This paper presents solutions of dynamics, inverse dynamics, and control problems of multi-link flexible manipulators. In deriving the manipulator dynamics, flexible deformations are assumed to be small in relation to the link length, angular rates of the links are assumed to be much smaller than their fundamental frequencies, and nonlinear terms (centrifugal and Coriolis forces) in the flexible manipulator model are assumed to be the same as those in the rigid body model. Flexible displacements are measured with respect to the rigid body configuration, obtained from its rigid body inverse kinematics. As a result, a linear time-varying system is obtained. The inverse dynamics problem consists of determination of joint torques for a given tip trajectory such that joint angles in the flexible configuration are equal to the angles in the rigid body configuration. The manipulator control system consists of the feedforward compensation and feedback control loops. Simulation results of a two-link space crane with a large payload show that the performance of this linearized dynamics and control approach is accurate, and at the same time is robust when subjected to parameter variations during slew operations.

Issue Section:
Research Papers
Topics:
Dynamics (Mechanics), Flexible manipulators, Control systems, Coriolis force, Cranes, Deformation, Feedback, Feedforward control, Kinematics, Manipulator dynamics, Manipulators, Simulation results, Time-varying systems, Trajectories (Physics)
1.
Anderson
B. D. O.
,
1967
, “
A System Theory Criterion for Positive Real Matrices
,”
J. SIAM Control
, Vol.
5
, No.
2
, pp.
171
–
182
.
2.
Asada, H., and Ma, Z.-D., 1989, “Inverse Dynamics of Flexible Robots,” Proc. 1989 American Control Conference, Pittsburgh, pp. 2352–2359.
3.
Bayo, E., et al., 1987, “Inverse Dynamics and Kinematics of Multi-Link Elastic Robots: An Iterative Frequency Domain Approach,” Report UCSB-ME-87-7.
4.
Bayo, E., and Moulin, H., 1989, “An Efficient Computation of the Inverse Dynamics of Flexible Manipulators in the Time Domain,” IEEE Robotics and Automation Conference, pp. 710–715.
5.
Benati
M.
, and
Morro
A.
,
1988
, “
Dynamics of a Chain of Flexible Links
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
110
, pp.
410
–
415
.
6.
Craig, J. J., 1988, Introduction to Robotics. Mechanics and Control, Addison-Wesley, Reading, PA.
7.
Cyril, X., Angels, J., and Misra, A. K., 1989, “Flexible-Link Robotic Manipulator Dynamics,” Proc. 1989 American Control Conference, Pittsburgh, pp. 2346–2351.
8.
Das, S. K., Utku, S., and Wada, B. K., 1989, “Inverse Dynamics of Adaptive Structures Used as Space Cranes,” JPL Internal Document D-6489.
9.
Gawronski, W., 1989, “Detection of Flexible Deformations in Space Crane Dynamics,” JPL Internal Document, Engineering Memo, EM 343–1149.
10.
Gawronski, W., and Ih, C. H., 1989a, “The Space Crane Kinematics, Dynamics and Parametric Study for Control Design (2D Rigid Body Model),” JPL Internal Document D-6657.
11.
Gawronski, W., and Ih, C. H., 1989b, “3D Rigid Body Dynamic Modeling of Space Crane for Control Design and Analysis,” JPL Internal Document D-6878.
12.
Gawronski, W., and Juang, J.-N., 1990a, “Model Reduction for Flexible Structures,” Control and Dynamic Systems, C. Leondes, ed., Vol. 36, Academic Press, New York.
13.
Gawronski
W.
, and
Juang
J.-N.
,
1990
b, “
Model Reduction in Limited Time and Frequency Intervals
,”
Int. J. Systems Science
, Vol.
21
, pp.
349
–
376
.
14.
Gawronski
W.
, and
Williams
T.
,
1991
, “
Model Reduction for Flexible Space Structures
,”
J. Guidance, Control and Dynamics
, Vol.
14
, pp.
68
–
76
.
15.
Huang
Y.
, and
Lee
C. S. G.
,
1988
, “
Generalization of Newton-Euler Formulation of Dynamic Equations to Nonrigid Manipulators
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
110
, pp.
308
–
315
.
16.
Judd
R. P.
, and
Falkenburg
D. R.
,
1985
, “
Dynamics of Nonrigid Articulated Robot Linkages
,”
IEEE Trans. Autom. Control
, Vol.
AC-30
, pp.
499
–
502
.
17.
Low
K. H.
,
1989
, “
Solution Schemes for the System Equations of Flexible Robots
,”
J. Robotic Systems
, Vol.
6
, pp.
383
–
405
.
18.
Moore
B. C.
,
1981
, “
Principal Component Analysis in Linear Systems: Controllability, Observability and Model Reduction
,”
IEEE Trans. Autom. Control
, Vol.
26
, pp.
17
–
32
.
19.
Naganathan
G.
, and
Soni
A. H.
,
1987
, “
Coupling Effects of Kinematics and Flexibility in Manipulators
,”
Int. J. Robotics Research
, Vol.
6
, pp.
75
–
84
.
20.
Padilla, C. E., and von Flotow, A. H., 1989, “Nonlinear Strain-Displacement Relations in the Dynamics of a Two-Link Flexible Manipulator,” Report SSL 6–89, MIT.
21.
Serna
M. A.
, and
Bayo
E.
,
1989
, “
A Simple and Efficient Computational Approach for the Forward Dynamics of Elastic Robots
,”
J. Robotic Systems
, Vol.
6
, pp.
363
–
382
.
22.
Skelton
R. E.
, and
Yousuff
A.
,
1983
, “
Component Cost Analysis of Large Scale Systems
,”
Int. Journal of Control
, Vol.
37
, pp.
285
–
304
.
23.
Tomei
P.
, and
Tornambe
A.
,
1988
, “
Approximate Modeling of Robots Having Elastic Links
,”
IEEE Trans. Systems, Man, Cybernetics
, Vol.
CAS-18
, pp.
831
–
840
.
24.
Usoro
P. B.
,
Nadira
R.
, and
Mahil
S. S.
,
1986
, “
A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulators
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
108
, pp.
198
–
205
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.