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.
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
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
Use the registry available here
To 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 intall
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
: usepython2
andpip2
instead ofpython
andpip
PYTHON_BINDING_FORCE_PYTHON3
: usepython3
andpip3
instead ofpython
andpip
PYTHON_BINDING_BUILD_PYTHON2_AND_PYTHON2
: builds two sets of bindings one withpython2
andpip2
, the other withpython3
andpip3
BUILD_TESTING
Enable unit tests building (ON/OFF, default: ON)
You can use the following AUR package.
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, x
for 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) |