$1$a$)$ Run the baseline simulator & generate a plot

Here's an example of how to run the simulator for a few timesteps. In this assignment, we told the simulator to return the true state of the

environment $($in future assignments, we'll only give noisy sensor data$).$

In this problem, you should make a plot of the system's state over time. This will be helpful as you debug future parts of the assignment. This

part uses the Unicycle kinematic model that's built into the simulator.

Deliverables:

Implement the plot$\_$path method. At a minimum, you should plot the $(x,y)$ position over time $($the first $2$ elements of the state vector$).$

You are welcome to add other capabilities to your plot$\_$path function as you go through the assignment $($e$.$g$.,$ visualizing the heading

angle and$/$or the goal coordinate$),$ but this is not necessary for this part. You probably should make your axes have the same scale $($e$.$g$.,$

using plt$.$axis $(\text{'}$equal$\text{'})).$

$[]$ def plot$\_$path$($env: gymnasium.Env, observation$\_$history: list$[$np$.$ndarray$])$ None:

## Your Implementation Here ##

raise NotImplementedError

$[]$ def dummy$\_$unicycle$\_$controller$($current$\_$state: np$.$ndarray$)$ np$.$ndarray:

return np$.$array$([3.,0\mathrm{.}2])$ # $[$linear speed, angular speed$]$

def simulate$\_$n$\_$steps$($env: gymnasium.Env, num$\_$steps: int, controller: Callable$)$:

observation$\_$history $=[]$

observation$\_$history.append $($obs$)$

print$($f$"$initial state: $\{$obs$\}")$

# run the simulator for a few steps and see how the state evolves

for $\_$ in range $($num$\_$steps$)$:

action $=$ controller$($obs$)$

obs, $\_,$ terminated, $,,\_=$ env.step$($action$)$

observation$\_$history.append $($obs$)$

print $($f$"$current state: $\{$obs$\}")$

if terminated:

break

return observation$\_$history

$[]$ # Tell the simulator to its built$-$in kinematic model

env.unwrapped. motion$\_$model $=$ gym$\_$neu$\_$racing. motion$\_$models.Unicycle$()$

# Run the simulation and plot the path taken

num$\_$steps $=10$

observation$\_$history $=$ simulate$\_$n$\_$steps$($env$,$ num$\_$steps, dummy$\_$unicycle$\_$controller$)$

plot$\_$path$($env$,$ observation$\_$history$)$