Introduction

This repository contains algorithms that allow us to determine an optimal racing line on a race track. You can chose between several objectives:

• Shortest path
• Minimum curvature (with or without iterative call)
• Minimum time
• Minimum time with powertrain behavior consideration

The minimum curvature line is quite near to a minimum time line in corners but will differ as soon as the car's acceleration limits are not exploited. However, the minimum time optimization requires a lot more parameters and takes more computation time. Please look into the main_globaltraj.py for all possible options.

List of components

• frictionmap: This package contains the functions related to the creation and handling of friction maps along the race track.
• helper_funcs_glob: This package contains some helper functions used in several other functions when calculating the global race trajectory.
• inputs: This folder contains the vehicle dynamics information, the reference track csvs and friction maps.

• opt_mintime_traj: This package contains the functions required to find the time-optimal trajectory.

  It also includes the powertrain components in opt_mintime_traj/powertrain_src used to calculate power losses and thermal behavior of the powertrain and to consider the state of charge of the battery.

• params: This folder contains a parameter file with optimization and vehicle parameters.

Trajectory Planning Helpers repository

Lots of the required functions for trajectory planning are cumulated in our trajectory planning helpers repository. It can be found on https://github.com/TUMFTM/trajectory_planning_helpers. They can be quite useful for other projects as well.

Dependencies

Use the provided requirements.txt in the root directory of this repo, in order to install all required modules.\ pip3 install -r /path/to/requirements.txt

The code is developed with Ubuntu 20.04 LTS and Python 3.7.

Solutions for possible installation problems (Windows)

• cvxpy, cython or any other package requires a Visual C++ compiler -> Download the build tools for Visual Studio 2019 (https://visualstudio.microsoft.com/de/downloads/ -> tools for Visual Studio 2019 -> build tools), install them and chose the C++ build tools option to install the required C++ compiler and its dependencies
• Problems with quadprog -> reason currently not clear, test using quadprog in version 0.1.6 instead 0.1.7

Solutions for possible installation problems (Ubuntu)

• matplotlib requires tkinter -> can be solved by sudo apt install python3-tk
• Python.h required quadprog -> can be solved by sudo apt install python3-dev

Creating your own friction map

The script main_gen_frictionmap.py can be used to create your own friction map for any race track file supplied in the input folder. The resulting maps are stored in the inputs/frictionmaps folder. These friction maps can be used within the minimum time optimization. In principle, they can also be considered within the velocity profile calculation of the minimum curvature planner. However, this is currently not supported from our side.

Running the code

• Step 1: (optional) Adjust the parameter file that can be found in the params folder (required file).
• Step 2: (optional) Adjust the ggv diagram and ax_max_machines file in inputs/veh_dyn_info (if used). This acceleration should be calculated without drag resistance, i.e. simply by F_x_drivetrain / m_veh!
• Step 3: (optional) Add your own reference track file in inputs/tracks (required file).
• Step 4: (optional) Add your own friction map files in inputs/frictionmaps (if used).
• Step 5: (optional) If you want to consider the powertrain behavior (thermal behavior, power loss, state of charge), enable the powertrain-option in the parameter file (/params) and adjust the powertrain parameters as needed. Set the number of race laps in the dict imp_opts in main_globaltraj.py and specify a non-regular discretization step length for faster optimization in the parameter file (/params) (if used). You can select a simple approximation of the powertrain components by setting /params/racecar.ini:simple_loss = True or consider more detailed models by specifying /params/racecar.ini:simple_loss = False.
• Step 6: Adjust the parameters in the upper part of main_globaltraj.py and execute it to start the trajectory generation process. The calculated race trajectory is stored in outputs/traj_race_cl.csv.

IMPORTANT: For further information on the minimum time optimization have a look into the according Readme.md which can be found in the opt_mintime_traj folder!

Wording and conventions

We tried to keep a consistant wording for the variable names:

• path -> [x, y] Describes any array containing x,y coordinates of points (i.e. point coordinates).\
• refline -> [x, y] A path that is used as reference line during our calculations.\
• reftrack -> [x, y, w_tr_right, w_tr_left] An array that contains not only the reference line information but also right and left track widths. In our case it contains the race track that is used as a basis for the raceline optimization.

Our normal vectors usually point to the right in the direction of driving. Therefore, we get the track boundaries by multiplication as follows: norm_vector w_tr_right, -norm_vector w_tr_left.

Trajectory definition

The global racetrajectory optimization currently supports two output formats:

• Race Trajectory - (default) holds detailed information about the race trajectory.
• LTPL Trajectory - holds source information about the race trajectory as well as information about the track bounds and tue reference line (the actual race trajectory has to be calculated based on the stored information).

In order to en-/disable the export of any of these files, add the respective entry to the 'file_paths'-dict in the 'main_globtraj.py'-script (search for # assemble export paths). By the default, the file path for the 'LTPL Trajectory' is commented out.

Details about the individual formats are given in the following.

Race Trajectory

The output csv contains the global race trajectory. The array is of size [no_points x 7] where no_points depends on stepsize and track length. The seven columns are structured as follows:

• s_m: float32, meter. Curvi-linear distance along the raceline.
• x_m: float32, meter. X-coordinate of raceline point.
• y_m: float32, meter. Y-coordinate of raceline point.
• psi_rad: float32, rad. Heading of raceline in current point from -pi to +pi rad. Zero is north (along y-axis).
• kappa_radpm: float32, rad/meter. Curvature of raceline in current point.
• vx_mps: float32, meter/second. Target velocity in current point.
• ax_mps2: float32, meter/second². Target acceleration in current point. We assume this acceleration to be constant from current point until next point.

LTPL Trajectory

The output csv contains the source information of the global race trajectory and map information via the normal vectors. The array is of size [no_points x 12] where no_points depends on step size and track length. The seven columns are structured as follows:

• x_ref_m: float32, meter. X-coordinate of reference line point (e.g. center line of the track).
• y_ref_m: float32, meter. Y-coordinate of reference line point (e.g. center line of the track).
• width_right_m: float32, meter. Distance between reference line point and right track bound (along normal vector).
• width_left_m: float32, meter. Distance between reference line point and left track bound (along normal vector).
• x_normvec_m: float32, meter. X-coordinate of the normalized normal vector based on the reference line point.
• y_normvec_m: float32, meter. Y-coordinate of the normalized normal vector based on the reference line point.
• alpha_m: float32, meter. Solution of the opt. problem holding the lateral shift in m for the reference line point.
• s_racetraj_m: float32, meter. Curvi-linear distance along the race line.
• psi_racetraj_rad: float32, rad. Heading of raceline in current point from -pi to +pi rad. Zero is north.
• kappa_racetraj_radpm: float32, rad/meter. Curvature of raceline in current point.
• vx_racetraj_mps: float32, meter/second. Target velocity in current point.
• ax_racetraj_mps2: float32, meter/second². Target acceleration in current point. We assume this acceleration to be constant from current point until next point.

The generated file can be directly imported by the graph-based local trajectory planner.

References

• Minimum Curvature Trajectory Planning\ Heilmeier, Wischnewski, Hermansdorfer, Betz, Lienkamp, Lohmann\ Minimum Curvature Trajectory Planning and Control for an Autonomous Racecar\ DOI: 10.1080/00423114.2019.1631455\ Contact person: Alexander Heilmeier.

• Time-Optimal Trajectory Planning\ Christ, Wischnewski, Heilmeier, Lohmann\ Time-Optimal Trajectory Planning for a Race Car Considering Variable Tire-Road Friction Coefficients\ DOI: 10.1080/00423114.2019.1704804\ Contact person: Fabian Christ.

• Friction Map Generation\ Hermansdorfer, Betz, Lienkamp\ A Concept for Estimation and Prediction of the Tire-Road Friction Potential for an Autonomous Racecar\ DOI: 10.1109/ITSC.2019.8917024\ Contact person: Leonhard Hermansdorfer.

• Powertrain Behavior\ Herrmann, Passigato, Betz, Lienkamp\ Minimum Race-Time Planning-Strategy for an Autonomous Electric Racecar\ DOI: 10.1109/ITSC45102.2020.9294681\ Preprint: https://arxiv.org/abs/2005.07127 \ Contact person: Thomas Herrmann.