In this paper, the finite-time regulation problem of robot manipulators under saturated actuator inputs with position measurements only is addressed. A simple saturated finite-time proportional-derivative (PD) plus gravity compensation (PD+) controller is presented, in which the joint velocity is estimated by constructing a simple nonlinear filter. Global finite-time stability is shown by using Lyapunov stability theory and geometric homogeneity technique. The benefits of this design are that the proposed control can be easily implemented and ensures global finite-time stability with bounded control by selecting control gains a priori. Simulations and experimental results illustrate the expected performance of the proposed approach.

References

References
1.
Wu
,
J.
,
Wang
,
J.
,
Wang
,
L.
, and
Li
,
T.
,
2009
, “
Dynamics and Control of a Planar 3-DOF Parallel Manipulator With Actuation Redundancy
,”
Mech. Mach. Theory
,
44
(
4
), pp.
835
849
.
2.
Wu
,
J.
,
Wang
,
D.
, and
Wang
,
L.
,
2015
, “
A Control Strategy of a Two Degrees-of-Freedom Heavy Duty Parallel Manipulator
,”
ASME J. Dyn. Syst., Meas., Control
,
137
(
6
), p.
061007
.
3.
Hsiao
,
T.
, and
Weng
,
M. C.
,
2013
, “
Robust Joint Position Feedback Control of Robot Manipulators
,”
ASME J. Dyn. Syst., Meas., Control
,
135
(
3
), p.
031010
.
4.
Mendoza
,
M.
,
Zavala-Río
,
A.
,
Santibáñez
,
V.
, and
Reyes
,
F.
,
2015
, “
A Generalised PID-Type Control Scheme With Simple Tuning for the Global Regulation of Robot Manipulators With Constrained Inputs
,”
Int. J. Control
,
88
(
10
), pp.
1995
2012
.
5.
Takegaki
,
M.
, and
Arimoto
,
S.
,
1981
, “
A New Feedback Method for Dynamic Control of Manipulators
,”
ASME J. Dyn. Syst. Meas. Control
,
103
(
2
), pp.
119
125
.
6.
Kelly
,
R.
,
1997
, “
PD Control With Desired Gravity Compensation of Robotic Manipulators: A Review
,”
Int. J. Rob. Res.
,
16
(
5
), pp.
660
672
.
7.
Kelly
,
R.
,
Santibáñez
,
V.
, and
Loría
,
A.
,
2005
,
Control of Robot Manipulators in Joint Space
,
Springer
,
London
.
8.
Kelly
,
R.
,
1993
, “
A Simple Set-Point Robot Controller by Using Only Position Measurements
,”
12th IFAC World Congress
, IFAC, Vol. 6, pp.
173
176
.
9.
Berghuis
,
H.
, and
Nijmeijer
,
H.
,
1993
, “
Global Regulation of Robots Using Only Position Measurements
,”
Syst. Control Lett.
,
21
(
4
), pp.
289
293
.
10.
Orlov
,
Y.
,
Alvarez
,
J.
,
Acho
,
L.
, and
Aguilar
,
L.
,
2003
, “
Global Position Regulation of Friction Manipulators Via Switched Chattering Control
,”
Int. J. Control
,
76
(
14
), pp.
1446
1452
.
11.
Kelly
,
R.
,
Santibáñez
,
V.
, and
Berghuis
,
H.
,
1997
, “
Point-to-Point Robot Control Under Actuator Constraints
,”
Control Eng. Practice
,
5
(
11
), pp.
1555
1562
.
12.
Zavala-Río
,
A.
, and
Santibáñez
,
V.
,
2007
, “
A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs
,”
IEEE Trans. Robot.
,
23
(
2
), pp.
386
391
.
13.
Zavala-Río
,
A.
, and
Santibáñez
,
V.
,
2006
, “
Simple Extensions of the PD-With-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs
,”
IEEE Trans. Control Syst. Technol.
,
14
(
5
), pp.
958
965
.
14.
Santibáñez
,
V.
, and
Kelly
,
R.
,
1996
, “
Global Regulation for Robot Manipulators Under SP-SD Feedback
,”
1996 IEEE International Conference Robotics and Automation
, Apr. 22–28, IEEE, Vol. 1, pp.
927
932
.
15.
Santibáñez
,
V.
,
Kelly
,
R.
, and
Reyes
,
F.
,
1998
, “
A New Set-Point Controller With Bounded Torques for Robot Manipulators
,”
IEEE Trans. Ind. Electron.
,
45
(
1
), pp.
126
133
.
16.
Loría
,
A.
,
Kelly
,
R.
,
Ortega
,
R.
, and
Santibáñez
,
V.
,
1997
, “
On Global Output Feedback Regulation of Euler–Lagrange Systems With Bounded Inputs
,”
IEEE Trans. Autom. Control
,
42
(
8
), pp.
1138
1143
.
17.
Laib
,
A.
,
2000
, “
Adaptive Output Regulation of Robot Manipulators Under Actuator Constraints
,”
IEEE Trans. Robot. Automat.
,
16
(
1
), pp.
29
35
.
18.
Su
,
Y.
, and
Parra-Vega
,
V.
,
2008
, “
Global Asymptotic Saturated Output Feedback Control of Robot Manipulators
,”
7th World Congress on Intelligent Control and Automation
, June 25–27, IEEE, pp.
3445
3450
.
19.
Alvarez-Ramirez
,
J.
,
Kelly
,
R.
, and
Cervantes
,
I.
,
2003
, “
Semiglobal Stability of Saturated Linear PID Control for Robot Manipulators
,”
Automatica
,
39
(
6
), pp.
989
995
.
20.
Alvarez-Ramirez
,
J.
,
Santibáñez
,
V.
, and
Campa
,
R.
,
2008
, “
Stability of Robot Manipulators Under Saturated PID Compensation
,”
IEEE Trans. Control Syst. Technol.
,
16
(
6
), pp.
1333
1341
.
21.
Gorez
,
R.
,
1999
, “
Globally Stable PID-Like Control of Mechanical Systems
,”
Syst. Contro Lett.
,
38
(
1
), pp.
61
72
.
22.
Meza
,
J. L.
,
Santibañez
,
V.
, and
Hernández
,
V. M.
,
2005
, “
Saturated Nonlinear PID Global Regulator for Robot Manipulators: Passivity Based Analysis
,”
IFAC Proc
.,
38
(
1
), pp.
433
438
.
23.
Su
,
Y.
,
Müller
,
P. C.
, and
Zheng
,
C.
,
2010
, “
Global Asymptotic Saturated PID Control for Robot Manipulators
,”
IEEE Trans. Control Syst. Technol.
,
18
(
6
), pp.
1280
1288
.
24.
Haimo
,
V. T.
,
1986
, “
Finite Time Controllers
,”
SIAM J. Control Optim.
,
24
(
4
), pp.
760
770
.
25.
Bhat
,
S. P.
, and
Bernstein
,
D. S.
,
1997
, “
Finite-Time Stability of Homogeneous Systems
,”
American Control Conference
, Albuquerque, NM, June, pp.
2513
2514
.
26.
Bhat
,
S. P.
, and
Bernstein
,
D. S.
,
1998
, “
Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators
,”
IEEE Trans. Autom. Control
,
43
(
5
), pp.
678
682
.
27.
Hong
,
Y.
,
Huang
,
J.
, and
Xu
,
Y.
,
2001
, “
On an Output Feedback Finite-Time Stabilization Problem
,”
IEEE Trans. Autom. Control
,
46
(
2
), pp.
305
309
.
28.
Hong
,
Y.
,
Xu
,
Y.
, and
Huang
,
J.
,
2002
, “
Finite-Time Control for Robot Manipulators
,”
Syst. Control Lett.
,
46
(
4
), pp.
243
253
.
29.
Su
,
Y.
, and
Zheng
,
C.
,
2009
, “
A Simple Nonlinear PID Control for Finite-Time Regulation of Robot Manipulators
,”
IEEE
International Conference on Robotics and Automation
, May 27–29, IEEE, pp.
2569
2574
.
30.
Zavala-Río
,
A.
, and
Fantoni
,
I.
,
2014
, “
Global Finite-Time Stability Characterized Through a Local Notion of Homogeneity
,”
IEEE Trans. Autom. Control
,
59
(
2
), pp.
471
477
.
31.
Su
,
Y.
,
Zheng
,
C.
, and
Müller
,
P.
,
2008
, “
Global Continuous Finite-Time Output Feedback Regulation of Robot Manipulators
,”
International Conference on Robotics and Automation
, IEEE, pp.
3383
3388
.
32.
Su
,
Y.
, and
Zheng
,
C.
,
2010
, “
A Simple Nonlinear PID Control for Global Finite-Time Regulation of Robot Manipulators Without Velocity Measurements
,”
Interenational Conference on Robotics and Automation
, May 3–7, IEEE, pp.
4651
4656
.
33.
Slotine
,
J. J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice-Hall
,
Englewood Cliffs, NJ.
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