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TECHNICAL PAPERS

Stable Forbidden-Region Virtual Fixtures for Bilateral Telemanipulation

[+] Author and Article Information
Jake J. Abbott1

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218jabbott@ethz.ch

Allison M. Okamura

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218aokamura@jhu.edu

1

Jake Abbott is now with the Institute of Robotics and Intellient Systems, ETH Zurich, CH-8092 Zurich, Switzerland.

J. Dyn. Sys., Meas., Control 128(1), 53-64 (Sep 16, 2005) (12 pages) doi:10.1115/1.2168163 History: Received March 14, 2005; Revised September 16, 2005

There has been recent interest in novel human-machine collaborative control laws, called “virtual fixtures,” which provide operator assistance for telemanipulation tasks. A forbidden-region virtual fixture is a constraint, implemented in software, that seeks to prevent the slave manipulator of a master/slave telemanipulation system from entering into a forbidden region of the workspace. In this paper, we consider the problem of unstable vibrations of the slave and/or master against forbidden-region virtual fixtures for a general class of telemanipulator control architectures, including those with haptic feedback. To the best of the authors’ knowledge, there has been no rigorous study of the stability of forbidden-region virtual fixtures in previous work. The system is evaluated around the master and slave equilibrium position resulting from a constant desired human input force, using a discrete state-space model. We present a method to analytically determine if instability is possible in the system. We thoroughly evaluate this method, experimentally, applying malicious user strategies that attempt to drive the system unstable. Our approach agrees with experimental results and can be used to design and analyze the stability and transient properties of a telemanipulator interacting with virtual fixtures. We show that the user can affect both slave- and master-side virtual fixture stability by modifying his or her impedance characteristics. However, the upper bound on stable slave-side virtual fixture stiffness does not depend on the particular user.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

General three-channel telemanipulator implemented with a digital computer

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Figure 2

Experimental data showing slave manipulator interacting with an unstable FRVF. The equilibrium position, based on the master position and the system gains, is also shown. Vibrations do not occur on the surface of the FRVF, but rather, around an unstable equilibrium. The system shown has Kps=600N∕m, Kvs=2Ns∕m, KsVF=3000N∕m, and all other gains are zero. The controller runs at 500Hz.

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Figure 3

Experimental 1-DOF impedance-type bilateral telemanipulation system based on modified haptic paddles

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Figure 4

Human-index-finger mass-spring-damper values for five users (21), with simple bounding lines added (original data courtesy Robert D. Howe)

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Figure 5

Algorithm for determining system stability

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Figure 6

The clouds of eigenvalues show how the system eigenvalues vary based on possible human users, for a system with T=0.002s, Kpm=Kps=800N∕m, and Kdm=Kds=6Ns∕m. Arrows indicate how the eigenvalues move as the FRVF stiffness is increased from KsVF=500N∕m to KsVF=5500N∕m. Eventually, the eigenvalues reach the imaginary axis, indicating possible instability for the worst-case user.

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Figure 7

Predicted and experimental stability bounds for slave FRVFs versus sampling rate, with Kp=600N∕m and Kd=2Ns∕m. Experimental data are shown for large (userL) and small (userS) users.

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Figure 8

Predicted and experimental stability bounds for slave FRVFs, at 500Hz sampling rate. Data are shown for large (userL) and small (userS) users.

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Figure 9

Predicted and experimental stability bounds for slave FRVF, at 1000Hz sampling rate. Data are shown for large (userL) and small (userS) users.

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Figure 10

Predicted and experimental stability bounds for slave FRVFs versus sampling rate for unilateral telemanipulation, with Kps=1000N∕m and Kds=6Ns∕m. A unilateral telemanipulator models saturation of the master actuator.

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Figure 11

Predicted and experimental stability bounds for master FRVFs versus sampling rate, with Kp=600N∕m and Kd=2Ns∕m. Experimental data are shown for large (userL) and small (userS) users.

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Figure 12

Predicted and experimental stability bounds for master FRVFs, at 500Hz sampling rate. Data are shown for large (userL) and small (userS) users.

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Figure 13

Predicted and experimental stability bounds for master FRVFs, at 1000Hz sampling rate. Data are shown for large (userL) and small (userS) users.

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Figure 14

Predicted and experimental stability bounds for master FRVFs versus sampling rate for unilateral telemanipulation, with Kps=1000N∕m and Kds=6Ns∕m (simple virtual wall). Experimental data are shown for large (userL) and small (userS) users. Requiring passivity of the FRVF gives a more conservative result.

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