Answer L7-C1

** Here are the correct answers to this question:

* Answer A is correct.
* Answer B is NOT correct.
* Answer C is NOT correct.

** Explanation

The question is about the robot localisation using a particle filter, and in particular about the motion model. On the right there is an illustration of a robot following a path drawn on the ground in a factory. The question is: "In a line-following differential robot for manufacturing we estimate the displacement of the robot based on a particle filter applied on data from the wheel encoders. The motion prediction is done every Δt seconds based on the line readings, with the robot running at speed v [mm/s] measured by the encoders. We use a referential with x [mm] aligned with the line, and y [mm] perpendicular to the line. What would the best candidate for a motion model be? The function rand() gives a random number between +0.1 and -0.1.". 

The motion model is a formula showing how xn+1 is based on xn and the speed v, and how yn+1 is based on yn and the speed v. The rand() adds randomness and the difference among answers is only about the multiplication of the last term representing the added error. The real final question is to know if there will be more error on the lateral coordinate (answer A), or on the forward coordinate (answer C) or non (answer B)

Three statements are proposed:

* Statement A. is "xn+1 = xn + v*Δt + v*Δt*rand() 	      yn+1 = yn + v*Δt*rand()*5". This statements is correct, as the simple odometry based on wheel encoders generates a variance that is bigger in angle (and therefore lateral coordinate) than in forward distance. This generates a "banana-like" error distribution with the banana placed perpendicularly to the trajectory.
In the explanation of the student we would like to see that they understand that the common error distribution is larger than deeper when looking forward in the direction of movement of the robot.

* Statement B. is "xn+1 = xn + v*Δt + v*Δt*rand() 	      yn+1 = yn + v*Δt*rand()". This statements is NOT correct, as the distribution of error is not equal among the two coordinates. The simple odometry based on wheel encoders generates a variance that is bigger in angle (and therefore lateral coordinate) than in forward distance. This generates a "banana-like" error distribution with the banana placed perpendicularly to the trajectory.
In the explanation of the student we would like to see that they understand that the common error distribution is larger than deeper when looking forward in the direction of movement of the robot. This is not the case here with this answer showing the same distribution in both directions.

* Statement C. is "xn+1 = xn + v*Δt + v*Δt*rand()*5     	      yn+1 = yn + v*Δt*rand()" This statements is NOT correct, as the distribution of error is not bigger in the forward coodinate in respect to the lateral coordinate. The simple odometry based on wheel encoders generates a variance that is bigger in angle (and therefore lateral coordinate) than in forward distance. This generates a "banana-like" error distribution with the banana placed perpendicularly to the trajectory.
In the explanation of the student we would like to see that they understand that the common error distribution is larger than deeper when looking forward in the direction of movement of the robot. This is not the case here with this answer showing the exact opposite.


