$(8)$ You are to develop your own controller for the omni$-$directional vehicle that follows a given trajectory.

Modify the pure pursuit example $($page $106)$ as follows

a$)$ In Simulink, make one block using 'User Defined function' to intergrate the code in the above problem to

compute the required wheel rotation speeds. In your code, set Ix and ly as $1m,$ Alpah $=$ pi$/4,$ and the wheel

radius $=30cm.$

b$)$ Make another block using another 'User Defined function' that takes the wheel rotational speeds as

inputs and computes horizontal and rotation velocities in body coordinates as outputs.

c$)$ Complete the simulation such that your vehicle reasonably follows the given trajectory.

Hint : One of the Simulink solution can be constructed as below