Using the Unicycle model you implemented above, you will now command the system to reach a goal position. Start with open$-$loop control,

i$.$e$.,$ measure the intial state $($returned by env. reset$)$ and then calculate a sequence of actions to apply.

After that sequence is computed, run the simulator forward for several steps, and at each step, simply grab the corresponding control value

from that pre$-$computed sequence. You can use this example open$\_$loop$\_$control$\_$policy implementation as a first try.

Your job is to implement a smarter open$\_$loop$\_$control$\_$policy that gets the system to reach $($close$)$ to the goal.

Remember: you are only provided with the initial state, goal position, and the maximum number of steps allowed $--$ you can't access the

system's state once it has started moving! That would be closed$-$loop control, which we'll implement next $$

Deliverables:

Implement the open$\_$loop$\_$control$\_$policy, which should produce a sequence of control commands that will lead to the goal. This can

be a very simple hard$-$coded policy $($e$.$g$.,$ always send the same $v,w)$

Generate $1$ plot that shows your open$-$loop controller drives the noise$-$free system to the goal $($it only has to work for $1$ test case$).$ Include

the path taken and the start$/$goal coordinates in your plot.

Generate $1$ plot that shows your open$-$loop controller running on the noisy system $($it$\text{'}$s ok if it doesn't work on this system$).$ Include the

path taken and the start$/$goal coordinates in your plot.

$[]$ def open$\_$loop$\_$control$\_$policy$($init$\_$state: np$.$ndarray, goal: np$.$ndarray, num$\_$steps: int $=10)$ list$[$np$.$ndarray$]$:

## Your Implementation Here ##

raise NotImplementedError

return control$\_$sequence

$o.$ np$.$random.seed $(0)$

max$\_$num$\_$steps $=200$

env. unwrapped.motion$\_$model $=$ Unicycle$($