02. Tips and Tricks

Tips and Tricks for the MPC Project

Displaying the MPC trajectory path in green, and the polynomial fitted reference path in yellow.

Displaying the MPC trajectory path in green, and the polynomial fitted reference path in yellow.

Simulator Misc

  • A singular unity unit in the simulator is equivalent to 1 meter.
  • For details on the data sent back from the server, read this file.

\psi Updates

In the classroom we've referred to the \large \psi update equation as:

\Large \psi_{t+1} = \psi_t + \frac {v_t}{L_f} \delta_t dt

Note if \large \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. Two possible ways to get around this are:

  1. Change the update equation to \Large \psi_{t+1} = \psi_t - \frac {v_t}{L_f} \delta_t dt
  2. Leave the update equation as is and multiply the steering value by -1 before sending it back to the server.

Visualization

When working on the MPC project it helps to visualize both your reference path and the MPC trajectory path.

You can display these connected point paths in the simulator by sending a list of optional x and y values to the mpc_x,mpc_y, next_x, and next_y fields in the C++ main script. If these fields are left untouched then simply no path will be displayed.

The mpc_x and mpc_y variables display a line projection in green. The next_x and next_y variables display a line projection in yellow. You can display these both at the same time, as seen in the image above.

These (x,y) points are displayed in reference to the vehicle's coordinate system. Recall that the x axis always points in the direction of the car’s heading and the y axis points to the left of the car. So if you wanted to display a point 10 units directly in front of the car, you could set next_x = {10.0} and next_y = {0.0}.

Remember that the server returns waypoints using the map's coordinate system, which is different than the car's coordinate system. Transforming these waypoints will make it easier to both display them and to calculate the CTE and Epsi values for the model predictive controller.

IPOPT Installation on Mac

When executing brew install ipopt, some Mac users have experienced the following error:

Listening to port 4567
Connected!!!
mpc(4561,0x7ffff1eed3c0) malloc: *** error for object 0x7f911e007600: incorrect checksum for freed object - object was probably modified after being freed.
*** set a breakpoint in malloc_error_break to debug

This error can be resolved by upgrading ipopt with
brew upgrade ipopt --with-openblas.