SpaceVecAlg aim to implement Spatial Vector Algebra with the Eigen3 linear algebra library.
All this implementation is based on appendix A of Roy Featherstone Rigid Body Dynamics Algorithms book.
Features:
- Featherstone Spatial Vector Algebra C++11 implementation
- Header only
- Use Eigen3 as linear algebra library
- Python binding
A short tutorial is available here.
To learn more about Spatial Vector Algebra you can find some presentations on the following page.
The SpaceVecAlg and RBDyn tutorial is also a big ressource to understand how to use SpaceVecAlg. Also you will find a lot of IPython Notebook that will present real use case.
Finally you can build a Doxygen documentation by typing make doc in the build directory. After a make install the documentation will be in CMAKE_INSTALL_PREFIX/share/doc/SpaceVecAlg (see the Installing section).
An up-to-date doxygen documentation is also available online.
When getting started with SpaceVecAlg it is important to know that PTransform utlizes the Left Hand Rule for rigid body transforms and not the Right Hand Rule used by many other libraries and classes. Switching the handedness of a rigid body transform can be done with the functions in Conversions.h, or inverting the rotation component. If your transforms are not working as you expect, the handedness is worth double checking.
In this section a stand for a double, v for a motion vector, f for a force vector,
I for a rigid body inertia, I^a for a articulated body inertia and
X for a plücker transfrom.
. stand for the dot product, xfor the cross product and x^{\*} for the cross product dual.
r stand for a 3d translation vector, E for a 3d rotation matrix,
m for a mass, c for the center of mass 3d vector from the body origin,
I_c for the 3d rotational inertia matrix at CoM frame.
| Operation | C++ |
|---|---|
| rx(theta) | sva::RotX(theta) |
| ry(theta) | sva::RotY(theta) |
| rz(theta) | sva::RotZ(theta) |
| X = rotx(theta) | sva::PTransformd(sva::RotX(theta)) |
| X = roty(theta) | sva::PTransformd(sva::RotY(theta)) |
| X = rotz(theta) | sva::PTransformd(sva::RotZ(theta)) |
| X = xlt(r) | sva::PTransformd(r) |
| x = crm(v) | sva::vector6ToCrossMatrix(v) |
| v x^{*} = crf(v) | sva::vector6ToCrossDualMatrix(v) |
| I = E*mcI(m, c, I_c)*E{^T} | inertiaToOrigin(I_c, m, c, E) |
| v = XtoV(X) | sva::transformVelocity(X) |
| Operation | C++ |
|---|---|
| a v | a*sva::MotionVecd() |
| a f | a*sva::ForceVecd() |
| a I | a*sva::RBInertiad() |
| a I^a | a*sva::ABInertiad() |
| v_1 + v_2 | sva::MotionVecd() + sva::MotionVecd() |
| f_1 + f_2 | sva::ForceVecd() + sva::ForceVecd() |
| I_1 + I_1 | sva::RBInertiad() + sva::RBInertiad() |
| I_1^a + I_2^a | sva::ABInertiad() + sva::ABInertiad() |
| I_1^a + I_2^a | sva::ABInertiad() + sva::RBInertiad() |
| v . f | sva::MotionVecd().dot(sva::ForceVecd()) |
| v_1 x v_2 | sva::MotionVecd().cross(sva::MotionVecd()) |
| v x^* f | sva::MotionVecd().crossDual(sva::ForceVecd()) |
| I v | sva::RBInertiad()\*sva::MotionVecd() |
| I^a v | sva::ABInertiad()\*sva::MotionVecd() |
| X_1 X_2 | sva::PTransformd()\*sva::PTransformd() |
| X^{-1} | sva::PTransformd().inv() |
| X v | sva::PTransformd()\*sva::MotionVecd() |
| X^{-1} v | sva::PTransformd().invMul(sva::MotionVecd()) |
| X^{*} f | sva::PTransformd().dualMul(sva::ForceVecd()) |
| X^{T} f | sva::PTransformd().transMul(sva::ForceVecd()) |
| X^{*} I X^{-1} | sva::PTransformd().dualMul(sva::RBInertiad()) |
| X^{T} I X | sva::PTransformd().transMul(sva::RBInertiad()) |
| X^{*} I^a X^{-1} | sva::PTransformd().dualMul(sva::ABInertiad()) |
| X^{T} I^a X | sva::PTransformd().transMul(sva::ABInertiad()) |
Here w stand for the 3d angular velocity, v for the 3d linear velocity,
n for the 3d torque, f for the 3d force, E for the 3d rotation matrix,
r for the 3d translation vector, q for a unit quaternion, m for a mass,
h for the first moment of mass (h = m c) at body frame,
I for the 3d rotational inertia at body frame, M for the 3d mass matrix,
and H for the 3d generalized inertia matrix.
| Operation | C++ |
|---|---|
| mv(w, v) | sva::MotionVecd(w, v) |
| fv(n, f) | sva::ForceVecd(n, f) |
| plx(E, r) | sva::PTransform(E, r) |
| plx(q, r) | sva::PTransform(q, r) |
| rbi(m, h, I) | sva::RBInertia(m, h, I) |
| abi(M, H, I) | sva::ABInertia(M, H, I) |
Use the multi-contact-unstable ppa:
sudo add-apt-repository ppa:pierre-gergondet+ppa/multi-contact-unstable
sudo apt-get update
sudo apt-get install libspacevecalg-dev libspacevecalg-docInstall from the command line using Homebrew:
# install homebrew package manager
ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"
# install caskroom application manager
brew install caskroom/cask/brew-cask
# tap homebrew-science package repository
brew tap homebrew/science
# tap ahundt-robotics repository
brew tap ahundt/robotics
# install tasks and all its dependencies
brew install spacevecalgTo compile you need the following tools:
For Python bindings:
- Cython >= 0.25
- Eigen3ToPython (to use the Python binding)
git clone --recursive https://github.com/jrl-umi3218/SpaceVecAlg
cd SpaceVecAlg
mkdir _build
cd _build
cmake [options] ..
make && make intallWhere the main options are:
-DCMAKE_BUIlD_TYPE=ReleaseBuild in Release mode-DCMAKE_INSTALL_PREFIX=some/path/to/installdefault is/usr/local-DPYTHON_BINDING=ONBuild the python binding-DUNIT_TESTS=ONBuild unit tests.-DPYTHON_DEB_LAYOUT=OFFinstall python library insite-packages(ON will install indist-packages)
You can use the following AUR package.
To update sync cmake or .travis directory with their upstream git repository:
git fetch git://github.com/jrl-umi3218/jrl-cmakemodules.git master
git subtree pull --prefix cmake git://github.com/jrl-umi3218/jrl-cmakemodules.git master --squash
git fetch git://github.com/jrl-umi3218/jrl-travis.git master
git subtree pull --prefix .travis git://github.com/jrl-umi3218/jrl-travis.git master --squash