Wheeled Robots are very used in industries for developping

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Wheeled Robots
贾斌（ 20722097 ）
2021.5.18

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PART 1
Part of Book review-
Wheeled Robot

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Overview
Wheeled robot has the advantages of simple structure,
energy saving, high speed and low manufacturing cost, which
is widely used to achieve mobility. This chapter provides a
general description of wheeled mobile robots, discusses their
characteristics from the perspective of mobility, describes the
most common implementation of this robot, and explains the
wheel terrain interaction model and suspension system.

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Overview
Structure
Structure
01 Overview

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Structure
Single-wheel rolling robot
Two-wheeled moving robot ：
Bicycle robot
A two-wheeled mobile robot with two
wheels arranged symmetrically from left
to right
Three - and four-wheel mobile
robots ：
Aikman turn
Sliding steering
Omni-directional mobile ：
McNamara
Omniwheel

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In order to achieve robot locomotion, wheeled mobile robots are widely
used in many applications. In general , wheeled robots consume less energy
and move faster than other locomotion mechanisms (e.g., legged robots or
tracked vehicles). From the viewpoint of control, less control effort is
required, owing to their simple mechanisms and reduced stability problems.
Although it is difficult to overcome rough terrain or uneven ground
conditions, wheeled mobile robots are suitable for a large class of target
environments in practical applications. When we think of a single-wheel
design, there are two candidates: a standard wheel or a special wheel. A
standard wheel can be understood as a conventional tire. Special wheels
possess unique mechanical structures including rollers or spheres.
Structure

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Fig.1 Legged robot Fig.2 Tracked vehicles
Structure

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Fig.3 The general design of a standard wheel.
Figure 3 shows the general design of a
standard wheel.
Three conditionsshould be defined for
a standard wheel design:
1. Determination of the two offsets d and
b
2. Mechanical design that allows steering
motion or
not (i. e., to fix the wheel orientation or
not)
3. Determination of steering and driving
actuation
(i.e., active or passive drive).
Structure

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Condition1 is the kinematic parameter
design problem for a single standard
wheel. The parameter d can be either
0 or some positive constant.
Parameter b is the lateral offset of the
wheel and is usually set to zero. In a
special design, a nonzero b may be
selected to obtain pure rolling contact
between the wheel and ground
without causing rotational slip at the
contact point. However, this is rarely
used and we mainly consider the case
of zero lateral offset b.
Structure

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Condition 2 is a design problem for
whether the wheel orientation can be
changed or not. If the steering axis is
fixed, the wheel provides a velocity
constraint on the driving direction.
Condition3 is the design problem of
whether to actuate steering or driving
motion by actuators or to drive
steering or motion passively.
Structure

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Fig.4 Structures of
standard wheels.
In summary, four types of
standard wheels are commonly used.
First is a passively driven wheel with a
fixed steering axis. Second is a passive
caster wheel with offset d. Third is an
active caster wheel with offset
d,where the steering and driving
motions are controlled by actuators.
An example of caster wheels is shown
in VIDEO 1. The fourth is an active
orientable wheel with zero offset d,
where steering and driving motions
are driven by actuators. The
structures of each wheel type are
shown in Fig. 4.
Structure

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Fig.5 Swedish wheel
and spherical wheel .
Although standard wheels are
advantageous because of their
simple structure and good reliability,
the nonholonomic velocity
constraint (i. e., no side-slip
condition) limits robot motion. On
the other hand , special wheels can
be employed in order to obtain
omnidirectional motion of a mobile
robot ( omnimo-bile robot ), I . e., to
ensure three degrees of freedom
for plane motion. We consider two
typical designs of special wheels: the
Swedish wheel and the spherical
wheel. Figure 5 and VIDEO 2 show
the Swedish wheel.
Structure

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Fig.5 Swedish wheel
Small passive free rollers are
located along the outer rim of the
wheel. Free rollers are employed in
order to eliminate the nonholonomic
velocity constraint. Passive rollers
are free to rotate around the axis of
rotation, which results in lateral
motion of the wheel. As a result, a
driving velocity should be controlled,
while the lateral velocity is passively
determined by the actuation of the
other wheels. A similar design can be
seen in VIDEO 3.
Structure

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Fig.5 Swedish wheel
With any desired linear/angular velocities at
any time. By using the spherical wheel, a
holonomic omnidirectional mobile robot can be
developed and the robot achieves smooth and
continuous contact between the sphere and the
ground. However, the design of the sphere-
supporting mechanism is difficult and the
payload must be quite low due to the point
contact. Another drawback is that the surface of
the sphere can be polluted when traveling over
dirty ground and it is difficult to overcome
irregular ground conditions. These drawbacks
limit the practical application of the spherical
wheel. The spherical structure can also be applied
to special robotic transmissions.
Structure

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Structure
Structure
02 Kinematic Constraints

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We assume, as a first step, that
the mobile robot under study is
made up of a rigid cart equipped
with nondeformable wheels, and
that it is moving on a horizontal
plane. The position of the robot on
the plane is described, with respect
to an arbitrary inertial frame, by the
posture vector where
x and y are the coordinates of a
reference point P of the robot cart ,
while describes the orientation of
a mobile frame attached to the
robot, with respect to the inertial
frame(Fig. 6).
Kinematic Constraints
Fig.6 The posture definition of
a mobile robot on a plane

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Conventional Wheels ：
As shown in Fig.4 there are several
variations of the conventional wheel design.
First, we focus on the off-centered orientable
wheel in Fig4.b.
The center of the wheel, B, is connected to
the cart by a rigid rod from A (a fixed point on
the cart) to B, aligned with the wheel plane.
The rod, whose length is denoted by d , can
rotate around a fixed vertical axle at point A.
The position of A is specified by two constant
polar coordinates, l and α, with respect to the
reference point P .The rotation of the rod with
respect to the cart is represented by the
angle β. The radius of the wheel is denoted by
γ, and its angle of rotation around its
horizontal axle is denoted by . The
description therefore involves four constant
parameters: a n d two variables:
Fig.7 Conventional Wheels ：

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First, we evaluate the velocity of the center of the wheel, which
results from the following vector expression The
two components of this vector in the robot frame are expressed as
：
and
The projections of this vector onto the direction of the wheel
plane, i. e., onto the vector ， and
the vector of the wheel axle ， are and 0,
respectively, corresponding to the pure rolling and nonslip
conditions.
After some manipulations, these conditions can be rewritten in
the following compact form.

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Pure Rolling Condition.
Nonslip Condition.
In the earlier given expressions, is the orthogonal rotation matrix
expressing the orientation of the robot with respect to the inertial
frame, i. e.,
As said before, these general expressions can be simplified for different
types of conventional wheels. For fixed wheels, the center of the wheel
is fixed with respect to the cart and the wheel orientation is constant.
This corresponds to a constant value of βand d = 0 (Fig 4.a). The nonslip
equation then reduces to

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For steering wheels, the center of the wheel is also
fixed with respect to the cart (i.e., d =0), with β time-
varying, so the nonslip equation takes the form

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Swedish Wheels ：
The position of a Swedish wheel with
respect to the cart is described, as for fixed
wheels, by three constant parameters: ˛α,β,
and l. An additional parameter is required to
characterize the direction, with respect to the
wheel plane, of the zero component of
the velocity at the contact point of the
wheel. This parameter is γ, which is the angle
between the axle of the rollers and the wheel
plane (Fig.8).
The kinematic constraints now impose
only one condition
Fig.8 Swedish Wheels

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Robot Configuration Variables
We now consider a wheeled robot equipped with N wheels of the
earlier described types. We use the following subscripts to identify
quantities related to these four types: f for fixed wheels, s for steering
wheels , c for caster wheels, and sw for Swedish wheels. The number of
wheels of each type are denoted by Nf, Ns, Nc, and Nsw, with N =
Nf+Ns+Nc+Nsw.
The configuration of the robot is fully described by the following
generalized coordinate vector:
 Posture coordinates: the posture vector
 Orientation coordinates : the Ns+Nc orientation angles of the
steering and caster wheels.
 Rotation coordinates: the N rotation angles of the Wheels.

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Robot Configuration Variables
This whole set of coordinates is termed as the set of configuration
coordinates.
The total number of configuration coordinates is
Nf+2Ns+2Nc+Nsw+3.

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Structure
Structure
03 Wheeled Robot Structures

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Wheeled Robot Structures
Robots with One Wheel:
A robot with a single wheel is basically unstable with-
out dynamic control in order to maintain its balance of
the body. A typical example is a unicycle.
A spherical robot can also be considered as a single-
wheel robot. A balancing mechanism such as a spinning
wheel is employed to achieve dynamic stability. This
approach has advantages including high maneuverabil-
ity and low rolling resistance. However, single-wheel
robots are rarely used in practical applications, because
additional balancing mechanisms are required, control
is difficult, and pose estimation by pure dead reckoning
is not available.

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Robots with Two Wheels:
In general, there are two types of two-wheel
robots,as shown in Fig.9. Figure 9.a shows a bicycle-
type robot. It is common to steer a front wheel and to
drive a rear wheel. Since the dynamic stability of a
bicycle-type robot increases with its speed, a
balancing mechanism is not necessarily required. The
advantage of this approach is that the robot width
can be reduced. However, a bicycle type is rarely used
because it cannot maintain its pose when the robot
stands still.Figure 9.b shows an inverted-pendulum-
type robot.It is a two-wheel differential drive robot.
It is possible to achieve static stability by
accurately placing the center of gravity on the wheel
axle. However, it is common to apply dynamic
balancing control,which is similar to the conventional
control problem for an inverted pendulum.
Fig.9 (a) Bicycle-type robot
and (b) inverted-pendu-lum-
type robot

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Robots with Three Wheels:
Since a robot with three wheels is statically
stable and has a simple structure, it is one of the
most widely used structures for wheeled robots.
There are a large number of designs according to the
choice of individual wheel types. Every wheel
introduced in Sect. Fig.4 can be used to construct
three-wheel robots. In this section,five popular
design examples are described (Fig.10):
1. Two-wheel differential drive
2. Synchronous drive
3. An omnimobile robot with Swedish wheels
4. An omnimobile robot with active caster wheels
5. An omnidirectional robot with steerable
wheels.
Fig.10 (a) Two-wheel differential drive,
(b) synchronous drive, (c) omnimobile
robot with Swedish wheels, (d) omn-
imobile robot with active caster wheels,
and (e) omnidirectional robot with active
steerable wheels

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Fig.10
(a) Two-wheel differential drive,
(b) synchronous drive,
(c) omnimobile robot with Swedish
wheels,
(d) omn-imobile robot with active
caster wheels, and
(e) omnidirectional robot with active
steerable wheels

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1.Two-Wheel Differential-Drive Robot:
A two-wheel differential-drive robot is one
of the most popular designs and is composed of
two active fixed wheels and one passive caster
wheel.
It is possible to extend the robot to a four-wheel
robot by adding passive caster wheels. The major
advantages of the robot can be summarized as
follows:
 A simple mechanical structure, a simple
kinematic model, and low fabrication cost.
 A zero turning radius is available. For a
cylindrical robot, the obstacle-free space can
easily be computed by expanding obstacle
boundaries by the robot radius r.
 Systematic errors are easy to calibrate.
Fig.10 (a) Two-wheel differential drive,

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2.Synchronous-Drive Robot:
A synchronous-drive robot can be built by using
centered or off-centered orientable wheels. The steering and
driving motions of each wheel are mechanically coupled by
chains or belts, and the motions are actuated synchronously,
so the wheel orientations are always identical. Therefore,
omnidirectional motion, motion in any direction can be
achieved by steering the wheel orientations to the desired
velocity direction. However, the orientation of the robot
chassis cannot be changed. Sometimes a turret is employed
to change the body orientation. The most significant
advantage of the synchronous-drive robot is that
omnidirectional movement can be achieved by using only
two actuators . Since the mechanical structure guarantees
synchronous steering and driving motions, less control
effort is required for motion control. Other advantages
include that odometry information is relatively accurate and
driving forces are evenly distributed among all the wheels.
Fig.10 (b) synchronous drive

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Fig.10 (c) omnimobile robot with
Swedish wheels
3.Omnimobile Robot with Swedish Wheels:
At least three Swedish wheels are required to
build a holonomic omnidirectional robot. A major
advantage of using the Swedish wheel is that
omnidirectional mobile robots can be easily
constructed. At least three Swedish wheels are
required to build a holonomic omnidirectional
robot. Since omnidirectional robots can be
built without using active steering of wheel
modules , the mechanical structures of actuating
parts can have simple structures. However, the
mechanical design of a wheel becomes slightly
complicated. One drawback of the Swedish wheel
is that there is a vertical vibration because of
discontinuous contacts during motion.
In order to solve this problem, a variety of
mechanical designs have been proposed.

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Fig.10 (d) omn-imobile robot with
active caster wheels,
4.Omnimobile Robot with Active Caster Wheels:
A holonomic omnidirectional robot can be constructed
by using at least two active caster wheels. The robot can
be controlled to generate arbitrary linear and angular
velocities regardless of the wheel orientations. Since the
robot uses conventional tires, the disadvantages of
Swedish Wheels, for example, vertical vibrations or
durability problems, can be solved.
The disadvantages of this robot can be summarized as
follows:
 Since the location of the ground contact changes with
respect to the robot chassis ,instability can take place
when the distance between the wheels is too short.
 If the robot switches its movement to the reverse
direction, an abrupt change of wheel orientations may
take place. This is called the shopping-cart effect ,which
may result in instantaneous high steering velocities.

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Fig.10 (e) omnidirectional robot with
active steerable wheels
5.Omnidirectional Robot with Active Steerable Wheels:
Centered orientable wheels are also employed
to build omnidirectional robots; at least two
modules are required. A significant difference
between the active caster wheel and the centered
orientable wheel is that the wheel orientation
should always be aligned with the
desired direction of velocity direction, as computed
by inverse kinematics. This fact implies that this
robot is nonholonomic and omnidirectional.
The mechanical drawbacks are similar to those
of using active caster wheels (many actuators and
complicated mechanical structures). Since the
driving motor is directly attached to the driving
axis in many cases, allowable steering angles are
limited in order to prevent wiring problems.

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Fig.11 Ackermann steering geometry
Robots with Four Wheels:
Among the various four-wheel robots, we focus on
the car-like structure. The car-like structure has been
called as the Ackermann steering geometry. The front
two wheels should be synchronously steered to keep the
same instantaneous center of rotation. It is clear that the
orientations of two front wheels are slightly different
because the curvatures of rotation are different. As a
result, this solution is kinematically equivalent to a single
orientable wheel. A major advantage of a car-like robot is
that it is stable during high-speed motion. However, it
requires a slightly complicated steering mechanism. If
the rear wheels are actuated, a differential gear is
required to obtain pure rolling of the rear wheels during
the turning motion. If the steering angle of the front
wheel cannot reach 90ı, the turning radius becomes
nonzero. Therefore, parking motion control in a cluttered
environment becomes difficult.

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Special Applications of Wheeled Robots:
A robot can be extended to an articulated robot, which is composed of a robot and
trailers. A typical example is the luggage-transporting trailer system at airports. By
exploiting trailers, a mobile robot obtains various practical advantages. For example,
modular and Reconfigurable robots can change their configuration according to service
tasks. A common design is a car with multiple passive trailers, which is the simplest design of
an articulated robot.VIDEO shows another example of a trailer robot.
A fundamental difficulty of using wheels is that they can only be used on flat surfaces.
To overcome this problem, wheels are often attached to a special link mechanism. Each
wheel is equipped with independent actuators and a linkage mechanism enables the robot
to adapt its configuration to irregular ground conditions (VIDEO 4). It can be understood as a
hybrid robot that is a combination of a legged robot and a wheeled robot. Another hybrid
example is a robot equipped with both tracks and wheels. Wheels and tracks have
complementary advantages and disadvantages. Wheeled robots are energy efficient;
however, tracked robots can traverse rough terrain. Therefore, a hybrid robot can selectively
choose its driving mechanism according to environmental conditions, although fabrication
cost increases.

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Structure
Structure
04 Wheel–Terrain Interaction Models

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Wheel–Terrain Interaction Models
Wheel–Terrain Interaction Models:
A wheeled robot’s mobility properties are
governed by forces generated at the wheel–terrain
contact interface. The ability to accurately model
wheel–terrain interaction forces is therefore an
important aspect of robot design, simulation, and
control. These forces are strongly influenced by the
relative stiffness of the wheel and
terrain.Generally, there are four possible wheel–
terrain interaction cases. The first case is that of a
rigid wheel traveling on rigid terrain (Fig.
24.10a).The second case is that of a rigid wheel
traveling on deformable terrain (Fig. 24.10b). The
third case is that of a deformable wheel traveling
on deformable terrain(Fig. 24.10c). The fourth case
is that of a deformable wheel traveling on rigid
terrain (Fig. 24.10d).
Fig.10(a) rigid wheel traveling over rigid terrain
(b) rigid wheel traveling over deformable terrain
(c) deformable wheel traveling over deformable
terrain
(d) deformable wheel traveling over rigid terrain

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1.Rigid Wheels on Rigid Terrain :
An interaction model based on classical Coulomb
friction can then be employed to describe bounds on
available tractive forces,Fx, and lateral forces, Fy, as a
function of the load on the wheel, W, for a robot with n
wheels traveling on a surface with coefficient of friction μ
Since the frictional force can be generated in any
direction, and its magnitude is limited, a bound on the
norm of the frictional and lateral forces can be expressed
as ：
It represents a concept known as the friction ellipse (Fig.
24.11). When the effective friction is equal in all directions
the ellipse becomes a circle.
Fig. 11 Illustration of friction ellipse concept to repre-
sent constraint on longitudinal and lateral friction

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2.Rigid Wheels on Deformable Terrain :
Wheel–terrain interaction occurs along an arc of the wheel, rather
than at a single point (Fig. 24.10b). In such scenarios, the Coulomb
friction model described in Last part does not accurately represent the
relationship between the wheel load and tractive forces. This is because
the mechanism for force generation derives primarily from shearing
along failure planes in the terrain, rather than from frictional contact at
a point on the wheel–terrain interface.
So ， Models of the interaction of rigid wheels on deformable surfaces
were developed by Bekker in the1950s and 1960s in the context of large
military vehicles

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3.Deformable Tires on Rigid Terrain :
In scenarios where the tire stiffness is significantly
lower than the terrain stiffness, only the tire will
experience significant deformation.
The brush model models the tire contact patch as
a row of elastic bristles in contact with the ground.
Carcass, belt, and tread element compliance is captured
by a lumped bristle compliance. For the case of pure
longitudinal slip, the tractive force can be calculated as
In a similar manner, the lateral force can be calculated
as follows
Fig. 12 brush model

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3.Deformable Tires on Rigid Terrain:
The magic formula model is an empirical model
that has found widespread application due to its
flexibility and reduced computational burden. The
model is based on a combination of trigonometric
functions that generate a curve that (usually) passes
through the origin, reaches a peak value, and then
tends to a horizontal asymptote: this behavior is
typical of force/moment versus slip characteristics of
modern tires, regardless of tire size, construction,
inflation pressure, and other characteristics. The
general form of the magic formula model is
Fig. 12 Magic model

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Structure
Structure
05 Wheeled Robot Suspensions

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Wheeled Robot Suspensions
Wheeled Robot Suspensions :
A suspension is a system of linkages, springs,
dampers,and actuators that govern the relative
motion between a robot’s wheels and body. These
mechanisms include a degree of freedom allowing the
wheel to spin, and optional degrees of freedom for
steering and vertical translation. Suspension
mechanisms are useful when driving over uneven
surfaces for several reasons.
Typical suspension mechanisms include simple
prismatic joints,rotational joints with a wheel attached
to a trailing arm,and 4-bar linkages. For car-like
wheeled robots, substantial inspiration can be drawn
from the design of passenger vehicle suspensions,
which has received vast research attention . Fig. 13 Suspension mechanisms

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Passive Suspension Dynamics:
Arguably the most common passive suspension
design consists of a parallel spring and damper mounted
between the robot body and wheels. A simple model for
analyzing the vertical dynamics of this suspension is
commonly referred to as the quarter car model and is
illustrated in Fig.14. The fraction of body mass supported
by the suspension element, mb, is connected to a wheel
with mass mw by a spring element with stiffness ks and a
damping element with damping coefficient bs. The wheel
stiffness is denoted by kw, and transmits vertical
excitation from the uneven terrain surface. The heights of
the body mass, wheel mass, and terrain surface are given
by zb, zw, a n d zμ, respectively.
A state vector x for this model is composed of
the suspension displacement ds=zb-zw, wheel spring
displacement dw=zw-zu, and velocities (zb)’,(zw)’
Fig. 14 Quarter car model for
passive suspension modelling

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Passive Suspension Dynamics:
So we can get his mathematical model ：
Fig. 14 Quarter car model for
passive suspension modelling

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Structure
Structure
06 Conclusions

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Conclusions
Conclusions:
Wheels are the most commonly employed running gear for mobile
robots due to their relative simplicity, robustness, and low cost. The number of
possible wheeled mobile robot realizations is almost infinite , depending on
the number, type, implementation, geometric characteristics, and
motorization of the wheels . This chapter has described several such
realizations . Notwithstanding this variety, it is possible to classify WMRs into
only five generic categories. This categorization aids understanding of wheel
structures through simplification . Practical robot structures have been
classified according to the number and type of wheels . Wheel-terrain
interaction models have been presented to allow the analysis of tractive force
generation capability, for design and simulation purposes. Finally , a brief
description of common suspension systems has been presented, including a
presentation of structures and dynamic models.

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PART 2
Part of Paper review
Autonomous Navigation for Multiple Mobile Robots
under Time Delay in Communication

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Structure
Structure
01 OVERVIEW

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Abstract
This paper addresses the navigation problem for mobile robots under uncertain
working conditions. It is assumed that the environment is unknown at the beginning of
any experiment and that a visual feedback module supports the navigation strategy to
make a set of robots achieve a goal in an environment with obstacles. The proposed
navigation algorithm depends on the obstacle localization, and it is based on visibility
conditions of the goal and control points that are defined from the geometric
distribution of the environment. however, in this work it is solved by means of a low cost
vision system which incorporates a natural restriction in the rate of capture. This fact
limits the maximal velocity of each robot, therefore high accelerations imply that the
robot could not be detected in time, affecting the control system stability. This high
acceleration problem is addressed by means of delay compensation on the
communication channel with a scattering transformation strategy that guarantees to
reach the goal position, allowing the robot to perform high velocities if needed. Real
time experiments are developed to validate the effectiveness of the proposed strategy.

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Introduction
The main contribution of the paper consists on the adaptability of the navigation
strategy under uncertain conditions, provided by a low cost vision system which
produces time delays in the information capture. Even more, the strategy navigation is
improved with respect to common implementations regarding the efficiency of arriving
a goal by means of both, a simple feedback control and a control point switching
strategy that reduces an expected path, saving time and resources in the general
process despite hardware conditions. Though some characteristics from literature are
incorporated to the proposed solution, a robust low cost experimental platform is
provided, disposing of complex probabilistic models, learning maps strategies and
artificial neural intelligent methods.

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Description of the Problem
The problem considered in this work is to make a group of different mobile
robots navigate to a workspace with individual goals and independent routes, which
has a low-cost visual feedback device and its meaning in experimental performance.
In several applications of manufacturing process or material transportation, there
may be similar scenarios in which synchronous tasks of multiple agents are
required. Each robot is an obstacle to the movement of another robot. Navigation
strategy is necessary, because any robot must find its own target, not only to avoid
static obstacles, but also to avoid other robots in the environment.

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Structure
Structure
02 Navigation Algorithm

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Navigation Algorithm
Triangulation and control points :
Let robot Ri be on an initial posture PRi =
as depicted in Fig. 1 with knowledge of
the goal location The real time access to an
absolute localization system allows to detect any
possible obstacle at Before starting
to move, all position points except their own starting
point are connected in turn, but there can be
no intersection points Then,Divide the workspace into
triangles on the interconnection lines.
A control point serves
as a local minimum for the robot path towards the goal
and it is defined as the middle point of each (2k-3)
resulting traces of the polygon triangulation, including
edges and diagonals. For a specific robot, it
is in the process of motion, which means that the
environment is dynamic, and the divided triangles and
control points are also changing

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Any control point turns into a
reference position to be achieved when
the goal Gi can not be directly reached
since it is not visible from the i robot.
−
However, since the control points are
time varying, the robot is only expected
to get close to any of them in order to
improve its location from where the goal
is visible, not been forced to achieve the
commanded control point. This
represents an improvement.
Triangulation and control points :

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Visibility condition:
In this work, the definition of the goal
visibility from any robot is stated as

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Structure
Structure
03 Results and conclusion

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Navigation:
Fig.4 Resulting trajectories for the robots
with two fixed obstacles
Fig.5 Control points and decision from R1perspective

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Conclusions
An integral navigation strategy for a set of mobile robots has been
successfully implemented, overcoming the principal weakness of simple and
low cost experimental platform, a time delay in communication. Essentially, the
strategy deals with sensor-less robots, a low velocity camera as position
feedback device, and an environment with obstacles initially unknown. In an
attempt to make the robots to perform a task into a dynamic workspace, in this
paper it has been proposed a scheme for low cost feedback devices and the
corresponding induced time delay, by means of scattering transformations,
which has only been implemented for manipulator robots in the literature. The
navigation strategy guarantees the goal achievement by means of the
evaluation of visibility conditions that implies a real time calculation of
environment data, however though this work does not calculate the cost, a
discrimination of elements according to the posture the robots suggests a
reduction of computational requirements and time calculations, since useless
processing is avoided. This fact contributes not only with a map but also with a
path reduction in the navigation strategy. This issue represents a need for
improvement in order to obtain an optimal reduction
of computational resources.

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