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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.
• `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.

## Project details

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