MOBILE ROBOTS ADAPTIVE CONTROL USING NEURAL NETWORKS  
 
I. Dumitrache, M. Drăgoicea 
 
University “Politehnica” Bucharest 
Faculty of Control and Computers 
Automatic Control and System Engineering Department 
Splaiul Independentei 313, 77206 - Bucharest, Romania 
Tel.+40 1 4119918, Fax: +40 1 4119918 
E-mail: {idumitrache, mdragoicea}@ics.pub.ro 
 
 
Abstract: The paper proposes a feed-forward control strategy for mobile robot control that 
accounts for a non-linear model of the vehicle with interaction between inputs and 
outputs. It is possible to include specific model uncertainties in the dynamic model of the 
mobile robot in order to see how the control problem should be addressed taking into 
consideration the complete dynamic mobile robot model. By means of a neural network 
feed-forward controller a real non-linear mathematical model of the vehicle can be taken 
into consideration. The classical velocity control strategy can be extended using artificial 
neural networks in order to compensate for the modelling uncertainties. It is possible to 
develop an intelligent strategy for mobile robot control. 
 
Keywords: intelligent control systems, mobile robots, autonomous navigation, artificial 
neural networks.  
 
 
 
 
1. INTRODUCTION 
 
Technological improvements in the design and 
development of the mechanics and electronics of the 
systems have been followed by the development of 
very efficient and elaborate control strategies. The 
framework of mobile robotics is challenging from 
both theoretical and experimental point of view.  
 
The two important aspects related to mobile robotics 
can be addressed: a) the derivation of kinematic 
and/or dynamic models for wheeled mobile robots, 
for particular prototypes as well as for general robots 
equipped with wheels of several types; b) the mobile 
robot navigation problem that accounts for the 
ability of the mobile vehicle to plan and execute 
collision-free motions in its environment. From an 
engineering point of view, the problem of navigation 
can be addressed by taking into consideration a list 
of functions (collision avoidance, localisation, path-
finding, 
representation 
of 
space, 
control 
architecture).  The last function, control architecture, 
embodies all the other functions to allow the agent to 
move in its environment. 
 
Robot autonomy requests today the leading edge of 
advanced robotics research. The variety of tasks to 
be performed by the robots from object manipulation 
to machine mobility, within a world environment 
which may be largely unknown and unpredictable 
impose to take into consideration improved control 
strategies for mobile robots. Based on the functional 
description of a robotic system (see figure 1), several 
important issues are consequently brought up such as 
the levels of modelling to be used, both for the task 
and the work environment, the computational system 
structure, the operating functionality and the sensor 
based execution control system. From an engineering 
point of view, the navigation problem (as a whole) of 
a mobile robot can be accounted for based on the 
Dumitrache, I., Monica Drãgoicea, Mobile Robots Adaptive Control Using Neural Networks.
Proceedings of the 13th Int. Conference on Control Systems and Computer Science CSCS13,
Bucuresti, Romania, pp:176-181, 2001
 
following list of functions that defines elementary 
functionalities for navigating an autonomous mobile 
agent: representation of space, localisation, collision 
avoidance, path-finding, control architecture.  
 
Mobile vehicles are non-holonomic systems for 
which the control problem was addressed in 
(Campion, et al., 1991), (Bloch and Reyhanoglu, 
1992), (d’Andrea Novel, et al., 1995). Many other 
theoretical control problems have been studied 
concerning mobile vehicles, the difficulty of the 
control problem depending also on the control 
objective, not only on the non-holonomic nature of 
the system. Different architectures of autonomous 
control systems for mobile robots taking into 
consideration intelligent techniques like fuzzy logic, 
neural networks, genetic algorithms and symbolic AI 
are presented in the literature (Tunstel et al., 1998). 
 
 
Figure 1 Functional description of a robotic system 
 
Even though significant progress has been made in 
the study of such non-holonomic mechanical 
systems, both in the topic of modelling and control, 
there are still some problems to be addressed. One of 
this refers to the control problem of non-holonomic 
systems when the model of the system, in particular, 
of the mobile vehicle, is affected by uncertainties, 
arising from neglected dynamics or parameter 
variations. In such cases, the performances of any 
control strategy that uses such model will be 
affected. This article proposes a control strategy 
based on neural network architectures, that can take 
into consideration this modelling uncertainties. 
Researches made in the recent years demonstrate that 
artificial neural networks (ANN) offer a great 
promise for the modelling and control of non-linear 
systems. 
Even 
though 
the 
required 
network 
complexity for non-linear control applications and 
the computational expenses are still important 
problems to be solved, more and more results are 
reported in the field of neural control, such that ANN 
proved to be a real challenge for modern engineering 
technology that have to deal with increasingly 
complex space structures with ever more demanding 
performance criteria.  
 
 
2. THE PROCESS  
 
A car-like mobile robot rolling on a flat ground was 
selected as a case study for the proposed control 
strategy.  
 
This type of vehicle can be represented by a 
rectangular shape moving in R2 (figure 2). The 
movement of the robot in an empty space can be 
described by the posture vector ξ = (x, y, θ), where 
(x, y) are the coordinates of the midpoint P between 
the two rear wheels, and θ ∈ [0, 2π) is the rotation 
angle between the coordinate system that does not 
move with the robot (x0 O0 y0) and  the coordinate 
system attached to the robot (xrPyr). 
 
The linear velocity along the main axis of the robot 
(VAV) and its rotation velocity (θ
•
) are the two 
parameters that determines the instantaneous motion 
of this type of vehicle. Based on these, the kinematic 
state model of the robot can be defined (Betourne, 
1995): 
 
(
)
(
)
x
x
x
u
x
x
x
u
x
L
x
u
x
u
x
r u
x
r
x
D
L
x
u
x
r
x
D
L
x
u
•
•
•
•
•
•
•
=
= −
=
=
=
=
+
=
−
1
3
4
1
2
3
4
1
3
4
1
4
2
5
1
6
4
4
1
7
4
4
1
1
1
1
1
cos(
) cos(
)
sin(
) cos(
)
sin(
)
cos(
)
(
/
) sin(
)
cos(
)
(
/
) sin(
)
 
(1)  
 
where the state vector is x = [x y θ φ ϕc ϕs ϕd ] ∈ R7 . 
With the above mentioned definitions, the equations 
of the steering system can be rewritten: 
 
x
y
S q
•
•
•












=













=
θ
θ
θ
η
η
η
cos
sin
( )
0
0
0
1
1
2
     (2) 
 
 
where 








θ
=




η
η
=
η
•
AV
2
1
V
, |η1| < VAv_max  and |η2| 
< θ
•
max.  
 
The entries of the vector η represent the velocity 
control inputs, and x4 = φ is an internal state 
associated to the orientable wheel of the robot. 
 
 
3. NEURAL NETWORKS BASED  
CONTROL STRATEGY 
 
The 
most 
important 
function 
necessary 
for 
navigating an autonomous agent, the control 
architecture, embodies all the other mentioned 
functions and makes the agent to be “alive”. In 
particular, this work addresses a trajectory tracking 
problem (Sarkar, 1994) in the presence of modelling 
uncertainties of the controlled system. An important 
control problem for mobile robots is to include 
certain specific model uncertainties in the dynamic 
model of the mobile robot. It seems attractive to 
initiate 
an 
adaptive 
control 
for 
parameter 
uncertainties (e.g., unknown mass, wheel-radius; 
etc…).  
The aim of the present paper is to formulate a 
control strategy for mobile robot control based on 
artificial neural networks (ANN). The approach 
considered in the present paper combines the 
stabilisation properties of an feedback conventional 
PID controller with the above mentioned learning 
capabilities of a neural network based feed-forward 
controller. 
 
Conceptually, most of the approaches that accounts 
for neural networks based control structures make 
use of the “inverse” model of the process as a 
controller. From this category, the two strategies that 
gained increased importance lately are IMC (Internal 
Model Control) and feed-forward control. In this 
article the feed-forward controller is implemented as 
a neural network controller that represents the 
inverse model of the process. 
 
The mobile robot can be considered to be a two 
inputs - (the torques for the dc. motors) - two outputs 
(the linear velocity along the main axis, VAV, and the 
rotation velocity, θ
•
) system. 
 
The two levels hierarhical control structure is 
presented in figure 3. The inner loop is used to 
control the velocities of the wheels (velocity 
control), while the outer loop forces the vehicle to 
move on the desired trajectory (motion control). The 
motion controller is the generator of the velocities 
references for the velocity controller. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2 Posture definition 
 
 
A feed-forward adaptive control strategy based on 
neural networks is used in order to implement the 
velocity controller. Figure 3 depicts the two 
components of the velocity controller: 
 
• 
a feedback component (PID control of linear and 
angular velocities, VAV and θ
•
), based on a 
 
ICR 
θ 
Y 
X 
O0 
Y0 
L 
ϕs 
ϕd 
 
φ 
yr 
xr 
ϕc 
D 
D 
X0 
 
simplified model of the process (dc motors and 
mobile platform) (equation 3) (Mazo, 1995); it 
will stabilise the process and will reject the 
perturbations. 
 
M V
r P
P
J
r
D P
P
P
N k
R U
k
k
R
N
r V
k
I
AV
d
s
d
s
s d
M
a
s d
M
E
a
s d
M
••
••
=
+
=
−
=
−
−




1
2
2
60
2
0
(
)
(
)
,
,
,
θ
π
 (3) 
 
      where Pl, r are the left/right torques obtained from 
the dc motors, M is the mass of the platform, r 
radius of the wheels, D half distance between 
rear wheals, J the inertia momentum of the 
platform, N gear ratio, kM torque constant, Ra 
terminal rezistance, kE back emf constant, I0 no 
load current, Vl,r left/right wheels velocities.  
• 
a 
feed-forward 
component, 
with 
learning 
abilities, will allow a fast trajectory tracking. 
This component is important in improving the 
system 
performances 
by 
learning 
on-line 
information about the process, through direct 
interaction. Actually, this component will learn 
on-line the inverse dynamics of the process.   
 
In this way, it is possible to implement an adaptive 
control strategy at the execution level, based on 
neural networks. The neural network (feed-forward 
controller) generates a command signal Uff that will 
adjust the signal generated by the feedback controller, 
Ufb, in order to minimise the velocity reference error, 
while compensating the modelling uncertainties. The 
original contribution of this work consists in 
obtaining the command vector u = [Ul Ur], using the 
reference velocity vector ηc from the motion 
controller. The motion controller was implemented 
following the procedure presented in (Kanayama, 
1990). 
 
Figure 3 Two level hierarchical control structure  
 
 
Some results are depicted in figures 4 and 5. Figure 
4 presents results obtained using a feed-forward 
control strategy (average velocity, rotation velocity 
and tracking errors). Figure 5 presents, for 
comparison, the tracking errors for the two strategies 
(conventional PID and feed-forward with neural 
networks). 
 
The typical evolution of the neural network outputs 
(the feed-forward control signal Uff) is presented in 
figure 6. 
 
 
 
Motion 
Controller 
ηc = f(ep, η, K) 
Feedback 
Controller 
(PID) 
Feedforward 
Controller 
(NN) 
ep 
S(q) 
∫ 
q 
S(q) 
ηr 
ηc = [VAV_c θ‘_c ] 
η 
Ufb 
Uff 
Ul 
qr 
+ 
+ 
  
 
Left motor 
Right motor 
Gear box 
Gear box 
Encoder 
Encoder 
Ur 
Te 
 
 
 
Figure 4 a) 
 
 
 
 
Figure 4 b) 
 
 
 
 
Figure 4 c)Velocity control - neural networks feed-
forward control strategy 
 
 
 
Figure 5 Tracking errors - conventional PID control 
versus neural networks feed-forward control 
 
 
 
 
Figure 6 Neural network feed-forward controller 
outputs 
 
 
4. CONCLUSIONS 
 
This paper proposes a feed-forward control strategy 
for mobile robot control that accounts for the real 
non-linear model of the vehicle with interaction 
between inputs and outputs. In this respect, it is 
possible to include specific model uncertainties in 
the dynamic model of the mobile robot in order to 
see how the control problem should be addressed 
taking into consideration the complete dynamic 
mobile robot model. By means of a neural network 
feed-forward 
controller 
a 
real 
non-linear 
mathematical model of the vehicle can be taken into 
consideration. The classical velocity control strategy 
was extended using artificial neural networks in 
order to compensate for the modelling uncertainties. 
In this way it is possible to develop an intelligent 
strategy for mobile robot control. 
 
 
REFERENCES 
 
d’Andrea Novel B., Campion G., Bastin G., (1995), 
Control of nonholonomic wheeled mobile robots 
by state feedback linearization, Int. Journal of 
Robotics Research, 14(6), pp:543-559  
Betourné A., (1995), Etude de robots mobiles 
omnidirectionnels: modelisation et simulation. 
These de doctorat, Universite Motpellier 
Bloch A., Reyhanoglu M., (1992), Control and 
stabilization of nonholonomic dynamic systems, 
In IEEE Trans. on Automatic Control, 37(11), 
pp. 1746-1757 
Campion G.,  d’Andrea-Novel B., Bastin G., (1991), 
Modelling and state feedback control of 
nonholonomic  mechanical systems, Proceedings 
of the 1991 IEEE Conference on Decision and 
Control, December 1991 
Campion G., Bastin G., d’Andrea-Novel B., (1996), 
Structural 
properties 
and 
classification 
of 
kinematic and dynamic models of wheeled 
mobile robots, IEEE Trans. on Robotics and 
Automation, 12(1), pp. 47-61 
Kanayama Y., Kimura Y., Miyazaki F., (1990), A 
stable tracking control method for an autonomous 
mobile robot, Proc. IEEE Int. Conf. Robot. 
Automat., pp: 384-389 
Latombe J.-C., (1991), Robot Motion Planning, 
Kluwer, Boston 
Mazo M., Rodriguez F.J., et.al, (1995), Electronic 
Control of a Wheelchair guided by voice 
commands, Control Eng. Practice, Vol. 3, No. 5, 
pp: 665-674  
Sarkar N., Yun X., Kumar V., (1994), Control of 
mechanical systems with rolling constraints: 
application to dynamic control of mobile robots, 
Int. Journal of Robotics Research, Vol. 13, No. 
1, pp: 55-69 
Tunstel E.W. Jr., Jamshindi M., (1998), Intelligent 
Control 
and 
Evolution 
of 
Mobile 
Robot 
Behavior, NASA Center for Autonomous Control 
Engineering 
 
 
 
 
 
 
 
 
 
 
 
.