Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots
Abstract This paper presents a general methodology for the analysis and synthesis of a positive semi-definite system described by mass, damping and stiffness matrices that is often encountered in impedance control in robotics research. This general methodology utilizes the fundamental kinematic conc...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-03-01
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| Series: | ROBOMECH Journal |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s40648-021-00199-0 |
| _version_ | 1823957286689701888 |
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| author | Imin Kao Carlos Saldarriaga |
| author_facet | Imin Kao Carlos Saldarriaga |
| author_sort | Imin Kao |
| collection | DOAJ |
| description | Abstract This paper presents a general methodology for the analysis and synthesis of a positive semi-definite system described by mass, damping and stiffness matrices that is often encountered in impedance control in robotics research. This general methodology utilizes the fundamental kinematic concept of rigid-body and non-rigid-body motions of which all motions consist. The rigid-body mode results in no net change in the potential energy from the stiffness matrix of the multiple degree-of-freedom (DoF) discrete mechanical system. Example of an unconstrained discrete mechanical system is presented to illustrate the theoretical principle as applied in obtaining the free and forced vibration responses, as well as the dynamic characteristics of the system in natural frequency, $$\omega_n$$ ω n and damping ratio, $$\zeta$$ ζ . In addition, the methodology is applied to the impedance control of redundant robots. The rigid-body mode is equivalent to the motions of a redundant robot which result in no net change in potential energy, also called the zero-potential or ZP mode, of impedance control. Example of a redundant robot is used to demonstrate the application of the methodology in robotics. The dynamic characteristics of $$\omega _n$$ ω n and $$\zeta$$ ζ in the modal space are analyzed, which can be synthesized to modulate the damping of the system analytically. |
| first_indexed | 2024-12-17T15:58:21Z |
| format | Article |
| id | doaj.art-a5e17d24e02a47c7befac534e7c490c0 |
| institution | Directory Open Access Journal |
| issn | 2197-4225 |
| language | English |
| last_indexed | 2024-12-17T15:58:21Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | ROBOMECH Journal |
| spelling | doaj.art-a5e17d24e02a47c7befac534e7c490c02022-12-21T21:42:10ZengSpringerOpenROBOMECH Journal2197-42252021-03-018112110.1186/s40648-021-00199-0Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robotsImin Kao0Carlos Saldarriaga1Department of Mechanical Engineering, Stony Brook UniversityDepartment of Mechanical Engineering, Stony Brook UniversityAbstract This paper presents a general methodology for the analysis and synthesis of a positive semi-definite system described by mass, damping and stiffness matrices that is often encountered in impedance control in robotics research. This general methodology utilizes the fundamental kinematic concept of rigid-body and non-rigid-body motions of which all motions consist. The rigid-body mode results in no net change in the potential energy from the stiffness matrix of the multiple degree-of-freedom (DoF) discrete mechanical system. Example of an unconstrained discrete mechanical system is presented to illustrate the theoretical principle as applied in obtaining the free and forced vibration responses, as well as the dynamic characteristics of the system in natural frequency, $$\omega_n$$ ω n and damping ratio, $$\zeta$$ ζ . In addition, the methodology is applied to the impedance control of redundant robots. The rigid-body mode is equivalent to the motions of a redundant robot which result in no net change in potential energy, also called the zero-potential or ZP mode, of impedance control. Example of a redundant robot is used to demonstrate the application of the methodology in robotics. The dynamic characteristics of $$\omega _n$$ ω n and $$\zeta$$ ζ in the modal space are analyzed, which can be synthesized to modulate the damping of the system analytically.https://doi.org/10.1186/s40648-021-00199-0VibrationDiscrete systemsUnconstrained systemsImpedanceDampingStiffness |
| spellingShingle | Imin Kao Carlos Saldarriaga Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots ROBOMECH Journal Vibration Discrete systems Unconstrained systems Impedance Damping Stiffness |
| title | Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots |
| title_full | Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots |
| title_fullStr | Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots |
| title_full_unstemmed | Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots |
| title_short | Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots |
| title_sort | analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots |
| topic | Vibration Discrete systems Unconstrained systems Impedance Damping Stiffness |
| url | https://doi.org/10.1186/s40648-021-00199-0 |
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