3 Mobile Robotic Systems
3.1 Introduction
Mobile Robotics is an active research area where researchers from all over
the world find new technologies to improve mobile robots intelligence and
areas of application. Today robots navigate autonomously in office
environments as well as outdoors. They show their ability to beside
mechanical and electronic barriers in building mobile platforms, perceiving
the environment and deciding on how to act in a given situation are crucial
problems.
Mobile Robotic Systems are and will be used for new application areas.
The range of potential applications for mobile robots is enormous. It
includes agricultural robotics applications, routine material transport in
factories, warehouses, office buildings and hospitals, indoor and outdoor
security patrols, inventory verification, hazardous material handling,
hazardous site cleanup, underwater applications, and numerous military
applications.
Global competition and the tendency to reduce production cost and
increase efficiency creates new applications for robots that stationary
robots cannot perform. These new applications require the robots to move
and perform certain activities at the same time. The availability and low
cost of faster processors, better programming, and the use of new hardware
allow robot designers to build more accurate, faster, and even safer robots.
Currently, mobile robots are expanding outside the confines of buildings
and into rugged terrain, as well as familiar environments like schools and
city streets (Wong 2005).
3.2 Autonomous Mobile Robotic Systems
Vehicles that can perform desired tasks in unstructured environments
without continuous human guidance are called autonomous mobile robots.
Many kinds of robots are autonomous to some degree, including
teleoperated robots. Different robots can be autonomous in different ways,
but generally a high degree of autonomy is particularly desirable in fields
such as in dynamically changing environments, space or cave explorations;
where communication, delays and interruptions are unavoidable.
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
This concept of autonomy is not only related to mobile robots, some
modern factory robots manipulators are autonomous within the strict
confines of their direct environment. Initially, factory robots have not been
subject to continuous human guidance or even work necessarily under any
human guidance at all. One important area of robotics research is to enable
the robot to cope with its environment whether this is on land, underwater,
in the air, underground or in space (Toibero 2007). An ideally fully
autonomous robot in the real world should have the ability to:





Gain information about the environment
Work for months or years without human intervention
Travel from point A to point B, without human navigation assistance
Avoid situations that are harmful to people, property or itself
Repair itself without outside assistance.
One of the ultimate goals in robotics is to create autonomous robots. Such
robots must accept high-level descriptions of tasks and will execute them
without further human intervention. The input descriptions will specify
what the user wants to be done rather than how to do it (Latombe 1991). It
would however take some time before something close to the goals of
Latombe appears. The early robots primary used for manufacturing, i.e.,
welding, painting and so-called pick and place operations were used in
environments where very few unexpected events occurred and where exact
repeatability of actions was the main measure of excellence.
Figure 3.1: Autonomous Mobile Robot Pioneer 3AT
The biggest obstacle in the design of robots for other areas of application is
uncertainty. Starting from the premise that coping with uncertainty is the
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
59
most crucial problem a mobile robot must face, it can be concluded that the
robot must have the following basic capabilities:
Sensory Interpretation. The robot must be able to determine its
relationship to the environment by sensing. A wide variety of sensing
technologies are available: contact, odometry, ultrasonic, infrared and laser
range sensing; monocular cameras and stereo vision have all been explored.
The difficulty is in interpreting these data, i.e., in deciding what the sensor
signals tell about the external world. The trend to attack this problem is by
sensor fusion, i.e., by combining the outputs of multiple feature detectors
possibly operating on a variety of sensors or simply multiple observations
of the same object. Much of this work has focused on applications of
Kalman filtering, which essentially provides a mechanism for weighting
the various pieces of data based on estimates of their reliability: e.g., the
sonar present some difficulties due to the reflections on the objects, and
laser rangefinders have difficulties when sensing dark objects due to the
absorption, but both can be used together in order to allow the object
detection in critical situations.
Reasoning. The robot must be able to decide what actions are required to
achieve its goals in a given environment. This may involve decisions
ranging from the selection of the paths to take, to what sensors and
controller use. This is done usually in a higher level, namely the supervisor,
which takes into consideration all the control system available information,
and depends strongly on the employed control system architecture.
As expected, in areas where humans move about, positions of things are
subject to change all the time. Furthermore, the variety of obstacles and
objects the robot will encounter is very large. In such circumstances, both
sensing and control become much more complex. Here appears the
importance of the control architecture in order to increase the autonomy of
the robotic platform. This item will be discussed with more detail in the
next sections.
3.2.1 Types of Mobile Robots
Many different types of mobile robotic systems had been developed
depending on the kind of application, velocity, and the type of environment
whether its water, space, terrain with fixed or moving obstacles. Four major
categories had been identified (Dudek & Jenkin 2000):
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
Terrestrial or Ground-contact Robotic Systems. There are three main
types of ground-contact robots: wheeled robots, tracked vehicles, and
limbed (legged) vehicles.
Wheeled robots exploit friction or ground contact to enable the robot to
move. Different kinds of wheeled robots exist: the differential drive robot,
synchronous drive robot, steered wheels robots and Ackerman steering (car
drive) robots, the tricycle, bogey, and bicycle drive robots, and robots with
complex or compound or omnidirectional wheels.
Figure 3.2: Pioneer Robots (ActivMedia Inc.)
Tracked vehicles are robust to any terrain environment, their construction
are similar to the differential drive robot but the two differential wheels are
extended into treads which provide a large contact area and enable the
robot to navigate through a wide range of terrain.
Figure 3.3: Tracked Robots – COMET Group (Oklahoma State University)
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
61
Limbed vehicles are suitable in rough terrains such as those found in
forests, near natural or man-made disasters, or in planetary exploration,
where ground contact support is not available for the entire path of motion.
Limbed vehicles are characterized by the design and the number of legs,
the minimum number of legs needed for a robot to move is one, to be
supported a robot need at least three legs, and four legs are needed for a
statically stable robot, six, eight, and twelve legs robots exists. For example
of a limbed robot, ASIMO which is a humanoid two legs walking robot
developed by Honda and features the ability to pursue key tasks in a reallife environment such as an office (Honda 2008).
Figure 3.4: ASIMO Robot (Honda)
Aquatic Robotic Systems. Aquatic vehicles support propulsion by
utilizing the surrounding water. There are two common structures: torpedolike structures (Feruson & Pope 1995; Kloske et al. 1993) where a single
propeller provides forward, and reverse thrust while the navigation
direction is controlled by the control surfaces, the buoyancy of the vessel
controls the depth. The disadvantage of this type is poor maneuverability.
Figure 3.5: Madeleine Underwater Robot (NSF's Collaborative Research at
Undergraduate Institutions)
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
Flying Robotic Systems. First, fixed-wing autonomous vehicles utilize
control systems very similar to the ones found in commercial autopilots.
Ground station can provide remote commands if needed, and with the help
of the Global Positioning System (GPS) the location of the vehicle can be
determined.
Automated helicopters use onboard computation and sensing and ground
control, their control is very difficult compared to the fixed-wing
autonomous vehicles.
Figure 3.6: CL327 Guardian Helicopter (AHS)
Buoyant (aerobots, aerovehicles, or blimps) vehicles can float and are
characterized by having high energy efficiency ration, long-range travel
and duty cycle, vertical mobility, and they usually has no disastrous results
in case of failure.
Unpowered autonomous flying vehicles reach their desired destination by
utilizing gravity, GPS, and other sensors.
Figure 3.7: Bell Eagle Eye - Military Unmanned Aerial Vehicle (UAV)
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
63
Space Robotic Systems. These are needed for applications related to space
stations like construction, repair, and maintenance. Free-flying systems
have been proposed where the spacecraft is equipped with thrusters with
one or more manipulators, the thrusters are utilized to modify the robot
trajectory (Dudek & Jenkin 2000).
Figure 3.8: Mars Exploration Rover Mission – Spirit Robot (NASA 2004)
3.2.2 Kinematic Modeling
Kinematic models of mobile robots are used into the design of controllers
when the vehicle develops tasks or missions with low speed and load.
Mobile robots have quite simple mathematical models to describe their
instantaneous motion capabilities. However, this only holds for single
mobile robots only, because the modeling does become complex as soon as
one begins to add trailers to mobile robots. Airport luggage carts are a fine
example of such mobile robot trains.
Real-world implementations of car-like or differentially-driven mobile
robots have three or four wheels, because the robot needs at least three noncollinear support points in order not to fall over. However, the kinematics
of the moving robots are most often described by simpler equivalent robot
models.
Holonomic Constraint. A constraint that restricts the system motion to a
smooth hyper surface in the configuration space is called a holonomic
constraint.
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
Pfaffian Constraint. Given a system with configuration variables q, a
constraint of the following type:
A q  q  0
(3.1)
where A(q)  mxn and q  n is called a Pfaffian constraint.
Unicycle-like Mobile Robot. A unicycle mobile robot is a driving robot
that can rotate freely around its axis.
The term unicycle is often used in robotics and control theory to mean a
generalized cart or car moving in a two-dimensional world; these are also
often called "unicycle-like" or "unicycle-type" vehicles. These theoretical
vehicles are typically shown as having two parallel driven wheels, one
mounted on each side of their centre, and (presumably) some sort of offset
castor to maintain balance; although in general they could be any vehicle
capable of simultaneous arbitrary rotation and translation. An alternative
realization uses a single driven wheel with steering, and a pair of idler
wheels to give balance and allow a steering torque to be applied.
A physically realizable unicycle, in this sense, is a nonholonomic system.
This is a system in which a return to the original internal (wheel)
configuration does not guarantee return to the original system (unicycle)
position. In other words, the system outcome is path-dependent.
Nonholonomic constraint. The common characteristic of mobile robots is
that they cannot autonomously produce a velocity which is transversal to
the axle of their wheels. A differentially-driven robot has one such
constraint (the caster wheels are mounted on a swivel and hence give no
constraint, except for friction); bicycles and cars have two constraints: one
on the front wheel axle and one on the rear wheel axle. These constraints
are nonholonomic constraints on the velocity of the robots (Latombe 1991),
i.e., they cannot be integrated to give a constraint on the robots Cartesian
pose (the word ―holonomic‖ is built from the Greek words holos ―integral‖ and nomos - ―law‖).
In other words, the vehicle cannot move transversally instantaneously, but
it can reach any position and orientation by moving backward and forward
while turning appropriately. Parking your car is a typical example of this
maneuver phenomenon. The nonholonomic constraints reduce the mobile
robot instantaneous velocity degrees of freedom
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
65
A Pfaffian constraint that is not equivalent to a holonomic constraint is
called a Nonholonomic constraint.
Nonholonomic Kinematic Model. The kinematics of a nonholonomic
mobile robot can be modeled by the equation (3.2)
 x  u cos   

 y  u sin   
  

(3.2)
where u and  are the control inputs: the linear and the angular velocity,
respectively. The robot state variables are x, y and ; where (x, y) are the
coordinates of the middle point between the driving wheels and  denotes
the heading of the vehicle relative to the x-axis of the world coordinate
system. The vector [x y ]T defines the posture of the vehicle. A rear wheel
turns freely and balances the rear end of the robot above the ground.
It is assumed a non-slip condition on the wheels, so the robot cannot move
sideways. This is the nonholonomic constraint of the unicycle robot. Figure
3.9 shows a diagram of a unicycle-like mobile robot.

u

(x, y)
y
x
Figure 3.9: Unicycle-like nonholonomic mobile robot diagram
Holonomic Kinematic Model. The kinematics of a holonomic mobile
robot can be modeled by (3.3)
 x  u cos     a sin   

 y  u sin     a cos   
  

(3.3)
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
If the unicycle-like mobile robot position is defined by a point, which is
located in front of the wheels axis center (see Fig. 3.10); then, the
holonomic model of the mobile robot is obtained.

u
(x, y)
a

y
x
Figure 3.10: Unicycle-like holonomic mobile robot diagram
The holonomic model does not have velocity restrictions on the plane, that
is, the point (x, y) is able to move in any direction.
3.2.3 Dynamic Modeling
Decoupled dynamic model. The decoupled dynamics of the unicycle-like
mobile robot is given by two differential equations: one as regards the
translational movement and other as regards the rotational movement.
u  Tu u  K gu v
  T  K gv
(3.4)
(3.5)
where, v  vr  vl , v  vr  vl are voltages applied to the right and left
engines of the mobile robot, respectively; v+ and v- are the common and
differential voltages; Tu and T are constants of time; and Kgu and Kg are
the relevant gains of each differential equation. This model considers that
the center of mass of the mobile robot is located in the wheel baseline
center.
The decoupled dynamic model of the unicycle-like mobile robot is valid
provided that the center of mass is located on the wheel baseline center. If
this condition is not fulfilled, it is necessary using a coupled dynamic
model.
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
67
Coupled dynamic model. With the coupled dynamic model the
translational movement is affected by the rotational movement and, vice
versa, that is, the rotational movement is affected by the translational
movement.
The dynamic model introduced by De la Cruz (2006) is illustrated in Fig.
3.11, where h = (x, y) is the point that is required to tracks a trajectory; G is
the center of mass; B is the wheel baseline center; u and ū are the
longitudinal and lateral velocities of the center of mass;  and  are the
angular velocity and heading of the robot; d, b, a, e and c are distances;
Frrx’ and Frry’ are the longitudinal and lateral tire forces of the right wheel;
Frlx’ and Frly’ are the longitudinal and lateral tire forces of the left wheel;
Fcx’ and Fcy’ are the longitudinal and lateral force exerted on C by the
castor; Fex’ and Fey’ are the longitudinal and lateral force exerted on E by
the tool; and e is the moment exerted by the tool.
The force and moment equations for the robot are (Boyden & Velinsky
1994):
(3.5)
 F  m u  u   F  F  F  F
(3.6)
 Fy '  m u  u  Frly '  Frry '  Fey '  Fcy '
d
 M  I   2  F  F   b  F  F    e  b  F   c  b  F   (3.7)
x'
z
z
rlx '
rrx '
rlx '
rly '
rrx '
rry '
ex '
cx '
ey '
cy '
e
where m is the robot mass; and Iz is the robot moment of inertia about la
vertical axis located in G. The kinematics of point h is:
x  u cos     u sin      a  b  sin   
y  u sin     u cos      a  b  cos   
(3.8)
(3.9)
According to Zhang et al. (1998), velocities u,  and ū, including the slip
speeds, are:
1
 r  r  l    urs  uls 

2
1
   r  r  l    urs  uls 
d
b
u   r  r  l    urs  uls   u s
d
u
(3.10)
(3.11)
(3.12)
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
where r is the right and left wheel radius; r and l are the angular
velocities of the right and left wheels; urs and uls are the longitudinal slip
speeds of the right and left wheel, and u s is the lateral slip speed of the
wheels.
Frlx’
x’
u
Frly’
u
Fey E
e
y’
b

G
B
Frrx’
e

a
h
Fcy C
Fex
Fcx
Frry’
c
y
x
d
Figure 3.11: Coupled dynamic model of a mobile robot
The motor models attained by neglecting the voltage on the inductances
are:
r 
l 
ka  vr  kb r 
Ra
ka  vl  kb l 
Ra
(3.13)
(3.14)
where vr and vl are the input voltages applied to the right and left motors; kb
is equal to the voltage constant multiplied by the gear ratio; Ra is the
electric resistance constant; r and l are the right and left motor torques
multiplied by the gear ratio; and ka is the torque constant multiplied by the
gear ratio. The dynamic equations of the motor-wheels are:
I e r  Be r  r  Frrx ' Rt
I e l  Be l  l  Frlx ' Rt
(3.15)
(3.16)
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
69
where Ie and Be are the moment of inertia and the viscous friction
coefficient of the combined motor rotor, gearbox, and wheel, and Rt is the
nominal radius of the tire.
In general, most market-available robots have low level PID velocity
controllers to track input reference velocities and do not allow the motor
voltage to be driven directly. Therefore, it is useful to express the mobile
robot model in a suitable way by considering rotational and translational
reference velocities as control signals. For this purpose, the velocity
controllers are included into the model. To simplify the model, a PD
velocity controller has been considered which is described by the following
equations:
 vu   k PT  uref  ume   k DT ume 

v   
    k PR  ref  me   kDR me 
(3.17)
where
1
 r  r  l 
2
1
me   r  r  l 
d
ume 
Variables uref and ref are neglected in (3.17) to further simplify the model.
From (3.10 – 3.17) the following dynamic model of the mobile robot is
obtained:
u cos     a sin      0


 x  u sin     a cos      0
 y 
 0

  
 
   
3 2 4
1


u
  
  1
1
1
u  
 
   
5
6
 u     0

 
2
2
The parameters of the dynamic model are:
0
0
x 

 
0
 y
  uref    0 
0  ref   

 u 

 
1
2 
(3.18)
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
Ra
 mRt r  2 I e   2rkDT
ka
1 
2rk PT
Ra
I e d 2  2 Rt r  I z  mb 2   2rdk DR
k
2  a
2rdk PR
Ra
mbRt
ka
3 
2k PT


4 
6 

Ra  ka kb
 Be 

ka  Ra

rk PT
Ra
mbRt
ka
5 
dk PR
1

Ra  ka kb
 Be  d

ka  Ra

2rk PR
The elements of the uncertainty vector  x
y
1
0 u
T
  are:
 x  u s sin   
 y  u s cos   
u 
 
 I R  rka k DT  s
Rt Ra

s
mu s  Fex '  Fcx '   4  urs  uls    e a

  ur  ul 
21k PT ka
21
2

rk
k
1
PT a


 I R d  2rka k DR  s
6
5 s
Rt Ra
s
urs  uls    e a
u 

 eFey '  cFcy '  e 
  ur  ul  
2 d
2
2 dk PR ka
 22 rk PR ka d 
The uncertainty vector in (3.18) will not be considered, if the slip speed of
the wheels, the forces and moments exerted by the tool, and the forces
exerted by the castor are of no significant value.
Accelerations u and  do not depend on the states x, y and ; then these
variables can be expressed as follows:
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
71
1
 3 2 4

  u  uref 

1
1

 u   1
   u 
    
6
   
1
 
5
   u      ref 
 2

2
2
By re-arranging -and disregarding the uncertainty vector- the linear
parameterization is attained:
u 0 2

0
0 
u 0 0
 uref 
θ


 
0 u 
 ref 
where θ  1 2 3 4 5 6  ; with an identification method, the
vector θ can be easily identified.
T
3.3 Navigation of Mobile Robotic Systems
As for many robot tasks, mobility is an important issue, robots have to
navigate their environments in a safe and reasonable way. Navigation
describes, in the field of mobile robotics, techniques that allow a robot to
use information it has gathered about the environment to reach goals that
are given a priory or derived from a higher level task description in an
effective and efficient way.
The main question of navigation is how to get from where we are to where
we want to be. Researchers work on that question since the early days of
mobile robotics and have developed many solutions to the problem
considering different robot environments. Those include indoor
environments, as well is in much larger scale outdoor environments and
under water navigation.
Beside the question of global navigation, how to get from A to B
navigation in mobile robotics has local aspects. Depending on the
architecture of a mobile robot (differential drive, car like, submarine, plain,
etc.) the robot possible actions are constrained not only by the robots
environment but by its dynamics. Robot motion planning takes these
dynamics into account to choose feasible actions and thus ensure a safe
motion.
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
3.3.1 Navigation Systems
A navigation system is the method for guiding a vehicle. Several
capabilities are needed for autonomous navigation (Alhaj Ali 2003):
1. The ability to execute elementary goal achieving actions such as
going to a given location or following a leader;
2. The ability to react to unexpected events in real time such as
avoiding a suddenly appearing obstacle;
3. The ability to formulate a map of the environment.
Odometry. This method, like other dead-reckoning methods, uses encoders
to measure wheel rotation and/or steering orientation (Ojeda 2003).
There are several approaches to reduce the odometry errors in mobile
robots, e.g. for over-constrained mobile robots, three novel error-reducing
methods are mentioned: One method, called ―Fewest Pulses‖ method,
makes use of the observation that most terrain irregularities, as well as
wheel slip, result in an erroneous over-count of encoder pulses. A second
method, called ―Cross-coupled Control,‖ optimizes the motor control
algorithm of the robot to reduce synchronization errors that would
otherwise result in wheel slip with conventional controllers. A third method
is based on so-called ―Expert Rules‖, which readings from redundant
encoders are compared and utilized in different ways, according to
predefined rules.
Sensor based navigation: Sensor based navigation systems that rely on
sonar or laser scanners that provide one dimensional distance profiles have
been used for collision and obstacle avoidance. A general adaptable control
structure is also required. The mobile robot must make decisions on its
navigation tactics; decide which information to use to modify its position,
which path to follow around obstacles, when stopping is the safest
alternative, and which direction to proceed when no path is given. In
addition, sensors information can be used for constructing maps of the
environment for short term reactive planning and long term environmental
learning (Alhaj Ali 2003).
Vision based navigation. Computer vision and image sequence techniques
were proposed for obstacle detection and avoidance for autonomous land
vehicles that can navigate in an outdoor road environment. The object
shape boundary is first extracted from the image, after the translation from
the vehicle location in the current cycle to that in the next cycle, the
position of the object shape in the image of the next cycle is predicted, then
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
73
it is matched with the extracted shape of the object in the image of the next
cycle to decide whether the object is an obstacle (Chen & Tsai 2000).
Inertial navigation. This method uses gyroscopes and sometimes
accelerometers to measure the rate of rotation and acceleration.
Active beacon navigation systems. This method computes the absolute
position of the robot from measuring the direction of incidence of three or
more actively transmitted beacons. The transmitters, usually using light or
radio frequencies must be located at known sites in the environment
(Premvuti & Wang 1996; Alhaj Ali 2003).
Landmark navigation. In this method distinctive artificial landmarks are
placed at known locations in the environment to be detected even under
adverse environmental conditions.
Map-based positioning. In this method information acquired from the
robot onboard sensors is compared to a map or world model of the
environment. The vehicle absolute location can be estimated if features
from the sensor-based map and the world model map match.
Biological navigation. Biologically-inspired approaches were utilized in
the development of intelligent adaptive systems; biomimetic systems
provide a real world test of biological navigation behaviours besides
making new navigation mechanisms available for indoor robots.
Global positioning system (GPS). This system provides specially coded
satellite signals that can be processed in a GPS receiver, enabling it to
compute position, velocity, and time.
3.3.2 Controllers for Mobile Robots
Robots have complex nonlinear dynamics that make their accurate and
robust control difficult. On the other hand, they fall in the class of
Lagrangian dynamical systems, so that they have several extremely nice
physical properties that make their control straight forwarded (Lewis et al.
1999). Different controllers had been developed for the motion of robot
manipulators, however, not until recently where there has been an interest
in moving the robot itself, not only its manipulators.
From a mathematical point of view, the not slipping condition of the nonomnidirectional wheeled robots results in a kinematic constraint
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represented by a differential relationship. This kind of constraint cannot be
integrated and, in the nonholonomic systems, it is not possible to choose
generalized coordinates equal to the number of degrees of freedom. That is,
the number of generalized (e.g., Lagrangian) coordinates exceeds the
number of degrees of freedom by the number of independent, nonintegrable constraints. Hence, nonholonomic systems present an adjunct
complexity for the control system because these systems cannot be
stabilized at a point by smooth feedback (De Luca & Oriolo 1995). Thus,
the design of posture stabilization laws for nonholonomic systems has to
face a serious structural obstruction. As a consequence, opposite to the
usual situation, tracking is easier than regulation for a nonholonomic
vehicle. However, several alternative approaches have been proposed for
regulation of nonholonomic systems.
The simplest approach to designing feedback controllers for nonholonomic
systems is probably to decompose the control in two stages: first, find an
open-loop strategy that can achieve any desired reconfiguration for the
particular system under consideration. Second, transform the motion
sequence into a succession of equilibrium manifolds, which are then
stabilized by feedback. The overall resulting feedback is necessarily
discontinuous, because of the switching of the target manifolds.
Each stabilization problem in the succession should be completed in finite
time (that is, not just asymptotically), so as to have a well-defined
procedure. In order to achieve such convergence behavior, discontinuous
feedback is used within each stabilizing phase. The weakness of this
approach is that it requires the ability to devise an open-loop strategy for
the system. Moreover, any perturbation occurring on a variable that is not
directly controlled during the current phase will result in a final error. As a
result, feedback robustness is achieved only with respect to perturbation of
the initial conditions.
Another approach is to use a time-varying controller. The idea of allowing
the feedback law to depend explicitly on time is due to Samson (1993),
who presented smooth stabilization schemes for the car-like kinematic
models. When considering the point-stabilization of a time-invariant
nonholonomic system, the introduction of a time-varying component in the
control law may lead to a smoothly stabilizable system. However, these
time-varying control laws have typically slow rates of convergence and a
difficult tuning of the various parameters of the controller. An experimental
validation of these kinds of controllers can be found in Kim & Tsiotras
(2002).
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
75
Hybrid strategies for the stabilization of the unicycle have been proposed in
Pomet et al. (1992) and Toibero (2007). Namely, the first work, combining
the advantages of smooth static feedback far from the target and timevarying feedback close to the target. The second research introduces
asymptotically stable switched control systems with redundant controllers
that allow maintaining the robot navigating in the center of a corridor and
solving the parking problem for mobile robots.
Next, some control strategies for mobile robots will be introduced.
Position Control. The position control implies controlling the position and
the orientation of the mobile robot. This aim is not an easy task, because
the limitation given by Brockett (Stern 2002).
In the conventional position control algorithm of the mobile robots, the
output of the system, including the position and orientation sensing data,
are feedback together to the system input through a feedback loop.
Trajectory Tracking Control. The aim of the trajectory tracking control is
to achieve the robot reaches and follows with zero-error desired states timevariant. These desired states describe desired trajectories.
One way to perform a trajectory tracking control is by means of a virtual
robot (Canudas de Wit et al. 1997). The virtual robot model (see Fig. 3.12)
is given by
 xd  ud cos   d 

 yd  ud sin   d 
  
d
 d
(3.19)
 x   cos    sen    0   xd  x 
 y     sen  cos  0   y  y 
 
   d 
  
  
0
0
1   d   
(3.20)
Control errors are defined by
where x , y and  are the control errors. The matrix in (3.20) has inverse,
so that, when x  0 , y  0 and   0 , then x  xd , y  yd and
  d .
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CHAPTER 3: MOBILE ROBOTIC SYSTEMS
ud
Virtual Robot
d
d
Real Robot

(x, y)
(xd, yd)
u

y
x
Figure 3.12: Real and virtual mobile robots for trajectory tracking control
3.3.3 Collision Avoidance
The basic techniques for a mobile robot to move toward to the destination
are localization, path planning, and control. The localization technique is
required to know where the robot is about (Borenstein et al. 1996). It is
mainly dependant upon accuracy of sensors and sensor fusion algorithms.
The path planning technique includes collision avoidance and optimal
trajectory design (Xu et al. 2002; Khatib 1986). The control technique is
how the robot follows the prespecified trajectory with minimal tracking
errors (Rosales et al. 2008). Those techniques are must-have methods for
navigation of an autonomous mobile robot.
For indoor application of a mobile robot, localization can be done by
constructing an environmental map around the robot from sensors. The
map can be used to determine collision avoidance with the wall and objects
in the path. Constructing a map works quite well for a robot to find the path
not colliding with static objects such as wall. For moving objects such as
human beings, however, it is very difficult for a robot to draw dynamic
maps that generate the collision avoidance path and to maintain a desired
distance between the robot and the object. The robot requires prompt
dynamic reaction to avoid collision with moving objects rather than to rely
on static maps.
Current sensor technology available to obstacle avoidance includes GPS,
ladar (laser detection and ranging) in both two and three dimensions, sonar,
microwave radar and CCD cameras. In addition to the features specific to
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
77
each of these sensor technologies, the factors should be considered when
choosing a sensor setup for a platform include cost, computational
complexity of processing, response time, field of vision, resolution, range
of detection, operation in two/three dimensional plane and the effect of
adverse weather conditions.
y
Obstacle
x
Robot
Figure 3.13: Collision Avoidance by using the Ladar Technique
Most research to date in obstacle avoidance has made use of ultrasonic
sensors or sonar due to its low cost and simplicity of use. Unfortunately
these advantages are far outweighed by a very small range of detection (3m
at 40kHz), a poor angular accuracy (+/-5º) and total failure in adverse
weather conditions such as strong winds or platforms operating at high
speeds (Myers & Vlacic 2005). Furthermore, problems with crosstalk can
cause a sonar sensor with a 60ms response operating in a ring configuration
can have a response time of the entire ring of 300ms which is unacceptable
for real-time operation. These problems render the algorithms created
specifically for this type of sensor useless for all but the most trivial
applications in which the platform operates in an indoor static environment
at low speeds.
Another sensor to gain popularity more recently has been the ladar sensor.
Its large range of detection, fast response time, and low complexity of
processing make it ideal for outdoor high speed applications such as
autonomous driving. Its main drawback is that in adverse weather
conditions rain, snow, and dirt can be perceived as false objects. Also
different types of sensors are being continually developed.
A good compromise at this research stage would be to use data fusion to
combine information from a ladar sensor with short-wave radar, which is
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not susceptible to adverse weather conditions, thereby creating a failsafe
sensor setup. The only drawback to this configuration is the current high
cost of the short-wave radar technology.
The separation of obstacle avoidance into different methods is a very
controversial subject in which there are many differing opinions. Most
agree that there are two approaches, global and local (though not always
with these titles). This however is where the agreement ends and due to
different authors differing definitions it is common to find methods
classified as global by one author and local by another.
Global Methods. These methods operate in a static environment by
computing off-line an optimized path from start to finish that avoids all
known static obstacles. This approach cannot deal with incomplete or
inaccurate information or a time-varying environment and the complexity
of this approach means that re-planning is too computationally expensive.
Local methods. These methods use only a small fraction of the world
space and operate in real-time in a dynamic, time-varying environment.
They have the disadvantage of not being able to produce optimal solution
and can get trapped in local minima (such as a large U shaped obstacle).
Using this definition of local methods there are two distinct types of
methods that fit this category: local path planners and reactive methods.
Local path planning methods map out the entire path (made under the
assumption of static obstacles) and then make adjustments while following
the planned path. The most well-known local path planning method is the
potential field approach which has been implemented using a wide variety
of different methods including a method to remove local minima using
harmonic functions.
Reactive methods make angular and translation velocity commands based
upon information processed from current sensory data. Current Reactive
methods include the curvature velocity method, the Dynamic Window
approach (Fox et al. 1997), Velocity Obstacles approach (Nak et al. 1998),
Vector Field Histograms (Borenstein & Koren 1991), Polar Object Chart
method, and Fuzzy Logic.
The combination of local and global methods into an integrated system is
called a Hybrid method. These methods are designed to combine the
advantages of both methods and remove the disadvantages of each
operating singularly. Most hybrid methods operate by using a global path
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
79
planner to provide sub-points along an optimized path that are then used as
goal points for a local method.
Indoor mobile robots should perform goal-directed tasks in cramped and
unknown environments. Both global path planning and local reactive
obstacle avoidance algorithms must be implemented in order to make a
mobile robot with this capability. While a global path planning algorithm
calculates optimal path to a specified goal, a reactive local obstacle
avoidance module takes into account the unknown and changing
characteristics of the environment based on the local sensory information.
3.4 Multi-Robot Systems
In the last years, Multi-Robot Systems are receiving an increased attention
in the scientific community. In part, this is due to the fact that many
problems related to the control of a single robot have been – at least
partially – solved, and researchers start to look at the massive introduction
of mobile systems in real-world domains. In this perspective, multi-robot
systems are an obvious choice for all those applications which implicitly
take benefit of redundancy; i.e., applications in which, even in absence of a
coordination strategy, having more robots working in parallel improves the
system’s fault tolerance, reduces the time required to execute tasks,
guarantees a higher service availability and a quicker response to user
requests.
When taking into account more complex scenarios, multi-robot systems are
no more an option; consider, for example, a team of robots trying to
achieve an objective which cannot be attained by a single robot, or
maintaining a constant spatial relationship between each other in order to
execute a task more effectively.
One of the first issues to be faced is whether coordination should be
formalized and solved through a centralized control process, which
computes outputs to be fed to actuators to perform a coordinated motion of
all the components of the system, or distributed, with each member of the
team taking decisions in autonomy on the basis of its own sensorial inputs,
its internal state and – if available – information exchanged with other
robots.
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Figure 3.12: Multi-robot Cooperative System
The task can be considered as the aim of the multi-robot system, thus, it
changes depending on the different applications and on the typologies of
multi-robot system. The task of the system is usually decomposed in
elementary sub-tasks (task decomposition) easier to understand and control.
These sub-tasks can be distributed among multiple resources (task
allocation), while the overall behavior of the system depends on how these
sub-tasks are recombined to obtain the final action of the system.
The mechanism of cooperation represents the logic that originates the
cooperation and it may depend on the control architectures and strategies,
on aspects of the tasks specification or on the interaction dynamics among
the behaviors. Thus, the multi-robot system has to exhibit a collective
behavior or a set of actions that accomplishes the same behavior that was
required for the single more complex robot. To exhibit this cooperative
intelligent behavior, the members of the multi-robot system have to
communicate directly through an explicit communication channel or
indirectly through one robot sensing the others.
The system performance can be represented through characteristics like,
e.g., execution time of the mission, computational complexity, robustness
and fault tolerance, and it may depend on the global structure of the system,
e.g., typologies of the system, control architectures and strategies, task
definition and actuation, communication characteristics.
Thus, largely different kinds of control architectures for multi-robot
systems have been presented in literature; however, the main distinction
can be done between centralized and decentralized systems.
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
81
3.4.1 Centralized Control
Whereas central approaches often lead to an optimal solution, at least in a
statistical sense, distributed approaches usually lack the necessary
information to optimally solve planning and control problems. They are
nevertheless more efficient to deal with real-word, non-structured
scenarios: since decisions are taken locally, the system is still able to work
when communication is not available, and – in general – allow a quicker,
real-time response and a higher fault-tolerance in a dynamically changing
environment.
In centralized systems, a core unit collects and manages information about
the environment to coordinate and control the motion of the robots and to
guarantee the correct achievement of the mission. In such approaches, the
core unit plays a fundamental role because it manages the whole system,
i.e., it has to coordinate the information received by the distributed sensors
or to manage global information of the environment, to take all the eventual
decisions and to communicate with all the robots of the team; thus, it
should be powerful enough to satisfy all the technological requirement.
Most teams in RoboCup share these considerations, even if
counterexamples exist (Weigel et al. 2002). Notice also that, a part from
optimality, univocally accepted metrics or criteria to compare the
performance of centralized and distributed multi-robot systems are missing;
the problem is raised, for example, in (Schneider, 2005).
3.4.2 Decentralized Control
The dual problem is cooperative sensing, in which robots share their
perceptual information in order to build a more complete and reliable
representation of the environment and the system state. The most notable
example is collaborative localization and mapping (CLAM, see Madhavan
et al. 2004), which has been recently formalized in the same statistical
framework as simultaneous localization and mapping (SLAM), as an
extension of the single robot problem. However, the general idea is older
and different approaches exist in literature, often relying on a sharp
division of roles within the team. Cooperative sensing can include tracking
targets with multiple observers (Parker 2002), helping each other in
reaching target locations (Sgorbissa & Arkin 2003), or the pursuit of an
evader with multiple pursuers (Vidal et al. 2002). Notice also that
cooperative sensing often relies on cooperative motion, and therefore they
cannot be considered as totally disjoint classes of problems.
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In decentralized approaches, instead, the resources are distributed among
all the robots. Each vehicle uses its own sensors to extrapolate local
information of the environment and the relative positions of the close
robots to take its own decisions; moreover, each vehicle can communicate
and share information only with the close vehicles and it is aimed at
achieving only a part of the global mission.
Behaviour-based, auction based, or similar distributed approaches (with or
without explicit communication) are very common; this happens for the
reasons already discussed, not last the fact that optimality in task and role
assignment is computationally very expensive to achieve, and consequently
inappropriate for real-time operation.
(x1, y1)
(x2, y2)
u2, 2
2
u1, 1
1
d12F
Robot 1
ΘF
d13F
Robot 2
u3, 3
(x3, y3)
y
x
3
Robot 3
Figure 3.12: Basic Scheme of a Multi-robot System
Advantages and disadvantages of centralized and decentralized systems
have been object of several discussions in the scientific community.
Centralized systems, for example, can manage global information of the
environment and optimize the coordination among the robots or the
accomplishment of the mission; moreover, they can easily manage faults of
some of the robots. On the other hand, the core unit may represent a
weakness of the system, in fact, it can be the bottle-neck of the system both
for computational and communication time requirements; moreover, its
eventual fault compromises the whole system. Decentralized systems,
instead, permit to take all the advantages of distributed sensing and
actuation, i.e., make possible to use less powerful robots or to use more,
cheaper sensors; they permit to optimize the allocation of the resources and
to equip the robots of the team with different actuation and sensor systems;
moreover, decentralized systems can easily result tolerant to possible
vehicles faults. On the other hand, within decentralized systems it is
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
83
difficult to coordinate the robots and optimize the execution of the mission,
and problems like global localization and mapping, and communication
bandwidth represent limits of this system (Arrichiello 2006).
In practice, many systems are not strictly centralized/decentralized. In fact,
many largely decentralized architectures utilized leader agents (Tanner et
al. (2004)); moreover, different hybrid centralized/decentralized
architectures were presented to take partial advantages of both the
typologies (the hybrid architectures in Das et al. (2002); Feddema et al.
(2002); Stilwell et al. (2005), have central planners that perform an highlevel control over mostly autonomous robots).
The research in multi-robot systems has matured to the point where
systems with hundreds of robots are being proposed (Howard et al. (2006);
Parker (2003)). To achieve a given task, the robots have to share
information, thus, the increasing of the team dimension directly requires an
increasing of the needed resources (e.g., time, sensory efforts and
communication bandwidth). In this sense, all the communication
characteristics like the topology of the network, the communication
bandwidth, the message coordination strategy, the traffic of information
among robots and remote units represent open issues for mobile robot
applications.
The term scalability can represent both static and dynamic scalability. That
is, a system is statically scalable when the control architecture can be kept
exactly the same whether thousands of robots are deployed or only few are
used; a system is dynamically scalable when robots can be added to or
removed from the system on the fly; they may also have the ability to
reallocate and redistribute themselves in a self-organized way. The
scalability properties can be used as evaluation parameters for multi-robot
systems.
Moreover, among evaluation parameters, robustness, rather than efficiency,
is promoted. In fact, a multi-robot system may result robust to malfunctions
like unreliable communication and robot failures. Moreover, a multi-robot
system may be robust to a priori unknown environmental and team changes
not only through unit redundancy but also through a balance between
exploratory and exploitative behavior.
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3.4.3 Architectures of Formation
There exist a large number of publications on feedback in the fields of
cooperative control of autonomous systems—recent results are found in
Beard et al. (2001), Nijmeijer & Rodriguez-Angelez (2003), Fax & Murray
(2004), Spry & Hedrick (2004), Ögren et al. (2004), Kingston et al. (2005),
Kumar et al. (2005), and references therein. A recent survey paper by Ren
et al. (2005) connects various coordinated control problems with consensus
problems known from other scientific fields. While the applications are
different, some common fundamental parts can be extracted from the many
approaches to vehicle formation control. Roughly three approaches are
found in the literature.
Leader-Follower. Briefly explained, the leader-following architecture
defines a leader in the formation while the other members of the formation
follow that leader’s position and orientation with some prescribed offset.
One of the first studies on leader-following formation control for mobile
robots is reported in Wang (1991). Sheikholeslam & Desoer (1992)
formulate decentralized control laws for the highway congestion problem
using information from the leader’s dynamics and the distance to the
proceeding vehicle. Variations on this theme include multiple leaders,
forming a chain, and other tree topologies. This approach has the advantage
of simplicity in that the internal stability of the formation is implied by
stability of the individual vehicles, but is heavily dependent on the leader
for achieving the control objective.
Over-reliance on a single vehicle in the formation may be disadvantageous,
and the lack of explicit feedback from the formation to the leader may
destabilize the formation. A leader-follower architecture for marine craft
has been approached in Encarnação & Pascoal (2001a), where an
autonomous underwater vehicle is forced to track the motion of an
autonomous surface craft, projected down to a fixed depth.
Behavioral Methods. The behavioral approach prescribes a set of desired
behaviors for each member in the group, and weighs them such that
desirable group behavior emerges without an explicit model of the
subsystems or the environment. Possible behaviors include trajectory and
neighbor tracking, collision and obstacle avoidance, and formation keeping.
One paper that describes the behavioral approach for multi-robot teams is
Balch & Arkin (1998) where formation behaviors are implemented with
other navigational behaviors to derive control strategies for goal seeking,
collision avoidance and formation maintenance. In formation control,
several objectives need to be met and from the behavioral approach it is
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
85
expected that averaging the weighted (perhaps competing) behaviors give a
control law that meets the control objectives.
This approach motivates a decentralized implementation where feedback to
the formation is present, since a vehicle reacts according to its neighbors.
When the behavioral rules are given as algorithms, this approach is hard to
analyze mathematically: the group behavior is not explicit, and
characteristics such as stability cannot generally be guaranteed. Systemtheoretic approaches to behavioral control can be found in Stilwell &
Bishop (2002) and Antonelli & Chiaverini (2004). The authors use a set of
functions and control techniques for redundant robotic manipulators given
in Siciliano & Slotine (1991) to control a platoon of autonomous vehicles.
Different tasks can be merged, according to their priority, with an inverse
kinematics algorithm.
Virtual Structures. In the virtual structure approach, the entire formation
is treated as a single, virtual, structure and acts as a single rigid body. The
control law for a single vehicle is derived by defining the dynamics of the
virtual structure and then translate the motion of the virtual structure into
the desired motion for each vehicle. Virtual structures have been achieved
by, for example, having all members of the formation tracking assigned
nodes which move through space in the desired configuration, and using
formation feedback to prevent members leaving the formation as in Beard
et al. (2001) and Ren & Beard (2004). In Egerstedt & Hu (2001) each
member of the formation tracks a virtual element, while the motion of the
elements is governed by a formation function that specifies the desired
geometry of the formation. This approach makes it easy to prescribe a
coordinated behavior for the group, while formation keeping is naturally
assured by the approach. However, if the formation has to maintain the
exact same virtual structure at all times, the potential applications are
limited. Skjetne, Moi & Fossen (2002) create a virtual structure of marine
surface vessels by using a centralized control law that maneuvers the
formation along a predefined path.
3.4.4 Configuration of the Formation
Depending on its current coordination goal a formation can have many
different shapes. For example, marine surface vessels can be in a side-byside formation during underway replenishment operations or in a V
formation during transit (to save energy). Thus, formation control systems
should be able to encompass changing configurations during operation. In
addition, with a stable dynamic formation topology, vehicles are permitted
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to leave and join the formation without changing the formation stability
properties. This can further be extended to allow formations to split and
merge. Dynamic topologies are considered in, e.g., Tanner et al. (2004),
Fax & Murray (2004), Olfati-Saber & Murray (2004), and Arcak (2006).
When several control systems are to be coordinated, information must be
exchanged between them in order to complete the control task. Ren et al.
(2005) states the following intuitive axiom:
Shared information is a necessary condition for coordination. The amount
of communicated information depends on the coordination task: if two
systems must synchronize their position, some information about the other
systems position must be known. If the goal is synchronized motion (both
position and velocity), the systems must also share information about their
velocity.
The coordination goal might be: assembling into a desired formation
configuration, ending up at a given location at an appointed time, or
synchronized motion. An alternative to sharing both position and velocity
information during operations is to consider synchronized paths which
incorporates information of not only position but also velocity and
acceleration assignments. Thus, motion can be coordinated with a smaller
amount of shared information since a position on the path implies fixed
speed and velocity assignments. In order to achieve proper synchronization,
the individual paths must be coordinated at the start of the operation.
Information must be exchanged over a communication channel. Typically,
for a set of independent vehicles, a communication protocol is set up over a
physical medium, e.g., using radio-, acoustic, or optic signals. Moreau
(2005) study multi-agent systems with time-dependent communication
links; Olfati-Saber & Murray (2004) investigate consensus problems with
time-delays. Standard communication protocols offer robustness to signal
loss, delays, etc., but communication issues such as inconsistent delays,
noise, signal dropouts, and possible asynchronous updates should be taken
into account in the formation control architecture.
3.4.5 Multi-Agent Systems
The multi-agent system concepts appeared recently and it is extremely
distributed in all research areas; to solve problems by many agents
cooperation. These agents, which have been using for multi-agent system,
are defined as an entity; software routine, robot, sensor, process or person,
DYNAMIC CONTROL OF MOBILE ROBOTIC SYSTEMS
87
which performs actions, works and makes decision. In human society
concepts, the cooperation means ―an intricate and subtle activity, which has
defied many attempts to formalize it‖. Artificial and real social activity in
social systems is the paradigm examples of Cooperation. In multi-agent
concepts side, there are many definitions for cooperation; the most popular
definitions are
1. The multi-agents working together for doing something that creates a
progressive result such increasing performance or saving time.
2. One agent adopts the goal of another agent. Its hypothesis is that the
two agents have been designed in advance and, there is no conflict
goal between them, furthermore, one agent only adopts another agent
aim passively.
3. One autonomous agent adopts another autonomous agent goal. Its
hypothesis is that cooperation only occurs between the agents, which
have the ability of rejecting or accepting the cooperation.
An agent is a computer system that is capable of autonomous action on
behalf of its user or owner in some environment in order to meet its design
objectives.
An intelligent agent is a computer system capable of flexible autonomous
action in some environment. By flexible, it means: reactive, pro-active and
social.
A static environment is one that can be assumed to remain unchanged
except by the performance of actions by the agent. A dynamic environment
is one that has other processes operating on it, and which hence changes in
ways beyond the agent control.
The assumed task condition is like a group of mobile robots are randomly
allocated in an unknown area, the area has limited boundary and may
contain some obstacles. The robots should be finally programmed to have
ability to find their way out to gather at certain desired place in that area;
ability to plan their path and avoid collisions; ability to communicate with
each peer robot and the server through wireless network; ability to from a
line and move alone a line, from a circle and move surround a circle.