$($a$)$ Figure $3\mathrm{.}1$ shows a differentially driven robot navigating in a room. Each wheel has an

optical encoder for localization. It is also equipped with two whiskers at the front,

which give a binary signal when in contact with an object: i$.$e$.,0($no$-$contact$)$ and $1$

$($contact$).$ Explain how you could make the robot localise and navigate in the

environment, say from A $->$ B $->$ C $->$ D $->...->$ H$.$

Figure $3\mathrm{.}1$

$($b$)$ In this course, you have learnt the concept of relative positioning and global positioning.

Explain their difference briefly.

$($c$)$ Suppose you have been asked to design a global path planning algorithm for an outdoor

mobile robot to monitor the security in a car park. Explain whether you may use sensor

data in your global planning algorithm or not, as well as the reason for your choice.