Haptic Systems 530 655 Mohsen Mahvash Lecture 12
- Slides: 10
Haptic Systems 530 -655 Mohsen Mahvash Lecture 12 25/1/06 1
Effects of time-discritization and position quantization on the stability of haptic systems Ø An overview of the last lecture Ø An estimate of energy leakage Ø Passivity of several classes of virtual environments Ø Quantization noise Ø References 2
An overview of the last lecture continuous-time wall Haptic system = operator +device+ virtual wall passive system stable interaction energy leakage in sample and hold causes oscillations discrete-time wall 3
An estimate of energy leakage during one period 4
Device damping and energy leakage A virtual wall is an active element! Device damper takes the energy leakage Device+Virtual Wall 5
Passivity of a spring-damper virtual wall Device Virtual Wall Virtual damper reduce the passivity margin! 6
Passivity of nonlinear virtual environments nonlinear virtual wall device damping Passivity condition 7
Passivity of 3 D nonlinear elastic virtual environments nonlinear device with static friction minimum device damping computational delay T nonlinear 3 d elastic environment Passivity condition 8
Position quantization maximum noise energy leakage in one period 9
References 1. 2. 3. 4. 5. R. B. Gillespie and M. R. Cutkosky, “Stable user-specific haptic rendering of the virtual wall, ” Proc. ASME Dyn. Syst. Control Div. , vol. 58, pp. 397– 406, 1996. J. E. Colgate and G. G. Schenkel, “Passivity of a class of sampled-data systems: Application to haptic interfaces, ” J. Robot. Syst. , vol. 14, no. 1, pp. 37– 47, 1997. BE Miller, JE Colgate, RA Freeman , Guaranteed stability of haptic systems with nonlinear virtual environments, IEEE Transactions on Robotics and Automation, 2000. M. Mahvash and. V. Hayward, “High-fidelity passive force-reflecting virtual environments, ” IEEE Trans. Robot. , vol. 21, no. 1, pp. 38– 46, Feb. 2005. J. J. Abbott and A. M. Okamura, "Effects of Position Quantization and Sampling Rate on Virtual Wall Passivity, '' IEEE Transactions on Robotics, Vol. 21, No. 5, pp. 952 - 964, 2005. 10
