Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
권호 표지
DOI QR코드

DOI QR Code

Effects of a First-order-hold Method and a Virtual Damper on the Stability Boundary of a Virtual Spring

일차홀드 방식과 가상 댐퍼가 가상 스프링의 안정성 영역에 미치는 영향

  • Lee, Kyungno (School of Mechanical, Automotive and Aeronautical Engineering, Korea National University of Transportation)
  • 이경노 (국립 한국교통대학교 기계자동차항공공학부)
  • Received : 2019.03.21
  • Accepted : 2019.06.07
  • Published : 2019.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

A virtual rigid is modeled as the parallel structure of a virtual spring and a virtual damper. The reflective force from the virtual model is designed to be as large as possible to improve the realism of the virtual environment while maintaining the stable interaction. So, it is important to analyze the stability boundary of the virtual spring and damper. In the previous researches, the stability boundary is analyzed based on the zero-order-hold (ZOH) method, but it is analyzed based on the first-order-hold (FOH) method and the virtual damper in the paper. The boundary value of the stable virtual damper is inverse proportional to the sampling time and the maximum value of stable virtual stiffness is inverse proportional to the square of the sampling time. And the maximum value in the FOH method is increased to 110% of the value in the ZOH method. If the virtual damper is smaller than about 50% of the boundary value of the virtual damper in the FOH method, the stable virtual stiffness in the FOH method is several times larger than that in the ZOH method.

가상환경 속 가상 강체는 가상 스프링과 가상 댐퍼의 병렬구조로 모델링되며 가상 강체의 현실감을 증강시키기 위해서는 가상 모델로부터의 반력을 안정적으로 최대한 크게 제시해야 한다. 따라서 햅틱 인터페이스의 안정성을 유지시킬 수 있는 가상 스프링과 가상 댐퍼의 영역을 분석하여 가상 강체모델을 선정하는 것이 중요하다. 기존에는 영차홀드를 이용하는 시스템에 대해 안정성 영역이 분석되었으나, 본 논문에서는 일차홀드 방식과 가상 댐퍼를 이용하는 햅틱 시스템에 대한 안정성 영역을 분석한다. 안정적인 가상 댐퍼 영역의 경계값은 샘플링 주기와 반비례 관계를 가지며, 안정적인 가상 스프링 영역의 최대값은 샘플링 주기의 제곱에 반비례 관계를 갖는다. 그리고 그 최대값은 일차홀드 방식을 이용하여 기존의 영차홀드의 경우보다 약 110% 향상시킬 수 있다. 가상 댐퍼의 크기가, 일차홀드 방식에서의 안정적인 가상댐퍼 경계값의 약 50% 보다 작다면, 일차홀드를 이용함으로써 기존의 영차홀드의 경우보다 안정적인 가상 스프링의 영역을 수 배 더 크게 할 수 있다.

Keywords

SHGSCZ_2019_v20n6_396_f0001.png 이미지

Fig. 1. Block diagram for a haptic interface

SHGSCZ_2019_v20n6_396_f0002.png 이미지

Fig. 2. Boundary values of stable stiffness according to the virtual damper (a) sampling time = 1 ms (b) sampling time = 10 ms.

SHGSCZ_2019_v20n6_396_f0003.png 이미지

Fig. 3. The relation between boundary value of virtual damper and the sampling time according to sample- and-hold methods, respectively.

SHGSCZ_2019_v20n6_396_f0004.png 이미지

Fig. 4. Relation between stable maximum stiffness and sampling time

SHGSCZ_2019_v20n6_396_f0005.png 이미지

Fig. 5. The ratio of the boundary values of stable stiffness in the FOH method to that in the ZOH method.

SHGSCZ_2019_v20n6_396_f0006.png 이미지

Fig. 6. The relation between the ratio of the boundary values of stable stiffness in the FOH method to that in the ZOH method and the sampling time.

Table 1. Comparison between the simulation results and the previous results according to virtual damper.

SHGSCZ_2019_v20n6_396_t0001.png 이미지

Table 2. Boundary values of stable virtual damper and the ratio of the boundary value in the FOH method to that in ZOH method.

SHGSCZ_2019_v20n6_396_t0002.png 이미지

Table 3. The stable maximum stiffness, the virtual damper at the maximum stiffness, and the ratio of the stable maximum stiffness, according to the sample-and-hold methods, respectively.

SHGSCZ_2019_v20n6_396_t0003.png 이미지

Table 4. Maximum virtual damper that satisfying (3) and the ratio of the maximum value to the boundary value of the stable damper.

SHGSCZ_2019_v20n6_396_t0004.png 이미지

References

  1. J. E. Cogate and G. Schenkel, "Passivity of a class of sampled-datav systems: application to haptic interfaces," Journal of Robotic Systems, Vol. 14, No. 1, pp.37-47, 1997. DOI:http://dx.doi.org/10.1002/(SICI)1097-4563(199701)14:1%3C37::AID-ROB4%3E3.0.CO;2-V
  2. J. E. Colgate and J. M. Brown, "Factors affecting the Z-width of a haptic display," Proceedings of 1994 IEEE Int. Conf. Robotics and Automation, CA, USA, pp.3205-3210, May 1994. DOI: http://dx.doi.org/10.1109/ROBOT.1994.351077
  3. J. J. Gil, A. Avello, A. Rubio, and J. Florez, "Stability analysis of a 1 DOF haptic interface using the Routh-Hurwitz criterion," IEEE Trans. on Control Systems Technology, Vol. 12, No. 4, pp. 583-588, July 2004. DOI: https://doi.org/10.1109/tcst.2004.825134
  4. M. Koul, M. Manivannan, S.K. Saha,"Effect of dual-rate sampling on the stability of a haptic interface," Journal of Intelligent & Robotic Systems, Vol. 91, No.3-4, pp. 479-491, 2018. DOI: https://doi.org/10.1007/s10846-017-0691-6
  5. V. Chawda, O. Celik, and M. K. O'Malley, "A method for selecting velocity filter cut-off frequency for maximizing impedance width performance in haptic interface," Journal of Dynamic Systems, Measurement, and Control, Vol. 137, Issue 2, 2014. DOI: http://dx.doi.org/10.1115/1.4028526
  6. K. Lee, "Stability analysis for a virtual spring model with an extrapolation and high-frequency ZOH," Journal of the Korea Academia-Industrial cooperation Society, vol. 19, no. 1, pp. 12-17, 2018. DOI: https://doi.org/10.5302/J.ICROS.2014.13.1970
  7. K. Lee, "Stability analysis of a haptic system with a first-order-hold method," Journal of Institute of Control, Robotics and Systems, vol. 20, No. 4, pp. 389-394, 2014. DOI: https://doi.org/10.1007/s00163-010-0086-1