Useful functions used for path and trajectory planning at TUM/FTM

# Description

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

The folder 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 import_veh_dyn_info. The files are taken from our global trajectory planner repository which can be found on https://github.com/TUMFTM/global_racetrajectory_optimization.

### 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

### Solutions for possible installation problems (Ubuntu)

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

Contact persons: Alexander Heilmeier, Tim Stahl.