$2$b$)$ Closed$-$Loop Control: Pure Pursuit Algorithm

One of the most powerful ideas in robotic control is feedback. In this next part, we will implement a controller that measures the system's state

at each step and uses that measurement to compute an action. This way, if the system ended up in a slightly different state than was expected

from the simple model, the measurement will contain information about this discrepancy. Feedback control is often a great way to compensate

for imperfect knowledge of the system you are working with.

Your job is to implement the PurePursuitController class with a get$\_$action method that takes in the current obs and the env.goal

coordinate $($expressed in the global frame$),$ and outputs one action $=[v,].$ This get$\_$action method will be called at each step, so there is

no need to calculate a whole sequence of actions. The controller that you implement should be capable of driving the system to the goal.

$[]$ class PurePursuitController:

def$\_$init$\_($self$,$ L$=3.)$:

$""\text{'}"$Store any hyperparameters here.""$\text{'}"$

self.L $=$ L

def get$\_$action$($self$,$ obs: np$.$ndarray, goal: np$.$ndarray$)$ np$.$ndarray:

$"""\text{'}$Your implementation goes here""""

raise NotImplementedError$()$

return np$.$array$([$linear$\_$speed, angular$\_$speed$])$

This validation function may come in handy for debugging$/$testing your controller in some random scenarios

$($ def validation$($controller$,$ motion$\_$model$=$Unicycle, sensor$\_$model$=$StateFeedbackWrapper, plot$=$False, num$\_$runs$=100,$ max$\_$num$\_$steps$\_$per$\_$rur

success$\_$per$\_$run $=$ np$.$ empty num$\_$runs,