Haptic Systems 530-655

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

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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

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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
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An estimate of energy leakage
energy leakage during one period
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Device damping and energy leakage
A virtual wall is an active element!
Device
Device damper takes the energy leakage
DeviceVirtual Wall
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Passivity of a spring-damper virtual wall
Device
Virtual Wall
Virtual damper reduces the passivity margin!
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Passivity of nonlinear virtual environments
nonlinear virtual wall
device damping
Passivity condition
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Passivity of 3D nonlinear elastic virtual
environments
nonlinear device with static friction
minimum device damping
computational delay T
nonlinear 3d elastic environment
Passivity condition
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Position quantization
maximum noise
energy leakage in one period
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References

1. R. B. Gillespie and M. R. Cutkosky, Stable
   user-specific haptic renderingof the virtual
   wall, Proc. ASME Dyn. Syst. Control Div., vol.
   58,pp. 397406, 1996.
2. J. E. Colgate and G. G. Schenkel, Passivity of a
   class of sampled-datasystems Application to
   haptic interfaces, J. Robot. Syst., vol. 14, no.
   1,pp. 3747, 1997.
3. BE Miller, JE Colgate, RA Freeman , Guaranteed
   stability of haptic systems with nonlinear
   virtual environments, IEEE Transactions on
   Robotics and Automation, 2000.
4. M. Mahvash andV. Hayward, High-fidelity passive
   force-reflecting virtual environments, IEEE
   Trans. Robot., vol. 21, no. 1, pp. 3846,
   Feb.2005.
5. 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.