0
Research Papers

Stability Boundary for Haptic Rendering: Influence of Damping and Delay

[+] Author and Article Information
Jorge Juan Gil1

Department of Applied Mechanics, CEIT and TECNUN, University of Navarra, San Sebastián E-20018, Spainjjgil@ceit.es

Emilio Sánchez

Department of Applied Mechanics, CEIT and TECNUN, University of Navarra, San Sebastián E-20018, Spain

Thomas Hulin

Institute of Robotics and Mechatronics, German Aerospace Center (DLR), Oberpfaffenhofen-Weßling D-82234, Germanythomas.hulin@dlr.de

Carsten Preusche, Gerd Hirzinger

Institute of Robotics and Mechatronics, German Aerospace Center (DLR), Oberpfaffenhofen-Weßling D-82234, Germany

1

Corresponding author.

J. Comput. Inf. Sci. Eng 9(1), 011005 (Feb 20, 2009) (8 pages) doi:10.1115/1.3074283 History: Received September 28, 2007; Revised February 25, 2008; Published February 20, 2009

The influence of viscous damping and delay on the stability of haptic systems is studied in this paper. The stability boundaries have been found by means of different approaches. Although the shape of these stability boundaries is quite complex, a new linear condition, which summarizes the relation between virtual stiffness, viscous damping, and delay, is proposed under certain assumptions. These assumptions include a linear system, short delays, fast sampling frequency, and relatively low physical and virtual damping. The theoretical results presented in this paper are supported by simulations and experimental data using the DLR light-weight robot and the large haptic interface for aeronautic maintainability (LHIfAM).

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Model of a haptic system

Grahic Jump Location
Figure 2

Linear model of a haptic system

Grahic Jump Location
Figure 3

Stability boundaries using the analytical conditions for small dimensionless physical damping (δ<10−3), without delay (d=0), and with a delay equal to the sampling period (d=1)

Grahic Jump Location
Figure 4

Close-up of the stability boundaries using the analytical conditions for small dimensionless physical damping (δ<10−3), without delay (d=0), and with a delay equal to the sampling period (d=1)

Grahic Jump Location
Figure 5

Linear continuous model of the haptic system

Grahic Jump Location
Figure 6

Bode diagram of the continuous transfer function (solid) and the discrete-time transfer function (dashed)

Grahic Jump Location
Figure 7

Bode diagram of the continuous transfer function without delay (solid) and with a delay of 5 ms (dashed)

Grahic Jump Location
Figure 8

Stability boundaries for small dimensionless physical damping (δ<10−3) and delays d=[0,0.25,0.5,0.75,1,1.5,2,3]

Grahic Jump Location
Figure 9

Close-up of the stability boundaries near the point of origin for small dimensionless physical damping (δ<10−3) and delays d=[0,0.25,0.5,0.75,1,1.5,2,3]

Grahic Jump Location
Figure 10

Third generation of the DLR light-weight robot arm

Grahic Jump Location
Figure 11

Experimental stability boundaries for a delay td of 5 ms, 6 ms, and 10 ms (pluses and solid) and theoretical boundaries (dashed)

Grahic Jump Location
Figure 12

Experimental stability boundaries for a delay td of 10 ms and 55 ms (pluses and solid) and theoretical boundaries (dashed)

Grahic Jump Location
Figure 13

LHIfAM haptic interface

Grahic Jump Location
Figure 14

Experimental stability boundaries for the LHIfAM and a delay td of 3 ms, 6 ms, and 12 ms (pluses and solid) and theoretical stability boundaries for a physical damping b of 4.6 N s/m (dashed) and same delays

Grahic Jump Location
Figure 15

Exact stability boundaries (solid) for different delays and places where the relative error of the linear condition 8 (dashed) is equal to 2% (circles) and equal to 5% (squares) for δ=0 and δ=0.01

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In