1 chapter 1 review mobile robot kinematics

- Two for position in the plane - One for orientation along the vertical axis, which is orthogonal to the plane  To specify the position of the robot on the plane we establish a relatio

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CHAPTER 1

REVIEW MOBILE ROBOT KINEMATICS

& LOCOMOTION

SYSTEM DYNAMICS & CONTROL

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Class Rules

submit the homework via ELearning system)

• Each team includes 3-4 students, each team will present

their research topic at the 3 final weeks of the semester

• English power point and english presentation in class are encouraged

while doing the exam Time for final exam: 90 minutes

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- Two for position in the plane

- One for orientation along the vertical axis, which is orthogonal to the plane

 To specify the position of the robot on the plane we establish a relationship between the global reference frame

(global coordinate) of the plane and the local reference frame

(local coordinate) of the robot

Mobile Robot Kinematics

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frame from some origin

O: {X I ,Y I }

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P on the robot chassis

as its position reference point

relative to P on the

robots chassis

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The position of P in the

global reference frame is

specified by coordinates x and y, and the angular

difference between the global and local reference frame is given by 

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0

0 cos

sin

0 sin

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This operation is denoted by

R( ) I because the computation

of this operation depends on the value of  :

0

0cos

sin

0sin

0

00

1

01

02



R

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 We can compute the components of motion along this

robot’s local axes X R and Y R

In this case, due to the specific angle of the robot, the motion

along X R is equal to y’ and motion along Y R is - x’

0

00

1

01

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Robot within an arbitrary initial frame

0

0cos

sin

0sin

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,,

f y

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The forward kinematic model of a differential drive robot is relatively straight-forward The differential drive robot has two

wheels each of diameter r

Given a point P centred between the two drive wheels, each wheel is a distance l from P

a forward kinematic model would predict the robots overall speed in the global reference frame as:

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the motion in its local reference frame

I = R(θ) -1R

 The strategy is to first compute the contribution of each of the two wheels in the local reference frame and then convert these to the global reference frame

translation speed at P in the direction of +X R is given as:

The total translation speed at P is given as:

2

1 1

 

x x

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speed at P is given as:

The total rotation speed at P is given as:

l

r

2

1 1

r

r r

R

I

2 2

0

2 2

2 1

0

0 cos

sin

0 sin

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l = 1 and the robot engages its wheels unevenly with φ 1 = 4

1 0 3

1 0

0

0 0

1

0 1

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Do we need to consider about the dynamics of mobile robot?

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Mobile Robot Locomotions

Wheels based mobile robot:

- Wheels are the most appropriate solution for most robotic applications

- There are lots of options for combinations of different kinds

of wheels in different orientations

- Selection of wheels depends on the application

Three key considerations when designing wheel robots:

- Stability

- Maneuverability

- Controllability

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Wheels types

a) Standard wheel: Two degrees

of freedom; rotation around the

(motorized) wheel axle and the

contact point

b) Castor wheel: Three degrees

of freedom; rotation around the

wheel axle, the contact point and

the castor axle

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c) Swedish wheel: Three

(motorized) wheel axle,

around the rollers and

around the contact point

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Wheels arrangements

• Legend

• Two wheels

Motorised Swedish wheel

Motorised standard wheel

Un-powered standard wheel

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• Three wheels

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• Four wheels

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• Six wheels

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