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DYNAMIC TRACKING CONTROL OF NONHOLONOMIC
MOBILE ROBOT WITH MODEL REFERENCE
ADAPTATION FOR UNCERTAIN PARAMETERS
Ali Gholipour, M.J.Yazdanpanah
Control and Intelligent Processing Center of Excellence,
Electrical and Computer Engineering Department, University of Tehran, P.O. Box 14395/515, Tehran, IRAN

gholipoor@ut.ac.ir ; yazdan@ut.ac.ir

Abstract
Dynamic control of parallel wheeled differential drive mobile
robot is considered. The dynamic model is composed of two
consecutive parts; kinematic model and equations of linear
and angular torques. By transforming dynamic error equations
of kinematic model to mobile coordinates, the tracking
problem changes to stabilization. controller is designed in two
consecutive parts: in the first part kinematic stabilization is
done using nonlinear control laws, in the second one
,acceleration rate control has been used for Exponential
stabilization of linear and angular velocities. Uncertainties in
the parameters of dynamic model (mass and inertia) have
been compensated using model reference adaptive control. By
introducing appropriate Lyapunov functions asymptotic
stability of state variables and stability of system is
guaranteed. The distinctive property of the proposed
controller is its robustness of performance in the presence of
uncertainties. Simulations illustrate quality and efficiency of
this method.
Keywords-Mobile Robot, Tracking, Nonlinear Control,
Adaptive Control, Nonholonomic.

1. Introduction
The robot studied in this research is a kind of a simple
nonholonomic mechanical system. Many studies in
nonholonomic control systems have been carried on in past
decade [1,2,3,4,5,6]. However, few of them have resulted in
reportable data, even for such a simple, but important issue as
wheeled mobile robot. Nonholonomic property is seen in
many mechanical and robotic systems, particularly those
using velocity inputs. Smaller control space compared with
configuration space (lesser control signals than independent
controlling variables) causes conditional controllability of
these systems. So the feasible trajectory is limited. This
means that a mobile robot with parallel wheels can’t move
laterally. Nonholonomic constraint is a differential equation
on the base of state variables, it’s not integrable. Rolling but
not sliding is a source of this constraint.
Kinematic model of parallel wheeled mobile robot fails to
meet Brockett’s necessary condition for feedback stabilization
(Brockett 1983). This implies that no smooth...
DYNAMIC TRACKING CONTROL OF NONHOLONOMIC
MOBILE ROBOT WITH MODEL REFERENCE
ADAPTATION FOR UNCERTAIN PARAMETERS
Ali Gholipour, M.J.Yazdanpanah
Control and Intelligent Processing Center of Excellence,
Electrical and Computer Engineering Department, University of Tehran, P.O. Box 14395/515, Tehran, IRAN
gholipoor@ut.ac.ir ; yazdan@ut.ac.ir
Abstract
Dynamic control of parallel wheeled differential drive mobile
robot is considered. The dynamic model is composed of two
consecutive parts; kinematic model and equations of linear
and angular torques. By transforming dynamic error equations
of kinematic model to mobile coordinates, the tracking
problem changes to stabilization. controller is designed in two
consecutive parts: in the first part kinematic stabilization is
done using nonlinear control laws, in the second one
,acceleration rate control has been used for Exponential
stabilization of linear and angular velocities. Uncertainties in
the parameters of dynamic model (mass and inertia) have
been compensated using model reference adaptive control. By
introducing appropriate Lyapunov functions asymptotic
stability of state variables and stability of system is
guaranteed. The distinctive property of the proposed
controller is its robustness of performance in the presence of
uncertainties. Simulations illustrate quality and efficiency of
this method.
Keywords-Mobile Robot, Tracking, Nonlinear Control,
Adaptive Control, Nonholonomic.
1. Introduction
The robot studied in this research is a kind of a simple
nonholonomic mechanical system. Many studies in
nonholonomic control systems have been carried on in past
decade [1,2,3,4,5,6]. However, few of them have resulted in
reportable data, even for such a simple, but important issue as
wheeled mobile robot. Nonholonomic property is seen in
many mechanical and robotic systems, particularly those
using velocity inputs. Smaller control space compared with
configuration space (lesser control signals than independent
controlling variables) causes conditional controllability of
these systems. So the feasible trajectory is limited. This
means that a mobile robot with parallel wheels can’t move
laterally. Nonholonomic constraint is a differential equation
on the base of state variables, its not integrable. Rolling but
not sliding is a source of this constraint.
Kinematic model of parallel wheeled mobile robot fails to
meet Brockett’s necessary condition for feedback stabilization
(Brockett 1983). This implies that no smooth or even
continuous time invariant static state feedback law exists
which makes the closed loop system locally asymptotically
stable. This has attracted interest of researchers to the
complicate and fascinating problem of mobile robot control.
Tracking control using direct Lyapunov method [7], time
variant state feedback [8] and many other primitive methods
are designed on the basis of kinematic model [12].
Stabilization and control of nonholonomic systems with
dynamic equations have been considered in [1], backstepping
based methods are presented in several papers [9,10,11].
Recently adaptive methods are used to compensate the effect
of uncertainties in dynamic model [3,4]. These are designed
for chained forms and have complicated equations. In
addition, the efficiency of method in the presence of
uncertainties is not compared with simple non-adaptive
controllers. Stability is studied in many articles, but there is
no straightforward solution for tracking problem and measure
of tracking error, so simple controllers are more suitable for
regular use [7,12].
In this study the effect of uncertain parameters of dynamic
model on system performance is considered. It’s shown that
the suggested method based on adaptive control can save the
closed loop performance vis-vis changing parameters of
mass and inertia of robot. In addition the distinctive simplicity
of the proposed controller leads to the possibility of adjusting
the parameters to achieve the desired performance including
tracking error and control signals. These properties are
especially obtained by this dynamic controller. Dynamic
model is divided into two consecutive parts. By using simple
control structures for each part, the effect of uncertain
parameters is studied. With model reference adaptive control
for uncertain parts of equations, stability and robustness of
performance is guaranteed. The article is composed of seven
sections; after this introduction, in the second section, the
dynamic model and its transformation to desired structure is
presented. Section three describes a Lyapunov based
nonlinear control method for asymptotic stability of kinematic
equations. In the forth section, the overall structure of
dynamic controller is considered. Section five deals with the
effect of uncertain parameters and presents the model
reference adaptive control law. The simulation results are
presented in section six and the last section contains the
concluding remarks.
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