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.

1.
Sheridan
,
T. B.
, 1992,
Telerobotics, Automation, and Human Supervisory Control
.
The MIT Press
,
Cambridge, MA
.
2.
Abbott
,
J. J.
, 2005, “
Virtual Fixtures for Bilateral Telemanipulation
,” Ph.D. dissertation, Department of Mechanical Engineering, The Johns Hopkins University.
3.
Abbott
,
J. J.
, and
Okamura
,
A. M.
, 2003, “
Virtual Fixture Architectures for Telemanipulation
,”
Proc. IEEE Int’l. Conf. on Robotics and Automation
,
IEEE
,
New York
, pp.
2798
2805
.
4.
Abbott
,
J. J.
, and
Okamura
,
A. M.
, 2003, “
Steady-Hand Teleoperation With Virtual Fixtures
,”
Proc. of 12th IEEE Int’l. Workshop on Robot and Human Interactive Communication (RO-MAN)
,
IEEE
,
New York
, pp.
145
151
.
5.
Bettini
,
A.
,
Marayong
,
P.
,
Lang
,
S.
,
Okamura
,
A. M.
, and
Hager
,
G. D.
, 2004, “
Vision-Assisted Control for Manipulation Using Virtual Fixtures
,”
IEEE Trans. Rob. Autom.
1042-296X,
20
(
6
), pp.
953
966
.
6.
Li
,
M.
, and
Taylor
,
R. H.
, 2004, “
Spatial Motion Constraints in Medical Robot Using Virtual Fixtures Generated by Anatomy
,”
Proc. of IEEE Int’l. Conf. on Robotics and Automation
,
IEEE
,
New York
, pp.
1270
1275
.
7.
Moore
,
C. A.
,
Peshkin
,
M. A.
, and
Colgate
,
J. E.
, 2003, “
Cobot Implementation of Virtual Paths and 3-D Virtual Surfaces
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
2
), pp.
347
351
.
8.
Park
,
S.
,
Howe
,
R. D.
, and
Torchiana
,
D. F.
, 2001, “
Virtual Fixtures for Robotic Cardiac Surgery
,”
Proc. 4th Int’l. Conf. on Medical Image Computing and Computer-Assisted Intervention
,
IEEE
,
New York
, pp.
1419
1420
.
9.
Payandeh
,
S.
, and
Stanisic
,
Z.
, 2002, “
On Application of Virtual Fixtures as an Aid for Telemanipulation and Training
,”
Proc. of 10th Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems
,
IEEE
,
New York
, pp.
18
23
.
10.
Rosenberg
,
L.
, 1993, “
Virtual Fixtures: Perceptual Tools for Telerobotic Manipulation
,”
Proc. of IEEE Virtual Reality Int’l. Symposium
,
IEEE
,
New York
, pp.
76
82
.
11.
Sayers
,
C.
, 1999,
Remote Control Robotics
.
Springer-Verlag
,
Berlin
.
12.
Turro
,
N.
, and
Khatib
,
O.
, 2000, “
Haptically Augmented Teleoperation
,”
Proc. of 7th Int’l. Symposium on Experimental Robotics
,
Springer-Verlag
,
Berlin
, pp.
1
10
.
13.
Guthart
,
G. S.
, and
Salisbury
,
J. K.
, 2000, “
The Intuitive™ Telesurgery System: Overview and Application
,”
Proc. of IEEE Int’l. Conf. on Robotics and Automation
,
IEEE
,
New York
, pp.
618
621
.
15.
Wagner
,
C. R.
,
Stylopoulos
,
N.
, and
Howe
,
R. D.
, 2002, “
The Role of Force Feedback in Surgery: Analysis of Blunt Dissection
,”
Proc. of 10th Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems
,
IEEE
,
New York
, pp.
68
74
.
16.
Colgate
,
J. E.
, and
Brown
,
J. M.
, 1994, “
Factors Affecting the Z-Width of a Haptic Display
,”
Proc. of IEEE Int’l. Conf. on Robotics and Automation
,
IEEE
,
New York
, pp.
3205
3210
.
17.
Abbott
,
J. J.
, and
Okamura
,
A. M.
, 2005, “
Effects of Position Quantization and Sampling Rate on Virtual-Wall Passivity
,”
IEEE Trans. Rob. Autom.
1042-296X,
21
(
5
), pp.
952
964
.
18.
Zilles
,
C. B.
, and
Salisbury
,
J. K.
, 1995, “
A Constraint-Based God-Object Method for Haptic Display
,”
Proc. of IEEE/RSJ Int’l. Conf. on Intelligent Robots and Systems
,
IEEE
,
New York
, pp.
146
151
.
19.
Lawrence
,
D. A.
, 1993, “
Stability and Transparency in Bilateral Teleoperation
,”
IEEE Trans. Rob. Autom.
1042-296X,
9
(
5
), pp.
624
637
.
20.
Bizzl
,
E.
,
Hogan
,
N.
,
Mussa-Ivaldi
,
F. A.
, and
Giszter
,
S.
, 1992, “
Does the Nervous System Use Equilibrium-Point Control to Guide Single and Multiple Joint Movements?
,”
Behav. Brain Sci.
0140-525X,
15
, pp.
603
613
.
21.
Hajian
,
A. Z.
, and
Howe
,
R. D.
, 1997, “
Identification of the Mechanical Impedance at the Human Finger Tip
,”
ASME J. Biomech. Eng.
0148-0731,
119
, pp.
109
114
.
22.
Salcudean
,
S. E.
, and
Vlaar
,
T. D.
, 1997, “
On the Emulation of Stiff Walls and Static Friction With a Magnetically Levitated Input/Output Device
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
119
, pp.
127
132
.
23.
Wickens
,
C. D.
, 2000,
Engineering Psychology and Human Performance
,
Harper Collins
,
New York
.
24.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Workman
,
M. L.
,
Digital Control of Dynamic Systems
,
2nd ed.
,
Addison-Wesley
,
Reading, MA
.
25.
Okamura
,
A. M.
,
Richard
,
C.
, and
Cutkosky
,
M. R.
, 2002, “
Feeling is Believing: Using a Force-Feedback Joystick to Teach Dynamic Systems
,”
J. Eng. Educ.
1069-4730,
92
(
3
), pp.
345
349
.
26.
Strang
,
G.
, 1988,
Linear Algebra and its Applications
,
3rd ed.
Harcourt Brace Jovanovich
,
Ft. Worth
.
27.
Horn
,
R.
, and
Johnson
,
C. R.
, 1985,
Matrix Analysis
,
Cambridge University Press
,
Cambridge, United Kingdom
.
28.
Smith
,
S. W.
, 1997,
The Scientist and Engineer’s Guide to Digital Signal Processing
,
California Technical Publishing
,
San Diego
.
29.
Kleinbaum
,
D. G.
,
Kupper
,
L. L.
,
Muller
,
K. E.
, and
Nizam
,
A.
,
Applied Regression Analysis and Other Multivariable Methods
,
3rd ed.
Duxbury Press
,
Pacific Cove, CA
.
30.
Hannaford
,
B.
, and
Anderson
,
R.
, 1988, “
Experimental and Simulation Studies of Hard Contact in Force Reflecting Teleoperation
,”
Proc. of IEEE Int’l. Conf. on Robotics and Automation
,
IEEE
,
New York
, pp.
584
589
.
31.
Diolaiti
,
N.
,
Niemeyer
,
G.
,
Barbagli
,
F.
,
Salisbury
,
J. K.
, and
Melchiorri
,
C.
, 2005, “
The Effect of Quantization and Coulomb Friction on the Stability of Haptic Rendering
,”
Proc. of World Haptics Conf.
,
IEEE
,
New York
, pp.
237
246
.
32.
Colgate
,
J. E.
, and
Schenkel
,
G. G.
, 1997, “
Passivity of a Class of Sampled-Data Systems: Application to Haptic Interfaces
,”
J. Rob. Syst.
0741-2223,
14
(
1
), pp.
37
47
.
33.
Craig
,
J. J.
, 1989,
Introduction to Robotics: Mechanics and Control
,
2nd ed.
,
Addison-Wesley
,
Reading, MA
.
34.
Kuchenbecker
,
K. J.
,
Park
,
J. G.
, and
Niemeyer
,
G.
, 2003, “
Characterizing the Human Wrist for Improved Haptic Interaction
,”
Proc. of ASME Int’l. Mechanical Engineering Congress and Exposition
, November, Washington, D.C.,
ASME
,
New York
, pp.
1
8
.
35.
Lundström
,
R.
, 1984, “
Local Vibrations—Mechanical Impedance of the Human Hand’s Glabrous Skin
,”
J. Biomech.
0021-9290,
17
(
2
), pp.
137
144
.
You do not currently have access to this content.