Using the template Webots project included on Canvas. Write a robot controller $($for the $$mybot$$

differential drive robot used in the lectures$)$ to move the robot from its initial position and

orientation $($Xo$=-0\mathrm{.}25$ m$,$ Yo$=0\mathrm{.}25$ m$,$ o$=-1\mathrm{.}3)$ to the final position and orientation $($Xf $=0\mathrm{.}38$ m$,$

Yf $=-0\mathrm{.}25$ m$,$ f $=$$/2).$ Both positions are measured with respect to the world$$s coordination. The

controller should use the following forward kinematics equations, as derived in the lecture, to

estimate the robot$$s current position:

$$

$$

$$

$$

$$

$$

$=$

$22$

$00$

$22$

$$

$$

$$

where r is the radius of both wheels, b is the distance from the center of the robot to the middle of

the wheel.

For this controller, the value of the $$ and $$ should be extracted using the embedded wheel$$s

encoder, and the robot orientation $$ should be extracted from the robot$$s IMU sensor$.$

The new robot is equipped with LDS$-01$ Lidar which should be used to draw a map of the robot$$s

environment. In this map, every captured point for the wall or the blocks should be considered as

a landmark. After building a map of the environment, use the extracted map to calculate a path

from the starting point to the endpoint using the A$*$ algorithm as explained in the lecture and the

provided example code.

Using the designed path with all intermediate points, your controller should use a Proportional

Controller to move the robot to these intermediate target points, one after the other until it arrives

at the final target point. The formulas of the proportional controller are:

$=()2+()2$

$=+$ tan$1$

$$

$=1+2$

$=1+2$

where $()$ are the robot$$s state w$.$r$.$t$.$ the world$$s frame, $()$ are the

intermediate target point coordination, $1,2$ are the proportional controller constants, $$ is the

distance error, $$ is the rotation error. You can adjust the final $$ of the robot after arriving at the

final position. Your controller should also provide the updated position of the robot after each

timestep on a figure or a Webots$$ screen monitor.