When modeling flexible robots and structures for control purposes, most often the assumed modes (AMs) method is used to describe the deformation in combination with a floating reference frame formulation. This typically has the benefit of obtaining a low-order, but accurate model of the flexible structure, if the number of modes and AMs are properly chosen. The basis for using this method is, however, that the vibrations (deflections) are time and position independent, i.e., the expression is separable in space and time. This holds for the classic Euler–Bernoulli beam equation, but essentially does not hold for translational links. Hence, special care has to be taken when including flexible translational links. In the current paper, different methods for modeling a hydraulic loader crane with a telescopic arm are investigated and compared using both the finite segment (FS) and AMs method. The translational links are approximated by a single beam, respectively, multiple beam elements, with both one and two modes and using different mode shapes. The models are all validated against experimental data and the comparison is made for different operating scenarios. Based on the results, it is found that in most cases a single beam, low mode order approximation is sufficient to accurately model the mechanical structure and this yields similar results as the FS method.

References

References
1.
Pedersen
,
M. M.
,
Hansen
,
M. R.
, and
Ballebye
,
M.
,
2010
, “
Developing a Tool Point Control Scheme for a Hydraulic Crane Using Interactive Real-Time Dynamic Simulation
,”
Model., Identif. Control
,
31
(
4
), pp.
133
143
.
2.
Bak
,
M. K.
, and
Hansen
,
M. R.
,
2013
, “
Analysis of Offshore Knuckle Boom Crane—Part I: Modeling and Parameter Identification
,”
Model., Identif. Control
,
34
(
4
), pp.
157
174
.
3.
Bak
,
M. K.
, and
Hansen
,
M. R.
,
2013
, “
Analysis of Offshore Knuckle Boom Crane—Part II: Motion Control
,”
Model., Identif. Control
,
34
(
4
), pp.
17
181
.
4.
Kovanen
,
J.
, and
Handroos
,
H.
,
2001
, “
Adaptive Open-Loop Control Method for a Hydraulically Driven Flexible Manipulator
,”
IEEE/ASME
International Conference on Advanced Intelligent Mechatronics
, Vol.
2
, pp.
942
947
.
5.
Yang
,
Y.
,
2008
, “
Fuzzy-Pi Damping Control for Hydraulic Crane Tip
,”
Fifth International Conference on Fuzzy Systems and Knowledge Discovery
(
FSKD’08
), Jinan Shandong, Oct. 18–20, Vol.
5
, pp.
75
79
.
6.
Wanner
,
M.
, and
Herkommer
,
T.
,
1994
, “
Off-Line Programming for the Aircraft Cleaning ‘SKYWASH’
,” IEEE/RSJ/GI International Conference on Intelligent Robots and Systems, Advanced Robotic Systems and the Real World (
IROS' 94
), Munich, Germany, Sep. 12–16, Vol.
3
, pp.
1972
1979
.
7.
Schraft
,
R. D.
, and
Wanner
,
M. C.
,
1993
, “
The Aircraft Cleaning Robot “SKYWASH”
,”
Ind. Rob.: Int. J.
,
20
(
6
), pp.
21
24
.
8.
Koivumaki
,
J.
, and
Mattila
,
J.
,
2013
, “
The Automation of Multi Degree of Freedom Hydraulic Crane by Using Virtual Decomposition Control
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
(
AIM
), Wollongong, NSW, July 9–12, pp.
912
919
.
9.
Koivumaki
,
J.
, and
Mattila
,
J.
,
2013
, “
An Energy-Efficient High Performance Motion Control of a Hydraulic Crane Applying Virtual Decomposition Control
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, pp.
4426
4433
.
10.
Morales
,
D. O.
,
Westerberg
,
S.
,
La Hera
,
P.
,
Mettin
,
U.
,
Freidovich
,
L.
, and
Shiriaev
,
A.
,
2011
, “
Open-Loop Control Experiments on Driver Assistance for Crane Forestry Machines
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Shanghai, May 9–13, pp.
1797
1802
.
11.
Aranovskiy
,
S.
, and
Vazquez
,
C.
,
2014
, “
Control of a Single-Link Mobile Hydraulic Actuator With a Pressure Compensator
,”
IEEE Conference on Control Applications
(
CCA
), Juan Les Antibes, Oct. 8–10, pp.
216
221
.
12.
Aranovskiy
,
S.
,
Losenkov
,
A.
, and
Vazquez
,
C.
,
2014
, “
Position Control of an Industrial Hydraulic System With a Pressure Compensator
,”
22nd Mediterranean Conference of Control and Automation
(
MED
), Palermo, June 16–19, pp.
1329
1334
.
13.
Hera
,
P. M. L.
, and
Morales
,
D. O.
,
2012
, “
Modeling Dynamics of an Electro-Hydraulic Servo Actuated Manipulator: A Case Study of a Forestry Forwarder Crane
,”
World Automation Congress (WAC)
, pp.
1
6
.
14.
La Hera
,
P.
,
Ur Rehman
,
B.
, and
Morales
,
D. O.
,
2012
, “
Electro-Hydraulically Actuated Forestry Manipulator: Modeling and Identification
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Vilamoura, Oct. 7–12, pp.
3399
3404
.
15.
Kuchler
,
S.
,
Mahl
,
T.
,
Neupert
,
J.
,
Schneider
,
K.
, and
Sawodny
,
O.
,
2011
, “
Active Control for an Offshore Crane Using Prediction of the Vessel's Motion
,”
IEEE/ASME Trans. Mechatron.
,
16
(
2
), pp.
297
309
.
16.
Kuchler
,
S.
, and
Sawodny
,
O.
,
2010
, “
Nonlinear Control of an Active Heave Compensation System With Time-Delay
,”
IEEE International Conference on Control Applications
(
CCA
), Yokohama, Japan, Sep. 8–10, pp.
1313
1318
.
17.
Kuchler
,
S.
,
Sawodny
,
O.
,
Schneider
,
K.
, and
Langer
,
K.
,
2009
, “
Vibration Damping for a Hydraulic Driven Luffing Cylinder at a Boom Crane Using Feedforward Control
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
(
AIM
), Singapore, July 14–17, pp.
1276
1281
.
18.
Chu
,
Y.
,
Sanfilippo
,
F.
,
Asoy
,
V.
, and
Zhang
,
H.
,
2014
, “
An Effective Heave Compensation and Anti-Sway Control Approach for Offshore Hydraulic Crane Operations
,”
IEEE International Conference on Mechatronics and Automation
(
ICMA
), Tianjin, Aug. 3–6, pp.
1282
1287
.
19.
Shabana
,
A. A.
,
1997
, “
Flexible Multibody Dynamics: Review of Past and Recent Developments
,”
J. Multibody Syst. Dyn.
,
1
(
2
), pp.
189
222
.
20.
Book
,
W.
,
1990
, “
Modeling, Design, and Control of Flexible Manipulator Arms: A Tutorial Review
,” 29th
IEEE
Conference on Decision and Control
, Honolulu, HI, Dec. 5–7, Vol.
2
, pp.
500
506
.
21.
Book
,
W.
, and
Obergfell
,
K.
,
2000
, “
Practical Models for Practical Flexible Arms
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), San Francisco, CA, Vol.
1
, pp.
835
842
.
22.
Wang
,
D.
, and
Vidyasagar
,
M.
,
1988
, “
Modelling of a 5-Bar-Linkage Manipulator With One Flexible Link
,”
IEEE
International Conference on Robotics and Automation
, Philadelphia, PA, Apr., 24–29, Vol.
1
, pp.
21
26
.
23.
Wang
,
D.
, and
Vidyasagar
,
M.
,
1992
, “
Modeling a Class of Multilink Manipulators With the Last Link Flexible
,”
IEEE Trans. Rob. Autom.
,
8
(
1
), pp.
33
41
.
24.
Linjama
,
M.
, and
Virvalo
,
T.
,
1997
, “
Modelling of Flexible Hydraulic Crane
,”
5th Scandinavian International Conference on Fluid Power (SICFP)
.
25.
Linjama
,
M.
, and
Virvalo
,
T.
,
1999
, “
Low-Order Dynamic Model for Flexible Hydraulic Cranes
,”
Proc. Inst. Mech. Eng., Part I
,
213
(
11
), pp.
11
22
.
26.
Linjama
,
M.
, and
Virvalo
,
T.
,
1999
, “
State-Space Model for Control Design of Multi-Link Flexible Hydraulic Cranes
,”
6th Scandinavian International Conference on Fluid Power (SICFP)
.
27.
Morita
,
Y.
,
Ukai
,
H.
, and
Iwazumi
,
T.
,
1996
, “
Trajectory Control of Multi-Link Elastic Robot Manipulators Via a Nonlinear Feedback Controller and a Robust Servo Controller
,”
Int. J. Syst. Sci.
,
27
(
11
), pp.
1099
1111
.
28.
Arteaga
,
M. A.
,
1998
, “
On the Properties of a Dynamic Model of Flexible Robot Manipulators
,”
ASME J. Dyn. Syst. Meas. Control
,
120
(
1
), pp.
8
14
.
29.
Love
,
L.
,
Kress
,
R.
, and
Jansen
,
J.
,
1997
, “
Modeling and Control of a Hydraulically Actuated Flexible-Prismatic Link Robot
,”
IEEE
International Conference on Robotics and Automation
, Albuquerque, NM, Apr. 20–25, Vol.
1
, pp.
669
675
.
30.
Al-Bedoor
,
B.
, and
Khulief
,
Y.
,
1996
, “
An Approximate Analytical Solution of Beam Vibrations During Axial Motion
,”
J. Sound Vib.
,
192
(
1
), pp.
159
171
.
31.
Al-Bedoor
,
B.
, and
Khulief
,
Y.
,
1997
, “
General Planar Dynamics of a Sliding Flexible Link
,”
J. Sound Vib.
,
206
(
5
), pp.
641
661
.
32.
Basher
,
H.
,
2007
, “
Modeling and Simulation of Flexible Robot Manipulator With a Prismatic Joint
,”
IEEE
SoutheastCon, Richmond, VA, Mar. 22–25, pp.
255
260
.
33.
Basher
,
A. H.
,
2000
, “
Dynamic Behavior of a Translating Flexible Beam With a Prismatic Joint
,”
IEEE Southeastcon
, pp.
31
38
.
34.
Pratiher
,
B.
,
2011
, “
Non-Linear Response of a Magneto-Elastic Translating Beam With Prismatic Joint for Higher Resonance Conditions
,”
Int. J. Non-Linear Mech.
,
46
(
5
), pp.
685
692
.
35.
Hansen
,
M. R.
,
Andersen
,
T. O.
, and
Conrad
,
F.
,
2001
, “
Experimentally Base Analysis and Synthesis of Hydraulically Actuated Loader Crane
,”
Bath PTMC (Power Transmission and Motion Control) Conference
.
36.
Huston
,
R. L.
, and
Wang
,
Y.
,
1993
, “
Flexibility Effects in Multibody Systems
,”
Computer-Aided Analysis of Rigid and Flexible Mechanical Systems
(NATO ASI Series, Series E: Applied Sciences), Vol.
268
, Springer, Tróia, Portugal, pp.
351
376
.
37.
Shabana
,
A. A.
,
1998
,
Dynamics of Multibody Systems
,
2nd ed.
,
Cambridge University
,
Chicago, IL
.
38.
Theodore
,
R. J.
, and
Ghosal
,
A.
,
1997
, “
Modelling of Flexible Link-Manipulators With Prismatic Joints
,”
IEEE Trans. Syst. Man Cybern. Part B Cybern.
,
27
(
2
), pp.
296
305
.
39.
Merritt
,
H.
,
1967
,
Hydraulic Control Systems
,
Wiley
,
Cincinnati, OH
.
40.
Handroos
,
H.
,
1989
, “
Mathematical Methods for Combining a Theoretical and an Emperical Approach in Modelling of Fluid Power Components
,”
Proceedings of the Second Bath International Fluid Power Workshop—Fluid Power Components and Systems
, 2nd ed., C. Burrows and K. Edge, eds., University of Bath, UK, pp.
291
314
.
41.
Sørensen
,
H. L.
,
1999
, “
Fluidmekanisk design af hydrauliske sædeventiler (in Danish), Report No. IKS99.41B
,” Ph.D. thesis,
Institut for Konstruktions- og Styreteknik
,
DTU, Copenhagen
.
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