This repository provides some helper functions we frequently use in our trajectory planning software stack at FTM/TUM. Many of the functions are based on third order splines because we use them as a basis for our path planning. Please keep in mind that some of the functions are designed to work on a closed (race-) track and might therefore not work properly on a common street network.
List of components
angle3pt: Calculates angle by turning from a to c around b.
calc_ax_profile: Calculate the longitudinal acceleration profile for a given velocity profile.
calc_head_curv_an: Analytical curvature calculation on the basis of third order splines.
calc_head_curv_num: Numerical curvature calculation.
calc_normal_vectors: Calculate normalized normal vectors on the basis of headings psi (psi - pi/2).
calc_normal_vectors_ahead: Calculate normalized normal vectors on the basis of headings psi (psi + pi/2).
calc_spline_lengths: Calculate spline lengths.
calc_splines: Calculate splines for a (closable) path.
calc_t_profile: Calculate the temporal duration profile for a given velocity profile.
calc_tangent_vectors: Calculate normalized tangent vectors on the basis of headings psi.
calc_vel_profile: Calculate velocity profile on the basis of a forward/backward solver. Important: ax_max_machines input must be inserted without drag resistance, i.e. simply by calculating F_x_drivetrain / m_veh
calc_vel_profile_brake: Calculate velocity profile on the basis of a pure forward solver.
check_normals_crossing: Check if normal vectors of a given track have at least one crossing.
conv_filt: Filter a given signal using a 1D convolution (moving average) filter.
create_raceline: Function to create a raceline on the basis of the reference line and an optimization result.
get_rel_path_part: Get relevant part of a given path on the basis of a s position and a specified range.
import_veh_dyn_info: Imports the required vehicle dynamics information from several files: ggv and ax_max_machines.
import_veh_dyn_info_2: Imports local gg diagrams, required for local friction consideration.
interp_splines: Interpolate splines to get points with a desired stepsize.
interp_track: Interpolate track to get points with a desired stepsize.
interp_track_widths: Interpolation function for track widths.
iqp_handler: Handler function to iteratively call the minimum curvature optimization.
nonreg_sampling: Function to sample in non-regular intervals (based on curvature) from a given track.
normalize_psi: Normalize heading psi such that the interval [-pi, pi[ holds.
opt_min_curv: Minimum curvature optimization.
opt_shortest_path: Shortest path optimization.
path_matching_global: Match own vehicle position to a global (i.e. closed) path.
path_matching_local: Match own vehicle position to a local (i.e. unclosed) path.
progressbar: Commandline progressbar (to be called in a for loop).
side_of_line: Function determines if a point is on the left or right side of a line.
spline_approximation: Function used to obtain a smoothed track on the basis of a spline approximation.
example_files contains an exemplary track file (
berlin_2018.csv), ggv (
ggv.csv) and ax_ax_machines file
ax_max_machines.csv). The two latter files can be easily imported (with checks) using
files are taken from our global trajectory planner repository which can be found on
Solutions for possible installation problems (Windows)
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
C++ build tools option to install the required C++ compiler and its dependencies
Solutions for possible installation problems (Ubuntu)
tkinter-> can be solved by
sudo apt install python3-tk
quadprog-> can be solved by
sudo apt install python3-dev