SpaceVecAlg

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.

Documentation

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.

Appendix A table transcription to C++

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.

Table A.2 transcription

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 = EmcI(m, c, I_c)E{^T}	`inertiaToOrigin(I_c, m, c, E)`
v = XtoV(X)	`sva::transformVelocity(X)`

Table A.4 transcription

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())`

Table A.3 transcription

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)`

Installing

Ubuntu 14.04 and 16.04 binary ppa install

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-doc

Homebrew OS X install

Install 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 spacevecalg

Manually build from source

Dependencies

To compile you need the following tools:

Git
CMake >= 2.8
pkg-config
doxygen
g++ >= 4.7 (for C++11 support)
Boost >= 1.49
Eigen >= 3.2

For Python bindings:

Cython >= 0.25
Eigen3ToPython (to use the Python binding)

Building

git clone --recursive https://github.com/jrl-umi3218/SpaceVecAlg
cd SpaceVecAlg
mkdir _build
cd _build
cmake [options] ..
make && make intall

Where the main options are:

-DCMAKE_BUIlD_TYPE=Release Build in Release mode
-DCMAKE_INSTALL_PREFIX=some/path/to/install default is /usr/local
-DPYTHON_BINDING=ON Build the python binding
-DUNIT_TESTS=ON Build unit tests.
-DPYTHON_DEB_LAYOUT=OFF install python library in site-packages (ON will install in dist-packages)

Arch Linux

You can use the following AUR package.

Pulling git subtree

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

haudren/SpaceVecAlg