We treat the question of position and force control of a three-axis elastic robotic system on a constraint surface based on nonlinear inversion of an input-output map and linear feedback stabilization. Unlike the rigid robots, the feedback linearizing control of end point motion gives rise to unstable zero dynamics. Instability of zero dynamics is avoided by controlling a parameterized output vector corresponding to a point close to the end point of the arm. Zero dynamics are stable or almost stable as long as the parameter in the output vector does not exceed a critical value. Using the inverse controller, the control of the force and the position of the end point is possible while the end effector moves on the constraint surface. However, this excites the elastic modes. For the final capture of the terminal state and vibration suppression, a linear stabilizer is designed. Simulation results are presented to show that in the closed-loop system trajectory and force control on the constraint surface is accomplished.

Issue Section:
Technical Papers
Topics:
Motion control, Robots, Dynamics (Mechanics), Feedback, Force control, Closed loop systems, Control equipment, End effectors, Robotics, Simulation results, Trajectories (Physics), Vibration suppression
1.
Asada
H.
,
Ma
Z.-D.
, and
Tokumaru
H.
,
1990
, “
Inverse Dynamics of Flexible Robot Arms: Modeling and Computation of Trajectory Control
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
112
, No.
6
, pp.
117
–
185
.
2.
Ahmad, S., 1991, “Control of Cooperative Multiple Flexible Joint Robots,” Proc. of IEEE Conf. on Decision and Control, Brighton, England, pp. 1413–1418.
3.
Bayo
E.
,
Papadopoulos
P.
,
Stubbe
J.
, and
Serna
M.
,
1989
, “
Inverse Dynamics and Kinematics of Multi-Link Elastic Robots: An Iterative Frequency Domain Approach
,”
Int. J. Robotics Research
, Vol.
8
, No.
6
, pp.
49
–
62
.
4.
Book
W. J.
,
Maizza-Neto
O.
, and
Whitney
D. E.
,
1975
, “
Feedback Control of Two Beam, Two Joint Systems with Distributed Flexibility
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
97
, No.
4
, pp.
424
–
431
.
5.
Chalhoub
N. G.
, and
Ulsoy
A. G.
,
1987
, “
Control of a Flexible Robot Arm: Experimental and Theoretical Results
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
109
, pp.
299
–
309
.
6.
Chiou
B. C.
, and
Shahinpoor
M.
,
1988
, “
Dynamic Stability Analysis of a One-Link Force-Controlled Flexible Manipulator
,”
Journal of Robotic Systems
, Vol.
5
, No.
5
, pp.
443
–
451
.
7.
Chiou, B. C., and Shahinpoor, M., 1989, “The Effects of Joint and Link Flexibilities on the Dynamic Stability of Force-Controlled Manipulators,” Proc. of IEEE Int. Conf. on Robotics and Automation, Scotsdale, AZ, pp. 398–403.
8.
De Luca
A.
,
Lucibello
P.
, and
Ulivi
G.
,
1989
, “
Inversion Techniques for Trajectory Control of Flexible Robot Arms
,”
J. Robotic Systems
, Vol.
6
, No.
4
, pp.
325
–
344
.
9.
Hirschorn
R. M.
,
1981
, “
Output Tracking in Multivariable Nonlinear Systems
,”
IEEE Trans. on Automatic Control
, Vol.
AC-26
, No.
2
, pp.
593
–
595
.
10.
Hu, F. L., and Ulsoy, A. G., 1993, “Dynamic Modeling of Constrained Flexible Robot Arms for Controller Design,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL, in press.
11.
Hu, F. L., and Ulsoy, A. G., 1993, “Force and Motion Control of a Constrained Flexible Robot Arm,” Proc. of American Control Conf., San Francisco, CA, pp. 2862–2867.
12.
Isidori, A., 1989, Nonlinear Control Systems, 2nd Edition, Springer-Verlag, Berlin.
13.
Khatib, O., 1985, “The Operational Space Formulation in the Analysis, Design, and Control of Robotic Manipulator,” Proc. 3rd Int. Symposium on Robotic Research, pp. 103–110.
14.
Lucibello, P., 1989, “Nonlinear Regulation with Internal Stability of a Two-Link Flexible Robotic Arm,” Proc. IEEE Conf. on Decision and Control, Tampa, FL, pp. 1645–1650.
15.
McClamroch
N. H.
,
1990
, “
Feedback Stabilization of Control Systems Described by a Class of Nonlinear Differential-Algebraic Equations
,”
Systems & Control Letters
, Vol.
15
, pp.
53
–
60
.
16.
McClamroch
N. H.
, and
Wang
D.
,
1988
, “
Feedback Stabilization and Tracking of Constrained Robots
,”
IEEE Transactions on Automatic Control
, Vol.
33
, pp.
419
–
426
.
17.
Mills
J. K.
, and
Goldenberg
A. A.
,
1989
, “
Force and Position Control of Manipulators During Constrained Tasks
,”
IEEE Transactions on Robotics and Automation
, Vol.
5
, pp.
30
–
46
.
18.
Nathan
P. J.
, and
Singh
S. N.
,
1991
, “
Sliding Mode Control and Elastic Mode Stabilization of a Robotic Arm with Flexible Links
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, No.
4
, pp.
669
–
676
.
19.
Nijmeijer, H., and van der Schaft, A. J., 1990, Nonlinear Dynamic Control Systems, Springer-Verlag, New York, 1990.
20.
Raibert
M. H.
, and
Craig
J. J.
,
1981
, “
Hybrid Position/Force Control of Manipulators
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
102
, pp.
126
–
133
.
21.
Siciliano
B.
, and
Book
W. J.
,
1988
, “
A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators
,”
The International Journal of Robotics Research
, Vol.
7
, No.
4
, pp.
79
–
88
.
22.
Singh
S. N.
, and
Schy
A. A.
,
1986
, “
Elastic Robot Control: Nonlinear Inversion and Linear Stabilization
,”
IEEE Transactions on Aerospace and Electronic Systems
, Vol. AES
22
, pp.
340
–
348
.
23.
Slotine, J-J. E., and Li, W., 1991, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ.
24.
Wang
D.
, and
Vidyasagar
M.
,
1991
a, “
Control of a Class of Manipulators with a Single Flexible Link—Part I: Feedback Linearization
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, No.
4
, pp.
655
–
661
.
25.
Wang
D.
, and
Vidyasagar
M.
,
1991
b, “
Control of a Class of Manipulators with a Single Flexible Link—Part II: Observer-Controller Stabilization
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, No.
4
, pp.
662
–
668
.
26.
Whitney
D. E.
,
1987
, “
Historical Perspective and State of the Art in Robot Force Control
,”
Int. Journal Robotics Research
, Vol.
6
, No.
7
, pp.
3
–
14
.
27.
Yoshikawa
T.
,
1987
, “
Dynamic Hybrid Position/Force Control of Robot Manipulators—Description of Hand Constraints and Calculation of Joint Driving Force
,”
IEEE Transactions of Robotics and Automation
, Vol.
RA-3
, No.
5
, pp.
386
–
392
.
28.
Yun, X., 1991, “Nonlinear Feedback for Force Control of Robot Manipulator,” Advances in Robotic Systems, C. T. Leondes, Vol. 40, Part 2 of 2, Academic Press, NY, pp. 259–284.
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