Curves

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

• Eigen (version >= 3.2.2)

Additional dependencies for python bindings

• Boost.Python
• eigenpy

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/curves $CURVES_DIR

Where $CURVES_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 $CURVES_DIR && mkdir build && cd build
cmake .. && make && make test

If everything went fine you should obtain the following output:

100% tests passed, 0 tests failed out of 3

Optional: 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 ${CURVES_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 a python tutorial, you can refer to the jupyter notebook. The test file is more exhaustive and rather self explanatory.