wjydym/hpp-spline

Library for creating smooth cubic splines

Spline

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.

The library is template-based, thus generic: the curves can be of any dimension, and can be implemented in double, float ...

While a Bezier curve implementation is provided, the main interest of this library is to create spline curves of arbitrary order

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Example of use for and end-effector trajectory

The library comes with an helper class to automatically generate end-effector trajectories. For instance, to create a 2 second long trajectory from the point (0,0,0) to (1,1,0), with a waypoint at (0.5,0.5,0.5), one can use the following code:

typedef std::pair<double, Eigen::Vector3d> Waypoint;
typedef std::vector<Waypoint> T_Waypoint;

// loading helper class namespace
using namespace spline::helpers;

// Create waypoints
waypoints.push_back(std::make_pair(0., Eigen::Vector3d(0,0,0)));
waypoints.push_back(std::make_pair(1., Eigen::Vector3d(0.5,0.5,0.5)));
waypoints.push_back(std::make_pair(2., Eigen::Vector3d(1,1,0)));

exact_cubic_t* eff_traj = effector_spline(waypoints.begin(),waypoints.end());

// evaluate spline
(*eff_traj)(0.); // (0,0,0)
(*eff_traj)(2.); // (1,1,0)

If rotation of the effector must be considered, the code is almost the same:

// initial rotation is 0, end rotation is a rotation by Pi around x axis
quat_t init_rot(0,0,0,1), end_rot(1,0,0,0);
effector_spline_rotation eff_traj_rot(waypoints.begin(),waypoints.end(), init_quat, end_quat);

// evaluate spline
eff_traj_rot(0.); // (0,0,0,0,0,0,1)
eff_traj_rot(1.); // (0.5,0.5,0.5,0.707107,0,0,0.707107) // Pi/2 around x axis
eff_traj_rot(2.); // (0,0,0,1,0,0,0)

Additional parameters for the same methods an be used to specify parameters for the take off and landing phases: height and duration of the phase, and along which normal. Please refer to the Main.cpp files to see all the unit tests and possibilities offered by the library

Installation

This package is available as binary in robotpkg/wip

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/stonneau/spline.git $SPLINE_DIR

The library is header only, so the build only serves to build the tests and python bindings:

	cd $SPLINE_DIR && mkdir build && cd build
	cmake .. && make
	../bin/tests

If everything went fine you should obtain the following output:

performing tests...
no errors found

Optional: Python bindings installation

To install the Python bindings, in the CMakeLists.txt file, first enable the BUILD_PYTHON_INTERFACE option:

OPTION (BUILD_PYTHON_INTERFACE "Build the python binding" ON)

Then rebuild the library:

cd $SPLINE_DIR/build
cmake -DCMAKE_INSTALL_PREFIX=${DEVEL_DIR}/install ..
make install

The python bindings should then be accessible through the package centroidal_dynamics. 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. For the moment, only bezier curves are binded.