
