일차-홀드 방법이 가상 질량-스프링 모델의 안정성 영역에 미치는 영향에 대한 연구

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2020 융ㆍ복합기술연구소 논문집 Vol.10 No.1

This paper presents the effects of a virtual mass on the stability boundary of a virtual spring in the haptic system with first-order-hold. The virtual rigid body is modeled as a virtual spring and a virtual mass. When first-order-hold is applied, we analyze the stability boundary of the virtual spring through the simulation according to the virtual mass and the sampling time. As the virtual mass increases, the stability boundary of the virtual spring gradually increases and then decreases after reaching the maximum value. The results are compared with the stability boundary in the haptic system with zero-order-hold. When a virtual mass is small, the stability boundary of a virtual spring in the system with first-order-hold is larger than that in the system with zero-order-hold.

가변적인 계산시간지연에 의한 햅틱 시스템에서의 안정성 영향 분석

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2015 융ㆍ복합기술연구소 논문집 Vol.5 No.2

This paper presents the effects of the computational time-varying delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a computational time-varying delay model. In this paper, the maximum of the computational time-varying delay is assumed to be as much as the sampling time. Using the simulation, it is analyzed how the sample-hold methods and the computational time-varying delay affect the maximum available stiffness. As the maximum of computational time-varying delay increases, the maximal available stiffness of a virtual wall model is reduced.

가상스프링 모델의 안정성 영역에 대한 가상질량의 영향에 대한 연구

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2016 융ㆍ복합기술연구소 논문집 Vol.6 No.2

This paper presents the effects of a virtual mass on the stability boundary of a virtual spring in the haptic system. A haptic system consists of a haptic device, a sampler, a virtual rigid body and zero-order-hold. The virtual rigid body is modeled as a virtual spring and a virtual mass. According to the virtual mass and the sampling time, the stability boundary of the virtual spring is analyzed through the simulation. As the virtual mass increases, the value of the virtual spring to guarantee the stability gradually increases and then decreases after reaching the maximum value. These simulation results show that the addition of the virtual mass enables to expand the stability boundary of the virtual spring.

가상질량과 저주파통과필터에 의한 햅틱 시스템의 안정성 영역에 관한 연구

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2017 융ㆍ복합기술연구소 논문집 Vol.7 No.2

This paper presents the effects of a virtual mass with a low-pass filter on the stability boundary of a virtual spring in the haptic system. In general, a haptic system consists of a haptic device, a sampler, a virtual impedance model and zero-order-hold. The virtual impedance is modeled as a virtual spring and a virtual mass. However the high-frequency noise due to the sampling time and the quantization error of sampled data may be generated when an acceleration is measured to compute the inertia force of the virtual mass. So a low-pass filter is needed to prevent the unstable behavior due to the high-frequency noise. A finite impulse response (FIR) filter is added to the measurement process of the acceleration and the effects on the haptic stability are simulated. According to the virtual mass with the FIR filter and the sampling time, the stability boundary of the virtual spring is analyzed through the simulation. The maximum available stiffness to guarantee the stable behavior is reduced, but simulation results still show that the stability boundary of the haptic system with the virtual mass is larger than that of the haptic system without the virtual mass.

인간 모델과 1차 샘플-홀드 방식이 가상 스프링 모델 시스템의 안정성에 미치는 영향 분석

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2013 융ㆍ복합기술연구소 논문집 Vol.3 No.2

When a human operator interacts with a virtual wall that is modeled as a virtual spring model, the lager the stiffness of the virtual spring is, the more realistic the operator feels that the virtual wall is. In the previous studies, it is shown that the maximum available stiffness of a virtual spring to guarantee the stability can be increased when the first-order-hold method is applied, however the effects of a human impedance on the stability are not considered. This paper presents the effects of a human impedance on stability of haptic system with a virtual spring and a first-order-hold (FOH) method. The human impedance model is modeled as a linear second-order system model. The relations between the maximum available stiffness of a virtual spring and the human impedance such as a mass, a damping and a stiffness are analyzed through the MATLAB simulation. It is shown that the maximum available stiffness is proportional to the square root of the human mass or damping respectively.

데이터 홀드 방식에 따른 햅틱 시스템의 안정성 분석

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2012 융ㆍ복합기술연구소 논문집 Vol.2 No.2

This paper presents the effect of data-hold methods on stability of haptic system with a virtual wall. When a human operator interacts with virtual wall, the lager the stiffness of the virtual wall is, the more realistic the operator feels that the virtual wall is. However, if the stiffness of the virtual wall becomes extremely large, the system may be unstable. When a virtual wall is designed, it is necessary to analyze the maximum available stiffness to guarantee a stable haptic interaction. The simulation model in this paper is developed based on the haptic device model, sampler, a virtual wall model, and data hold methods to compute the maximum stiffness for stability. The effectiveness of the simulation is evaluated through comparing the results of previous studies with the results of this simulation. In addition, the effects of two data hold methods, that is, zero-order hold (ZOH) and first-order hold (FOH) on the stability are analyzed and the values of the maximum available stiffness are compared through the simulation.

시간지연에 의한 일차홀드 방식을 포함하는 가상벽 모델의 안정성 영향 분석

이경노,Lee, Kyungno 한국교통대학교 융복합기술연구소 2014 융ㆍ복합기술연구소 논문집 Vol.4 No.2

This paper presents the effects of the time delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a time delay model. In this paper, the time delay is considered as the computational time delay that is assumed to be as much as the sampling time. As the time delay increases, the maximal available stiffness of a virtual wall model is reduced reversely. The relation among the time delay and the maximum available stiffness, the mass and the damper of the haptic device are analyzed using the MATLAB simulation.

자전거 가상현실 시뮬레이터

이경노(Kyungno Lee),이두용(Doo Yong Lee),권동수(Dong-Soo Kwon),양기훈(Gi-Hun Yang),박영진(Youngjin Park),이찬주(Chanjoo Lee),이종원(Chong-Won Lee),신재철(Jae-Cheol Shin),한순홍(Soon-Hung Han),유병현(Byoung-Hyun Yoo) 한국정보과학회 2001 한국정보과학회 학술발표논문집 Vol.2001 No.2

일차홀드 방식을 포함한 햅틱 시스템의 안정성 영역에 대한 통신시간지연과 햅틱장치 물성치의 영향 분석

이경노(Kyungno Lee) 한국산학기술학회 2017 한국산학기술학회논문지 Vol.18 No.1

사용자가 원격으로 가상환경에 접속하여 가상물체를 조작할 때 현실감을 증강시키기 위해서 햅틱 시스템이 사용된다. 그러나 원격 시스템 환경에는 통신시간지연이 발생하며, 발생된 통신시간지연은 햅틱 시스템을 불안정하게 만들 수 있다. 본 논문에서는 종래의 샘플-홀드 방식인 영차홀드 (ZOH; Zero-Order-Hold)가 아닌 일차홀드 (FOH; First-Order-Hold)를 포함하는 햅틱 시스템에서 시뮬레이션을 통해 통신시간지연과 햅틱 장치의 물성치 변화에 따른 가상 스프링상수의 안정성 영역을 분석하고 이를 통해 안정적인 햅틱 시스템을 구현하고자 한다. 통신시간지연이 없으면 일차홀드 (FOH) 방식이 영차홀드(ZOH) 방식보다 가상 스프링상수의 안정성 영역을 증가시킬 수 있었다. 그러나 통신시간지연이 증가하면, 샘플-홀드 방식보다 통신시간지연이 시스템 안정성에 더 큰 영향을 끼치므로, 샘플-홀드 방식에 따른 가상 스프링상수의 안정성 영역 크기에는 차이가 없어진다. 또한 통신시간지연과 일차홀드 방식이 포함되면 가상 스프링상수의 안정성 영역은 통신시간지연 크기에 반비례하고, 햅틱 장치의 댐핑상수 (Bd)에 정비례하여 증가하지만, 햅틱 장치의 질량 (Md)에는 영향받지 않음을 알 수 있었다. Haptic systems help users feel a realistic sensation when they manipulate virtual objects in the remote virtual environment. However, there are communication time delays that may make the haptic system unstable. This paper shows the relationship between communication time delay, properties of a haptic device, and the stability of the haptic system with the first-order hold method in a simulation. The maximum available stiffness of a virtual spring with the first-order hold method is larger than in the zero-order hold method when there is no time delay. However, when the communication time delay is much larger than the sampling time, the maximum available stiffness to guarantee the stability becomes the same, irrespective of the sample-hold methods. Besides, the maximum available stiffness increases in inverse proportion to the communication time delay and in proportional to the damping coefficient of the haptic device.

루드-후르비쯔 (Routh-Hurwitz) 안정성 판별법을 이용한 인간의 임피던스가 포함된 햅틱 시스템의 안정성 분석

이경노(Lee, Kyungno) 한국산학기술학회 2014 한국산학기술학회논문지 Vol.15 No.4

햅틱 시스템에는 사용자인 인간이 항상 포함되므로,인간 임피던스에 의한 시스템 안정성 분석이 필요하다.특히, 일차 홀드 방식의 햅틱 시스템에 대한 인간 임피던스의 안정성 영향 분석이 미진하다.본 논문에서는 선형 2차 시스템으로 모델화된 인간의 임피던스 모델을 포함하는,일차 홀드 방식의 햅틱 시스템에 대한 안정성을 루드-후르비쯔 (Routh-Hurwitz)안정성 판별법을 이용하여 해석했다.가상 벽 모델인 가상 스프링 상수 (K_w)의 안정성 영역과 인간 임피던 스의 질량 (M_h),댐핑 (B_h),그리고 스프링 상수 (K_h)와의 관계를 루드-후르비쯔 안정성 판별법을 이용하여 분석한 결과, 스프링 상수 (K_h)가 일정할 때 가상 스프링 상수 (K_w)는 인간 임피던스의 질량 (M_h)과 댐핑 (B_h)의 제곱근에 비례했다. 또한 인간 임피던스의 질량 (M_h)또는 댐핑 (B_h)가 일정할 때 가상 스프링 상수 (K_w)는 스프링 상수 (K_h)의 0.48배만큼 감소했다.이를 종합하여 K_w≤ 54413√(M_h+M_d)(B_h+B_d)-0.486K_h의 모델을 제안했고,이론 값들과 제시된 모델로부 터 계산된 값을 비교한 결과 평균적인 상대오차가 0.5%로 작게 나타났다.제시된 모델이 인간 임피던스 모델과 가상 스프링 상수와의 관계를 비교적 잘 표현하고 있다. This paper presents the stability analysis of the haptic system including a human impedance using the Routh-Hurwitz criterion. The reflective force is computed from a virtual spring model and is transferred to a human operator using the first-order-hold method. The stability boundary conditions are induced and the relation among a virtual spring (K_w), the mass (M_h), the damping (B_h) and the stiffness (K_h) of a human impedance is analyzed. Hence the stability boundary of the virtual spring (K_w) is proposed as K_w≤ 54413√(M_h+M_d)(B_h+B_d)-0.486K_hwhen the sampling time is 1 ms. The average relative error is about 0.5% when the mathematical analysis results are compared with the results of the stability boundary model.