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.

Installing

Ubuntu LTS (16.04, 18.04, 20.04)

You must first setup our package mirror:

curl -1sLf \
  'https://dl.cloudsmith.io/public/mc-rtc/stable/setup.deb.sh' \
  | sudo -E bash

You can also choose the head mirror which will have the latest version of this package:

curl -1sLf \
  'https://dl.cloudsmith.io/public/mc-rtc/head/setup.deb.sh' \
  | sudo -E bash

You can then install the package:

sudo apt install libspacevecalg-dev python-spacevecalg python3-spacevecalg

Homebrew (macOS and Linux)

Install from the command line using Homebrew:

# Use mc-rtc tap
brew tap mc-rtc/mc-rtc
# install SpaceVecAlg and its Python bindings
brew install spacevecalg

vcpkg

Use the registry available here

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

CMake options

By default, the build will use the python and pip command to install the bindings for the default system version (this behaviour can be used to build the bindings in a given virtualenv). The following options allow to control this behaviour:

• PYTHON_BINDING Build the python binding (ON/OFF, default: ON)
• PYTHON_BINDING_FORCE_PYTHON2: use python2 and pip2 instead of python and pip
• PYTHON_BINDING_FORCE_PYTHON3: use python3 and pip3 instead of python and pip
• PYTHON_BINDING_BUILD_PYTHON2_AND_PYTHON2: builds two sets of bindings one with python2 and pip2, the other with python3 and pip3
• BUILD_TESTING Enable unit tests building (ON/OFF, default: ON)

Arch Linux

You can use the following AUR package.

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.

Handedness - Left Hand Rule

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.

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 = E*mcI(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)