Submitted version of the thesis - Airlab, the Artificial Intelligence ...

42 Chapter 4. Control
⎡ ⎤ ⎡
−cosA sinA −1
⎢ ⎥ ⎢
where MF = ⎣ cosA sinA −1⎦
, V = ⎣
VF
VL
⎤
⎥
⎦
0 −1 −1 omega∗Rrobot
A is the angle of the front wheels, which is 30 ◦ for our robot. Indeed the
values (0.866, 0.5 ; -0.866, 0.5 ; 0, -1) in the Figure 4.1 coming from the
projection of cosine and sine of the motor vectors in the X-Y plane, which
are later used statically in the microcontroller for the calculation of the motor
contributions. VF represents the frontal speed, VL lateral speed and
omega∗Rrobot represents the angular velocity of the body.
The vector of tangential wheel speed is represented as Vt1,Vt2,Vt3 and
vector of ”sliding” velocity of the wheels due to rollers is represented as
Vn1,Vn2,Vn3. The vectors can have a positive or negative direction which
represents the direction in which the motor has to move (forward or backwards
respectively). The desired speeds set as frontal speed (VF) and lateral
speed (VL) are projected through the motor axes in order to find motor contributions.
The angular velocity of the wheels is found by dividing the Vt of the
desired wheel to the radius of the wheel. It can be formulated as follows:
⎡
⎢
⎣
4.2 Matlab Script
ω1
ω2
ω3
⎤ ⎡ ⎤
V t1
⎥ ⎢ ⎥
⎦ = ⎣V
t2
V t3
⎦/Rwheel
Inordertotest thebehaviorweimplementedasoftwaresimulator inMatlab,
that is calculating the motor contributions in order to go a specified position
in the world. It is possible to obtain three different movement model using
the inverse kinematics model. These are:
• Linear Movement
• Rotation
• Mixed Angular and Linear Movement
Linear Movement