NDCurves
A template-based Library for creating curves of arbitrary order and dimension, eventually subject to derivative constraints. The main use of the library is the creation of end-effector trajectories for legged robots.
To do so, tools are provided to:
- create exact splines of arbitrary order (that pass exactly by an arbitrary number waypoints)
- constrain initial / end velocities and acceleration for the spline.
- constrain take-off and landing phases to follow a straight line along a given normal (to avoid undesired collisions between the effector and the contact surface)
- automatically handle 3d rotation of the effector.
- create curves in SO3
- support partial symbolic differentiation of curves. You can represent control points as linear variables, and integrate / differentiate those variable curves. You can also compute the cross product of two curves, which is relevant for centroidal dynamics.
Several type of formulation are provided:
- Polynomials
- Bezier
- Hermite (only cubic hermite for now)
The library is template-based, thus generic: the curves can be of any dimension, and can be implemented in double or float and can work with kind variables like Vector, Transform, Matrix, ...
Installation
This package is available as binary in robotpkg
Dependencies
Additional dependencies for python bindings
To handle this with cmake, use the recursive option to clone the repository. For instance, using http:
git clone --recursive https://github.com/loco-3d/ndcurves $NDCURVES_DIR
Where $NDCURVES_DIR is to be replaced to your selected source folder. The library is header only, so the build only serves to build the tests and python bindings:
cd $NDCURVES_DIR && mkdir build && cd build
cmake -DBUILD_PYTHON_INTERFACE=ON .. && make && make testSwitch the BUILD_PYTHON argument to OFF if you don't want to use the python bindings of the package.
If everything went fine you should obtain the following output:
100% tests passed, 0 tests failed out of 3Optional: Python bindings installation
To install the Python bindings first enable the BUILD_PYTHON_INTERFACE option:
cmake -DBUILD_PYTHON_INTERFACE=ON ..
Then rebuild the library:
cd ${NDCURVES_DIR}/build
make && make test
To see example of use, you can refer to the test file which is rather self explanatory:
In spite of an exhaustive documentation, please refer to the C++ documentation, which mostly applies to python.
Documentation and tutorial
For the C++ / Python detailed documentation, you can consult this pdf available in the doc folder
For a python tutorial, you can refer to the jupyter notebook. The test file is more exhaustive and rather self explanatory.
Citation
If you wish to cite this work please use the bibtex below:
@software{ndcurves,
author = {Tonneau, Steve and Chemin, Jason and Fernbach, Pierre and Saurel, Guilhem},
title = {ndcurves},
url = {https://github.com/loco-3d/ndcurves},
year = {2013}
}