This is the 5th and last project of the Term 2. In this project I have implemented a MPC controller in C++. The goal is to control the steering of the vehicle in the simulator and successfully drive at least a lap around the track. This time, in order to better simulate a real environment, a 100ms delay is added to the simulator. Vehicle kinematic model is used to approximate to a real car behavior. The program evaluates the errors (cost) in order to optimize the route along the track in the simulator, taking in to account the model constrains. Udacity provides some starting coding and this has been also complemented with the code from the course’s Quizzes.

The code compiles without errors with cmake and make.

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

The kinematic model is based on CRTV (Constant Rate of Turn and Velocity). Complex interactions between the tires and the road are ignored. It takes into account the coordinates angle (psi) and velocity (v). The error is also considered: the cross-track error (cte) and psi error (epsi). The output of the model are: the actuator’s acceleration (a) and delta (steering angle). Information from previous timestep is considered for the calculation.

x_[t+1] = x[t] + v[t] * cos(psi[t]) * dt
y_[t+1] = y[t] + v[t] * sin(psi[t]) * dt
psi_[t+1] = psi[t] + v[t] / Lf * delta[t] * dt
v_[t+1] = v[t] + a[t] * dt
cte[t+1] = f(x[t]) - y[t] + v[t] * sin(epsi[t]) * dt
epsi[t+1] = psi[t] - psides[t] + v[t] * delta[t] / Lf * dt

If delta is positive we rotate counter-clockwise, or turn left. In the simulator however, a positive value implies a right turn and a negative value implies a left turn. Sign was changed in epsi and psi equations in the code. Lf is the distance between the car CoG and the front wheels.

Student discusses the reasoning behind the chosen N (timestep length) and dt (elapsed duration between timesteps) values.

The prediction horizon is defined by the number of points (N) and the time interval (dt). The chosen values for N and dt are 12 and 0.1, respectively. Many combinations were used. I tried to perform a long horizon with a high number of points but the simulator behaved slowly so I ended up decreasing the number down to 12. In the same way the time interval has to be big enough for prediction and small enough to provide accurate planning.

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.

The waypoints are converted from map coordinates to car coordinates. This way the coordinates of the vehicle are now located on the origin. Afterwards, a polynomial is defined to fit in the waypoints (polyfit function). The coefficients of the polynomial are used to calculate the errors and create the reference trajectory.

The student implements Model Predictive Control that handles a 100 millisecond latency.

The model and the delay interval were used to calculate the state values, in order to handle the delay.

The vehicle successfully drives a lap around the track.

This project is probably the most complex I have done so far in the Self driving Car Nanodegree. The use of additional libraries (as IPOPT and CPPAD to calculate an optimal trajectory) and its associated actuation commands, makes this project harder to implement if you are not familiar with them.

Course lessons are complete and they accomplish the educational purpose of understanding the MPC mechanics. However, once you try to translate this knowledge in to a piece of code things turn out to be a bit more difficult. The good thing is that the Quizzes and the Udacity walkthrough is very helpful (and key) to successfully accomplish this project.

J.C. Marti

Self-Driving Car Engineer Nanodegree Program

• cmake >= 3.5

• All OSes: click here for installation instructions

• make >= 4.1(mac, linux), 3.81(Windows)

  • Linux: make is installed by default on most Linux distros
  • Mac: install Xcode command line tools to get make
  • Windows: Click here for installation instructions

• gcc/g++ >= 5.4

  • Linux: gcc / g++ is installed by default on most Linux distros
  • Mac: same deal as make - [install Xcode command line tools]((https://developer.apple.com/xcode/features/)
  • Windows: recommend using MinGW

• uWebSockets

  • Run either install-mac.sh or install-ubuntu.sh.
  • If you install from source, checkout to commit e94b6e1, i.e.

    git clone https://github.com/uWebSockets/uWebSockets
    cd uWebSockets
    git checkout e94b6e1
    

    Some function signatures have changed in v0.14.x. See this PR for more details.

• Ipopt and CppAD: Please refer to this document for installation instructions.

• Eigen. This is already part of the repo so you shouldn't have to worry about it.

• Simulator. You can download these from the releases tab.

• Not a dependency but read the DATA.md for a description of the data sent back from the simulator.

1. Clone this repo.
2. Make a build directory: mkdir build && cd build
3. Compile: cmake .. && make
4. Run it: ./mpc.

1. It's recommended to test the MPC on basic examples to see if your implementation behaves as desired. One possible example is the vehicle starting offset of a straight line (reference). If the MPC implementation is correct, after some number of timesteps (not too many) it should find and track the reference line.
2. The lake_track_waypoints.csv file has the waypoints of the lake track. You could use this to fit polynomials and points and see of how well your model tracks curve. NOTE: This file might be not completely in sync with the simulator so your solution should NOT depend on it.
3. For visualization this C++ matplotlib wrapper could be helpful.)
4. Tips for setting up your environment are available here
5. VM Latency: Some students have reported differences in behavior using VM's ostensibly a result of latency. Please let us know if issues arise as a result of a VM environment.

We've purposefully kept editor configuration files out of this repo in order to keep it as simple and environment agnostic as possible. However, we recommend using the following settings:

• indent using spaces
• set tab width to 2 spaces (keeps the matrices in source code aligned)

Please (do your best to) stick to Google's C++ style guide.

Note: regardless of the changes you make, your project must be buildable using cmake and make!

More information is only accessible by people who are already enrolled in Term 2 of CarND. If you are enrolled, see the project page for instructions and the project rubric.

• You don't have to follow this directory structure, but if you do, your work will span all of the .cpp files here. Keep an eye out for TODOs.

Help your fellow students!

We decided to create Makefiles with cmake to keep this project as platform agnostic as possible. Similarly, we omitted IDE profiles in order to we ensure that students don't feel pressured to use one IDE or another.

However! I'd love to help people get up and running with their IDEs of choice. If you've created a profile for an IDE that you think other students would appreciate, we'd love to have you add the requisite profile files and instructions to ide_profiles/. For example if you wanted to add a VS Code profile, you'd add:

• /ide_profiles/vscode/.vscode
• /ide_profiles/vscode/README.md

The README should explain what the profile does, how to take advantage of it, and how to install it.

Frankly, I've never been involved in a project with multiple IDE profiles before. I believe the best way to handle this would be to keep them out of the repo root to avoid clutter. My expectation is that most profiles will include instructions to copy files to a new location to get picked up by the IDE, but that's just a guess.

One last note here: regardless of the IDE used, every submitted project must still be compilable with cmake and make./

A well written README file can enhance your project and portfolio. Develop your abilities to create professional README files by completing this free course.