This paper addresses to demonstrate the uniform-ultimately bounded stability (uniformly-ultimately-bounded (UUB)-stability) of the proportional derivative (PD+) compensator where, the joint velocity is not available to be measured but rather it is estimated. The proposed stabilization control strategy is developed for a “n” degrees-of-freedom (DOF) robotic manipulator process, where the joint speed is not available to be measured; furthermore, the external disturbances and/or uncertain dynamics are considered in the system dynamics. To conclude the closed-loop robust stabilization, the proposed feedback strategy is based on the nonlinear state estimation with a Luenberger-like observer and the classical PD+ used in robot manipulators.

References

References
1.
Lewis
,
F.
,
Dawson
,
M.
, and
Abdallah
,
T.
,
2003
,
Robot Manipulator Control: Theory and Practice
,
CRC Press
,
Boca Raton, FL
.
2.
Spong
,
M. W.
,
Hutchinson
,
S.
, and
Vidyasagar
,
M.
,
2006
,
Robot Modeling and Control
,
Wiley
,
New York
.
3.
Kim
,
S.
, and
Sanghyup
,
L.
,
2008
, “
Robust Velocity Estimation of an Omnidirectional Mobile Robot Using a Polygonal Array of Optical Mice
,”
Int. J. Control Autom. Syst.
,
6
(
5
), pp.
713
721
.
4.
Rio
,
A. Z.
,
Ruiz
,
E. A.
, and
Santibanez
,
V.
,
2011
, “
Global Trajectory Tracking Through Output Feedback for Robot Manipulators With Bounded Inputs
,”
Asian J. Control
,
13
(
3
), pp.
430
438
.
5.
Chan
,
S. P.
,
1998
, “
Velocity Estimation for Robot Manipulators Using Neural Network
,”
J. Intell. Rob. Syst.
,
23
(
2
), pp.
147
163
.
6.
Ordaz
,
P.
,
Espinoza
,
E.
, and
Munoz
,
F.
,
2014
, “
Global Stability of PD+ Controller With Velocity Estimation
,”
53rd IEEE Conference on Decision and Control
(
CDC
), Los Angeles, CA, Dec. 15–17, pp.
2580
2585
.
7.
Astrom
,
H. K. J.
,
Wit
,
C. C. D.
,
Gafvert
,
M.
, and
Lischinsky
,
P.
,
1998
, “
Friction Models and Friction Compensation
,”
Eur. J. Control
,
4
(
3
), pp.
176
195
.
8.
Leine
,
R. I.
,
Campen
,
D. H. V.
,
Kraker
,
A. D.
, and
Steen
,
L. V. D.
,
1998
, “
Stick-Slip Vibrations Induced by Alternate Friction Models
,”
Nonlinear Dyn.
,
16
(
1
), pp.
41
54
.
9.
Poznyak
,
A.
,
Polyakov
,
A.
, and
Azhmyakov
,
V.
,
2014
,
Attractive Ellipsoids in Robust Control
,
Springer International Publishing
, Urbana, IL.
10.
Haddad
,
W. M.
, and
Chellaboina
,
V.
,
2008
,
Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach
,
Princeton University Press
, Princeton, NJ.
11.
Poznyak
,
A.
,
2009
,
Advanced Mathematical Tools for Automatic Control Engineers
, Vol.
2
,
Elsevier
, Oxford, UK.
You do not currently have access to this content.