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Stability Analysis for a Virtual Spring Model with an Extrapolation and High-frequency ZOH

외삽법과 고주파 영차홀드 출력이 포함된 가상 스프링 모델의 안정성 영역 분석

  • Lee, Kyungno (School of Mechanical, Automotive and Aeronautical Engineering, Korea National University of Transportation)
  • 이경노 (국립 한국교통대학교 기계자동차항공공학부)
  • Received : 2017.12.07
  • Accepted : 2018.01.05
  • Published : 2018.01.31

Abstract

In order to enhance the realism of a virtual environment, a method of maximizing the stiffness of the virtual environment model is needed, which maintains the stability of the haptic system. In our previous research, we proposed a haptic system with a first order hold, instead of a zero order hold, and showed that the maximum available stiffness of a virtual spring with the first-order hold is larger than that with the zero-order hold. However, in terms of real system implementation, the zero order hold is a more common and easy method. In this paper, we propose an extrapolation method and a high frequency zero-order-hold output method in order to obtain the stability region using a zero order hold, which is equivalent to the method using the first-order-hold. The simulation results shows that the stability range of the virtual spring becomes almost the same as that of the method using the first order hold when the sampling period of the high frequency zero-order-hold method is decreased. Moreover, the stability range of the proposed method is several times to several tens of times greater than that of the method using the zero order hold only. Therefore, it is expected that the proposed method can enhance the realism of rigid bodies in a virtual environment.

가상환경에 대한 현실감을 증강시키기 위해서는 햅틱 시스템의 안정성을 유지하면서 가상환경 모델의 강성을 최대한 크게 할 수 있는 방법이 필요하다. 이에 기존 연구에서 영차홀드 대신 일차홀드를 적용하는 방법이 제시되었고, 영차홀드를 이용할 때보다 가상 스프링의 안정성 영역을 더 크게 확보할 수 있음을 시뮬레이션을 통해 제시했다. 그렇지만 실제로 시스템을 구현하는 측면에서 보면, 영차홀드가 일반적이고 손쉬운 방법이다. 이에 본 논문에서는 영차홀드를 사용하지만, 일차홀드와 동등한 안정성 영역을 확보하기 위한 방법으로 외삽법과 고주파 영차홀드 출력 방법을 제안한다. 제안된 방법에 대한 시뮬레이션을 통해 고주파 영차홀드의 샘플링 주기가 작아질수록 가상 스프링의 안정성 영역이 일차홀드를 적용한 경우와 거의 같아짐을 보였고, 기존 연구에서 제시된 영차홀드만을 적용한 경우보다는 수 배에서 수십 배 안정성 영역이 더 커질수 있음을 보였다. 따라서 제안된 방법을 통해 가상 환경 속 강체에 대한 현실감을 증강시킬 수 있을 것으로 기대된다.

Keywords

References

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