$($b$)$ Assume the Arduino$-$based mobile robot as in Q$2($b$)$ has a tick period of $20$ ms to keep track of time and consists of three independent tasks, A$,$ B and C$.$ The task priorities, periods and CPU $($execution$)$ times for the three$-$task system are tabulated in Table $1.$

TABLE $1$: Task Execution

$($i$)$ Plot a task activition diagram for time, $\backslash ($ t$=0\backslash$mathrm$\{$~ms$\}\backslash )$ to $\backslash (\backslash$mathrm$\{$t$\}=80\backslash$mathrm$\{$~ms$\}\backslash )$ for all tasks. $(6$ marks$)$

$($ii$)$ Analyse the start delay, elapse time, deadline and completion time by showing the result in a table for the three$-$task system.

$(6$ marks$)$

$($iii$)$ Reconstruct an appropriate priority assignment for each of the three tasks according to the rate monotonic scheduling $($RMS$)$ algorithm.

$(3$ marks$)$

$($iv$)$ Analyse the ability of each task to meet its deadline based on RMS calculation. $(8$ marks$)$