,(((
Adaptive manipulator control based on RBF
network approximation
Na Wang
Qingdao University
The college of Automation and Engineering
QingdaoˈChina
15764238701@163.com
Corresponding Author: Dongqing Wang
Qingdao University
The college of Automation and Engineering
QingdaoˈChina
dqwang64@163.com
Abstract
This paper proposes a neural network controller to
achieve the tracking of a robot manipulator with a highly
nonlinear structure, and presents a online adaptive control
algorithm. The controller based on RBF neural network
approximation is designed, and its stability and convergence is
analyzed under four different circumstances. By minimizing the
system error and considering the characteristic of manipulator,
the online adaptive algorithm is worked out. By Lyapunov
function method, the adaptive updated laws and the control laws
have been developed to guarantee that the resulting closed-loop
system is asymptotically stable. In addition, we also made neural
network approximation for each uncertainty, and analyzed the
overall stability of the system by its Lyapunov function. Finally,
simulation results of a two-joint robotic manipulator certificate
the effectiveness and accuracy of proposed methods .
Keywords—neural networks; highly nonlinear structure;
Lyapunov function; asymptotically stable ; trajectory tracking
I.
I
NTRODUCTION
The design of nonlinear adaptive control scheme with
applications to robot manipulators with model uncertainties is
one of the most challenging tasks in control engineering field.
Most of the control schemes have been confirmed in the field
of robot control, e.g., PID methods [1,6], variable structure
methods [9,10,13,18,20], adaptive methods [3,11,12,16,17],
intelligent methods [4,5,8,14,15], etc.
A control system, which comprises PID control and
neural network control, was presented by Shafiei, S.E for
improving the control performance of the system in real time
[6]. Piltan and Sulaiman designed adaptive fuzzy inference
sliding mode algorithm applied to robot arm [12]. Luca and
Siciliano suggested PD control with on-line gravity
compensation for robots with elastic joints [1]. The
application of intelligent control techniques (fuzzy control or
neural network control) to robot manipulators have received
considerable attentions [5, 6, 8, 10, 11, 14, 15, 18]. The
traditional feedback controllers, such as PID controllers, are
commonly applied in the control field, because their control
structures are simple and easy to implement. However, when
these conventional feedback controllers are used in non-linear
systems, there are some problems such as poor performance
and low robustness [2,3,20]. In order to design a controller for
the manipulator, It is necessary to have accurate trajectory
tracking performance for the reference input and the
robustness of external disturbances.
The dynamics of the robot manipulator is non-linear, and
robot manipulators face various uncertainties in practical
applications such as load parameters, internal friction and
external disturbances [9, 13, 16, 19]. As a result, much effort
has been made to develop control solutions to achieve precise
tracking control of robotic manipulators. Adaptive control
based on RBF network is an effective method for trajectory
tracking control of multi-link robots. Compared with the
multi-layer feedforward BP network, the RBF network has a
good generalization ability, the network structure is simple,
the computation is small, which attracts a wide range of
attention [4, 7, 9, 11]. RBF neural network studies have
shown that the RBF neural network can approximate any
nonlinear function of compact concentration and approximate
it with arbitrary precision. At present, a lot of research results
on RBF neural network control for nonlinear systems have
been published.
The rest of this article is organized as follows. Section 2
introduces the model of robot manipulator and find the
uncertain item in actual engineering, then introduces RBF
network approximation. Section 3 proposes a controller based
on RBF neural network approximation and analyzes the
stability and convergence under four different circumstances.
Section 4 further approximates each item of
)(xf
using neural
network. Section 5 describes the simulation of two-joint robot
manipulator. Finally section 6 gives a conclusion of this paper.
II.
MODEL
OF
ROBOT
MANIPULATOR
1. n-link robot manipulator model
The dynamic model of an n-link robot manipulator may be
expressed in the following Lagrange form:
() (,) () ()
d
MqqCqqqGq Fq
ττ
++++=
(1)
Where
,,
n
qqq R∈
are the joint position, velocity, and
acceleration vectors, respectively;
()
nn
RqM
×
∈
denotes the
inertia matrix;
(, )
nn
Cqq R
×
∈
expresses the coriolis and
centrifugal torques;
()
n
RqG ∈
is the gravity vector;