Abstract

An enhanced inverse dynamics approach is here presented for feedforward control of underactuated multibody systems, such as mechanisms or robots where the number of independent actuators is smaller than the number of degrees of freedom. The method exploits the concept of partitioning the independent coordinates into actuated and unactuated ones (through a QR-decomposition) and of linearly combined output, to obtain the internal dynamics of the nonminimum-phase system and then to stabilize it through proper output redefinition. Then, the exact algebraic model of the actuated sub-system is inverted, leading to the desired control forces with just minor approximations and no need for pre-actuation. The effectiveness of the proposed approach is assessed by three numerical test cases, by comparing it with some meaningful benchmarks taken from the literature. Finally, experimental verification through an underactuated robotic arm with two degrees of freedom is performed.

References

1.
Richiedei
,
D.
, and
Tamellin
,
I.
,
2021
, “
Active Control of Linear Vibrating Systems for Antiresonance Assignment With Regional Pole Placement
,”
J. Sound Vib.
,
494
, p.
115858
.
2.
Ouyang
,
H.
,
2010
, “
Pole Assignment of Friction-Induced Vibration for Stabilisation Through State-Feedback Control
,”
J. Sound Vib.
,
329
(
11
), pp.
1985
1991
.
3.
Araújo
,
J. M.
,
Dórea
,
C. E. T.
,
Gonçalves
,
L. M. G.
,
Carvalho
,
J. B. P.
, and
Datta
,
B. N.
,
2018
, “
Robustness of the Quadratic Partial Eigenvalue Assignment Using Spectrum Sensitivities for State and Derivative Feedback Designs
,”
J. Low Freq. Noise Vib. Act. Control
,
37
(
2
), pp.
253
268
.
4.
Audet
,
J. M.
, and
Gosselin
,
C.
,
2021
, “
Rotational Low-Impedance Physical Human–Robot Interaction Using Underactuated Redundancy
,”
ASME J. Mech. Rob.
,
13
(
1
), p.
014503
.
5.
Blajer
,
W.
,
2014
, “
The Use of Servo-constraints in the Inverse Dynamics Analysis of Underactuated Multibody Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
4
), p.
041008
.
6.
Bastos
,
Jr. G.
,
2018
, “
A Synergistic Optimal Design for Trajectory Tracking of Underactuated Manipulators
,”
ASME J. Dyn. Syst. Meas. Control
,
141
(
2
), p.
021015
.
7.
Wang
,
Q.
,
Quan
,
Q.
,
Deng
,
Z.
, and
Hou
,
X.
,
2016
, “
An Underactuated Robotic Arm Based on Differential Gears for Capturing Moving Targets: Analysis and Design
,”
ASME J. Mech. Rob.
,
8
(
4
), p.
041012
.
8.
Ma
,
R. R.
, and
Dollar
,
A. M.
,
2013
, “
Linkage-Based Analysis and Optimization of an Underactuated Planar Manipulator for In-Hand Manipulation
,”
ASME J. Mech. Rob.
,
6
(
1
), p.
011002
.
9.
Biao
,
L.
,
Youwei
,
L.
,
Xiaoming
,
X.
,
Haoyi
,
W.
, and
Longhan
,
X.
,
2022
, “
Design and Control of a Flexible Exoskeleton to Generate a Natural Full Gait for Lower-Limb Rehabilitation
,”
ASME J. Mech. Rob.
,
15
(
1
), p.
011005
.
10.
Fliess
,
M.
,
Levine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1995
, “
Flatness and Defect of Non-linear Systems: Introductory Theory and Examples
,”
Int. J. Control
,
61
(
6
), pp.
1327
1361
.
11.
Heyden
,
T.
, and
Woernle
,
C.
,
2006
, “
Dynamics and Flatness-Based Control of a Kinematically Undetermined Cable Suspension Manipulator
,”
Multibody Syst. Dyn.
,
16
(
2
), pp.
155
177
.
12.
Blajer
,
W.
,
Dziewiecki
,
K.
,
Kołodziejczyk
,
K.
, and
Mazur
,
Z.
,
2011
, “
Inverse Dynamics of Underactuated Mechanical Systems: A Simple Case Study and Experimental Verification
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
(
5
), pp.
2265
2272
.
13.
Biagiotti
,
L.
, and
Melchiorri
,
C.
,
2008
,
Trajectory Planning for Automatic Machines and Robots
,
Springer Science & Business Media
.
14.
Richiedei
,
D.
, and
Trevisani
,
A.
,
2016
, “
Analytical Computation of the Energy-Efficient Optimal Planning in Rest-to-Rest Motion of Constant Inertia Systems
,”
Mechatronics
,
39
, pp.
147
159
.
15.
Richiedei
,
D.
,
2018
, “
Integrated Selection of Gearbox, Gear Ratio, and Motor Through Scaling Rules
,”
Mech. Based Des. Struct. Mach.
,
46
(
6
), pp.
712
729
.
16.
De Luca
,
A.
,
Lucibello
,
P.
, and
Ulivi
,
A. G.
,
1989
, “
Inversion Techniques for Trajectory Control of Flexible Robot Arms
,”
J. Robot. Syst.
,
6
(
4
), pp.
325
344
.
17.
Devasia
,
S.
,
Chen
,
D.
, and
Paden
,
B.
,
1996
, “
Nonlinear Inversion-Based Output Tracking
,”
IEEE Trans. Autom. Control.
,
41
(
7
), pp.
930
942
.
18.
Devasia
,
S.
, and
Paden
,
B.
,
1998
, “
Stable Inversion for Nonlinear Nonminimum-Phase Time-Varying Systems
,”
IEEE Trans. Autom. Control.
,
43
(
2
), pp.
283
288
.
19.
Butterworth
,
J. A.
,
Pao
,
L. Y.
, and
Abramovitch
,
D. Y.
,
2012
, “
Analysis and Comparison of Three Discrete-Time Feedforward Model-Inverse Control Techniques for Nonminimum-Phase Systems
,”
Mechatronics
,
22
(
5
), pp.
577
587
.
20.
Seifried
,
R.
,
2012
, “
Integrated Mechanical and Control Design of Underactuated Multibody Systems
,”
Nonlinear Dyn.
,
67
(
2
), pp.
1539
1557
.
21.
Seifried
,
R.
,
2012
, “
Two Approaches for Feedforward Control and Optimal Design of Underactuated Multibody Systems
,”
Multibody Syst. Dyn.
,
27
(
1
), pp.
75
93
.
22.
Bastos
,
G.
,
Seifried
,
R.
, and
Brüls
,
O.
,
2017
, “
Analysis of Stable Model Inversion Methods for Constrained Underactuated Mechanical Systems
,”
Mech. Mach. Theory
,
111
, pp.
99
117
.
23.
Zanotto
,
V.
,
Gasparetto
,
A.
,
Lanzutti
,
A.
,
Boscariol
,
P.
, and
Vidoni
,
R.
,
2011
, “
Experimental Validation of Minimum Time-Jerk Algorithms for Industrial Robots
,”
J. Intell. Rob. Syst. Theory Appl.
,
64
(
2
), pp.
197
219
.
24.
Boscariol
,
P.
,
Gasparetto
,
A.
, and
Vidoni
,
R.
,
2012
, “
Planning Continuous-Jerk Trajectories for Industrial Manipulators
,”
Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
,
Nantes, France
,
Feb. 3
, pp.
127
136
.
25.
Oriolo
,
G.
, and
Nakamura
,
Y.
,
1991
, “
Control of Mechanical Systems with Second-Order Nonholonomic Constraints: Underactuated Manipulators
,”
Proceedings of the 30th IEEE Conference on Decision and Control
,
Brighton, UK
,
Dec. 11–13
, pp.
2398
2403
.
26.
García de Jalón
,
J.
,
1994
,
Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge
,
Springer
,
New York, NY
.
27.
Belotti
,
R.
,
Richiedei
,
D.
,
Tamellin
,
I.
, and
Trevisani
,
A.
,
2020
, “
Inverse Structural Modification for Improving the Design of Harmonic Excitation Forces in Underactuated Vibration Generators
,”
ISMA
,
Leuven, Belgium
,
Sept. 7–9
, pp.
1069
1079
.
28.
Belotti
,
R.
,
Richiedei
,
D.
,
Tamellin
,
I.
, and
Trevisani
,
A.
,
2021
, “
Response Optimization of Underactuated Vibration Generators Through Dynamic Structural Modification and Shaping of the Excitation Forces
,”
Int. J. Adv. Manuf. Technol.
,
112
(
1–2
), pp.
505
524
.
29.
Okabe
,
S.
,
Kamiya
,
Y.
,
Tsujikado
,
K.
, and
Yokoyama
,
Y.
,
1985
, “
Vibratory Feeding by Nonsinusoidal Vibration—Optimum Wave Form
,”
ASME J. Vib. Acoust.
,
107
(
2
), pp.
188
195
.
30.
Caracciolo
,
R.
,
Richiedei
,
D.
,
Trevisani
,
A.
, and
Zanardo
,
G.
,
2015
, “
Designing Vibratory Linear Feeders Through an Inverse Dynamic Structural Modification Approach
,”
Int. J. Adv. Manuf. Technol.
,
80
(
9–12
), pp.
1587
1599
.
31.
Richiedei
,
D.
, and
Trevisani
,
A.
,
2008
, “
Delayed-Reference Anti-swing Control of Overhead Crane Systems
,”
Proceedings of the 2008 10th IEEE International Workshop on Advanced Motion Control
,
Trento, Italy
,
Mar. 26–28
, Vol. 1, pp.
92
97
.
32.
Choi
,
S. B.
,
Seong
,
M. S.
, and
Ha
,
S. H.
,
2013
, “
Accurate Position Control of a Flexible Arm Using a Piezoactuator Associated With a Hysteresis Compensator
,”
Smart Mater. Struct.
,
22
(
4
), p.
045009
.
33.
Scalera
,
L.
,
Boscariol
,
P.
,
Carabin
,
G.
,
Vidoni
,
R.
, and
Gasparetto
,
A.
,
2020
, “
Enhancing Energy Efficiency of a 4-DOF Parallel Robot Through Task-Related Analysis
,”
Machines
,
8
(
1
), pp.
1
14
.
34.
Wang
,
X.
, and
Chen
,
D.
,
2006
, “
Output Tracking Control of a One-Link Flexible Manipulator via Causal Inversion
,”
IEEE Trans. Control Syst. Technol.
,
14
(
1
), pp.
141
148
.
35.
Kollmorgen
, “
S200 High Performance Compact Brushless Servo Drives
,” https://www.kollmorgen.com/sites/default/files/public_downloads/S200 Base Unit Reference Manual Rev C.pdf.
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