1. Haptic Systems
Mohsen Mahvash
Lecture 12
25/1/06

2. 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

3. 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

4. An estimate of energy leakage
energy leakage during one period

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

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

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

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

9. Position quantization
maximum noise
energy leakage in one period

10. 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 , 2005.