Build a simple simulator for a point robot that allows the user to specify (via some simple user interface) the next motion (x,y) that the robot will execute. When the robot makes this execution,...

Build a simple simulator for a point robot that allows the user to specify (via some simple user interface) the next motion (x,y) that the robot will execute. When the robot makes this execution, simulate the motion of the robot N times, but for each simulation generate a new instance of the robot but moved by (x + x ,y + y ), where x and y are random numbers drawn from a normal (Gaussian) distribution N(0,σ). Apply this same process at each time step to each instance of the robot. That is, rather than represent the robot as a single point, represent it as a cloud of points where each point in the cloud corresponds to a potential motion of the robot corrupted by noise. As the number of points in the cloud will grow without limit, after each movement, keep only N of the possible points. Choose which ones to keep by choosing from the available points randomly. Compare the distribution of points with the covariance matrix based on the motions performed.