FBGA

FBGA - Forward Backward Generic Acceleration constraints is a library specifically developed to solve optimal velocity profile given a complex g-g-v constraint envelope the described implementation is under review in the Robotics and Automation Letters (RAL) journal. This library will later evolve into a generic tool including multiple dimensions constraints and a more general approach to the problem. The library is able to compute the maximum performance longitudinal maneuver given a generic g-g-v envelope and a curvature profile (i.e., the trajectory path).

The fbga3d module ports the 3D forward-backward solver originally developed in FBGA_3D into this repository (generic over the vehicle's GG-diagram model via Fbga3dSolver<GggvModel>, with GggvIndy/GggvMoto as the two instantiations); it's opt-in via -DFBGA_BUILD_3D=ON -- see below.

For usage details, please refer to the FBGA Usage Guide.

Cite 2D FBGA in your publications as follows:

@article{piazza2025real,
  title={Real-Time Velocity Profile Optimization for Time-Optimal Maneuvering With Generic Acceleration Constraints},
  author={Piazza, Mattia and Piccinini, Mattia and Taddei, Sebastiano and Biral, Francesco and Bertolazzi, Enrico},
  journal={IEEE Robotics and Automation Letters},
  volume={11},
  number={2},
  pages={1674--1681},
  year={2025},
  
  publisher={IEEE}
}

Cite 3D FBGA in your publications as follows:

@article{piazza2026beyond,
  title={Beyond the Apex: Online Minimum-Time Velocity Planning on Three-Dimensional Paths With Variable Friction}, 
  author={Piazza, Mattia and Langmann, Alexander and Biral, Francesco and Betz, Johannes and Piccinini, Mattia},
  journal={IEEE Robotics and Automation Letters}, 
  volume={11},
  number={8},
  pages={10034-10041},
  year={2026},
  publisher={IEEE}
}

Download the bib

Requirements

General

• git
• cmake
• make

Third party libraries

Third party libraries (Catch2, cxxopts, rapidcsv, and -- when -DFBGA_BUILD_3D=ON -- libnpy) are fetched automatically by CMake via FetchContent during configuration, pinned to fixed release tags in Dependencies.cmake. You need an internet connection the first time you configure the project; nothing needs to be installed manually.

Building

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j

For a debug build, pass -DCMAKE_BUILD_TYPE=Debug instead. Useful options (see ProjectOptions.cmake):

• -DFBGA_BUILD_TESTS=OFF to skip the Catch2 unit tests (test/).
• -DFBGA_BUILD_EXAMPLES=OFF to skip the usage examples (examples/).
• -DFBGA_BUILD_3D=ON to also build the fbga3d module (src/fbga3d/, test/fbga3d/, examples/fbga3d/) -- off by default.
• -DFBGA_WARNINGS_AS_ERRORS=ON to treat compiler warnings as errors.

Running the tests

ctest --test-dir build --output-on-failure

Running the examples

Examples must be run from the repository root, since they read data files with paths relative to it (e.g. data/paper/..., or data/INDY/*.npy for fbga3d's GggvIndy):

./build/examples/fbga/fbga_example_basic
./build/examples/fbga/fbga_example_moto
./build/examples/fbga3d/fbga3d_example_gggv_demo         # -DFBGA_BUILD_3D=ON only
./build/examples/fbga3d/fbga3d_example_yas_marina_indy   # -DFBGA_BUILD_3D=ON only

Python bindings

Python bindings (fbga_py, covering both Fb2d and fbga3d's FbgaIndy/FbgaMoto) are built independently of the CMake build above, via setuptools/pybind11 -- see python_bindings/README.md.