Haptic Systems 530-655 Mohsen Mahvash Lecture 12 25/1/06

Effects of  time-discritization and position quantization on the stability of haptic systems An overview of the last lecture An estimate of energy leakage Passivity of several classes of virtual environments Quantization noise References

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

An estimate of energy leakage energy leakage during one period

Device damping and energy leakage A virtual wall is an active element! Device Device damper takes the energy leakage Device+Virtual Wall

Passivity of a spring-damper virtual wall Device Virtual Wall Virtual damper reduces the passivity margin!

Passivity of nonlinear virtual environments nonlinear virtual wall device damping Passivity condition

Passivity of 3D nonlinear elastic virtual environments nonlinear device with static friction minimum device damping computational delay T nonlinear 3d elastic environment Passivity condition

Position quantization maximum noise energy leakage in one period

References 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 andV. 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.