Abstract

The introduction of flexibility into rigid-body manipulator systems generally complicates the use of simple end-point feedback control. The application of force to these flexibilities induces an unmodeled oscillation that cannot be necessarily compensated through simple end-point feedback control. The normalized coprime factor based robustness metric (εmax) has been well established in the realm of optimal control and can be applied to a rigid system with flexible modes in order to determine postures that will be robust to the flexibilities. This work illustrates that for rigid (double integrator) systems there is fixed normalized coprime-factor robustness and, that for the special case of single-input, single-output flexible systems, deviation from rigidity yields a similar change in normalized coprime factor robustness.

References

1.
Ahmadi
,
M.
, and
Haeri
,
M.
,
2018
, “
Multimodel Control of Nonlinear Systems: An Improved Gap Metric and Stability Margin-Based Method
,”
ASME J. Dyn. Syst., Meas., Control
,
140
(
8
), p.
081013
.10.1115/1.4039086
2.
Abiko
,
S.
, and
Yoshida
,
K.
,
2005
, “
An Adaptive Control of a Space Manipulator for Vibration Suppression
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, Edmonton, AB, Canada, Aug. 2–6, pp.
2167
2172
.10.1109/IROS.2005.1545414
3.
Hishinuma
,
T.
, and
Nenchev
,
D. N.
,
2006
, “
Singularity-Consistent Vibration Suppression Control With a Redundant Manipulator Mounted on a Flexible Base
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, Beijing, China, Oct. 9–15, pp.
3237
3242
.10.1109/IROS.2006.282430
4.
Konno
,
A.
, and
Uchiyama
,
M.
,
1995
, “
Vibration Suppression Control of Spatial Flexible Manipulators
,”
Control Eng. Pract.
,
3
(
9
), pp.
1315
1321
.10.1016/0967-0661(95)00132-E
5.
Balatti
,
P.
,
Kanoulas
,
D.
,
Rigano
,
G. F.
,
Muratore
,
L.
,
Tsagarakis
,
N. G.
, and
Ajoudani
,
A.
,
2018
, “
A Self-Tuning Impedance Controller for Autonomous Robotic Manipulation
,” IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
), Madrid, Spain, Oct. 1–5, pp.
5885
5891
.10.1109/IROS.2018.8593860
6.
Balatti
,
P.
,
Kanoulas
,
D.
,
Tsagarakis
,
N.
, and
Ajoudani
,
A.
,
2020
, “
A Method for Autonomous Robotic Manipulation Through Exploratory Interactions With Uncertain Environments
,”
Auton. Robots
,
44
(
8
), pp.
1395
1410
. 10.1007/s10514-020-09933-w
7.
Abe
,
A.
,
2013
, “
Minimum Energy Trajectory Planning Method for Robot Manipulator Mounted on Flexible Base
,” Ninth Asian Control Conference (
ASCC
), IEEE, Istanbul, Turkey, June 23–26.10.1109/ASCC.2013.6606088
8.
Yang
,
B.-J.
,
Calise
,
A. J.
, and
Craig
,
J. I.
,
2007
, “
Adaptive Output Feedback Control of a Flexible Base Manipulator
,”
J. Guid. Control Dyn.
,
30
(
4
), pp.
1068
1080
.10.2514/1.23707
9.
Ueda
,
J.
, and
Yoshikawa
,
T.
,
2004
, “
Robust Arm Configuration of Manipulator Mounted on Flexible Base
,”
IEEE Trans. Rob.
,
20
(
4
), pp.
781
789
.10.1109/TRO.2004.829482
10.
Ueda
,
J.
, and
Yoshikawa
,
T.
,
2004
, “
Mode-Shape Compensator for Improving Robustness of Manipulator Mounted on Flexible Base
,”
IEEE Trans. Rob. Autom.
,
20
(
2
), pp.
256
268
.10.1109/TRA.2003.819726
11.
LiBretto
,
M.
,
Ahn
,
Y. H.
,
Han
,
C. S.
,
Cho
,
Y. K.
, and
Ueda
,
J.
,
2021
, “
Configuration Optimization for End-Point Stabilization of Redundant Manipulators With Base Flexibility
,”
ASME Lett. Dyn. Syst. Control
,
1
(
2
), p.
021001
.10.1115/1.4046684
12.
Zhou
,
K.
,
1996
,
Robust and Optimal Control
,
Prentice Hall
,
Upper Saddle River, NJ
.
13.
McFarlane
,
D.
, and
Glover
,
K.
,
1990
,
Robust Controller Design Using Normalized Coprime Factor Plant Descriptions
(Lecture Notes in Control and Information Sciences),
Springer
, New York.
14.
Yoshikawa
,
T.
, and
Ueda
,
J.
,
2001
, “
Task Priority Based Mode Shaping Method for in-Phase Design of Flexible Structures Aiming at High Speed and Accurate Positioning
,” IEEE International Conference on Robotics and Automation,
ICRA
(Cat. No.01CH37164), Vol.
2
, Seoul, Korea, May 21–26, pp.
1806
1812
.10.1109/ROBOT.2001.932871
15.
Doyle
,
J. C.
,
Glover
,
K.
,
Khargonekar
,
P. P.
, and
Francis
,
B. A.
,
1989
, “
State-Space Solutions to Standard h/Sub 2/and h/Sub Infinity/Control Problems
,”
IEEE Trans. Autom. Control
,
34
(
8
), pp.
831
847
.10.1109/9.29425
16.
Glover
,
K.
,
1987
, “
Model Reduction: A Tutorial on Hankel-Norm Methods and Lower Bounds on l 2 Errors
,”
IFAC Proc. Vols.
,
20
(
5
), pp.
293
298
.10.1016/S1474-6670(17)55515-9
17.
Horn
,
R.
,
2012
,
Matrix Analysis
,
Cambridge University Press
,
Cambridge, NY
.
18.
Kucera
,
V.
,
1973
, “
A Review of the Matrix Riccati Equation
,”
Kybernetika
,
9
(
1
), pp.
42
61
.
19.
Laub
,
A.
,
1979
, “
A Schur Method for Solving Algebraic Riccati Equations
,”
IEEE Trans. Autom. Control
,
24
(
6
), pp.
913
921
.10.1109/TAC.1979.1102178
20.
Kenney
,
C. S.
, and
Laub
,
A. J.
,
1995
, “
The Matrix Sign Function
,”
IEEE Trans. Autom. Control
,
40
(
8
), pp.
1330
1348
.10.1109/9.402226
21.
Byers
,
R.
,
1987
, “
Solving the Algebraic Riccati Equation With the Matrix Sign Function
,”
Linear Algeb. Appl.
,
85
, pp.
267
279
.10.1016/0024-3795(87)90222-9
22.
Hasanov
,
V. I.
,
2014
, “
Perturbation Theory for Linearly Perturbed Algebraic Riccati Equations
,”
Numer. Funct. Anal. Optim.
,
35
(
12
), pp.
1532
1559
.10.1080/01630563.2014.895765
23.
guang Sun
,
J.
,
1998
, “
Perturbation Theory for Algebraic Riccati Equations
,”
SIAM J. Matrix Anal. Appl.
,
19
(
1
), pp.
39
65
.10.1137/S0895479895291303
24.
Chun-hui
,
C.
, and
Junhui
,
C.
,
1988
, “
Perturbation Analysis for Solutions of Algebraic Riccati Equations
,”
J. Comput. Math.
,
6
(
4
), pp.
336
347
.http://www.jstor.org/stable/43692402
25.
Ueda
,
J.
, and
Ogasawara
,
T.
,
2004
, “
Global RAC-Measure for Redundancy Solution of Human-Like Manipulator Mounted on Flexible Body
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
) (IEEE Cat. No. 04CH37566), Vol.
4
, Sendai, Japan, Sept. 28–Oct. 2, pp.
3930
3935
.10.1109/IROS.2004.1390028
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