iuliaturc / CarND-MPC-Project

CarND Term 2 Model Predictive Control (MPC) Project

CarND-Controls-MPC (Project Write-up)

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The Model

Student describes their model in detail. This includes the state, actuators and update equations.

I used the Global Kinematic Model presented in the course.

State:

1. x: Position of the car on the horizontal axis of the map, in meters.
2. y: Position of the car on the vertical axis of the map, in meters.
3. psi: Angle between the horizontal axis of the map and the direction of the car, in radians.
4. v: Speed of the car, in meters per second.
5. cte: Cross Track Error, a measure of distance between the reference track and the actual track of the car.
6. epsi: Measure of distance between the desired/reference angle and the actual angle of the car. The reference angle is the tangential angle of the track function f evaluated at x.

Actuators:

1. delta: Change in angle.
2. a: Acceleartion; change in speed.

Update Equations:

x' = x + v * cos(psi) * dt
y' = y + v * sin(psi) * dt
psi' = psi + v / Lf * delta * dt
v' = v + a * dt
cte' = f(x) - y + v * sin(epsi) * dt
epsi' = psi - desired_psi + v / Lf * delta * dt

(where f is a polynomial function that approximates the correct track, usually of degree 3.)

Timestep Length and Elapsed Duration (N & dt)

Student discusses the reasoning behind the chosen N (timestep length) and dt (elapsed duration between timesteps) values. Additionally the student details the previous values tried.

My final values are N = 10 and dt = 0.1. When choosing these values, we are making a trade-off between speed and accuracy; higher values of N and lower values of dt require more computations. I tried, for instance, N = 25, and dt = 0.05 (as suggested in the Mind the Line quiz), but the results are not necessarily better.

Polynomial Fitting and MPC Preprocessing

A polynomial is fitted to waypoints. If the student preprocesses waypoints, the vehicle state, and/or actuators prior to the MPC procedure it is described.

First, I converted the waypoints from map coordinates to car coordinates, as advised in the YouTube Q&A. I did so by re-centering the car at position (x, y, psi) = (0, 0, 0) and applying the necessary transformations. Then I fed the resulting points to polyfit in order to fit a polynomial of degree 3 that approximates the reference track.

Model Predictive Control with Latency

The student implements Model Predictive Control that handles a 100 millisecond latency. Student provides details on how they deal with latency.

In order to deal with latency, I ran the MPC simulation starting from the current state for the duration of the latency. The resulting state from the simulation is the new initial state for MPC.