Admittance and impedance representations of friction based on implicit Euler integration

Ryo Kikuuwe, Naoyuki Takesue, Akihito Sano, Hiromi Mochiyama, Hideo Fujimoto

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)


Modeling of friction force is cumbersome because of its discontinuity at zero velocity. This paper presents a set of discrete-time friction models for the purpose of haptic rendering and virtual environment construction. These models allow friction to be treated as an admittance-type or impedance-type element of a virtual environment. They are derived from implicit Euler integration of Coulomb-like discontinuous friction and linear mass-spring-damper dynamics, and have closed-form expressions. They include rate-dependent friction laws, and their extension to multidimensional cases is easy in most practical cases. The validity of the models is demonstrated through numerical examples and implementation experiments.

Original languageEnglish
Pages (from-to)1176-1188
Number of pages13
JournalIEEE Transactions on Robotics
Issue number6
Publication statusPublished - Dec 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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