Configurations of robots, as well as some values like the position of a robot joint with respect to a fixed frame belong to differential manifolds that have the structure of Lie groups. These manifolds are the cartesian products of the following elementary Lie groups.
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Configurations of robots, as well as some values like the position of a robot joint with respect to a fixed frame belong to differential manifolds that have the structure of Lie groups. These manifolds are the cartesian products of the following elementary Lie groups.
- \(\mathbf{R}^n\),
- \(SO(2)\) the group of rotations in the plane represented by a vector of dimension 2 \((\cos \theta, \sin \theta)\) for a rotation of angle \(\theta\),
- \(SO(3)\)the group of rotations in the 3d space represented by a quaternion \(Xi + Yj + Zk + W\) (ie a vector of dimension 4),
- \(SE(2)\) the group of rigid-body motions in the plane, represented by a vector of dimention 4 \((x,y,\cos\theta,\sin\theta)\),
- \(SE(3)\), the group of rigid-body motion in 3d space, represented by a vector of dimension 7 \((x,y,z,X,Y,Z,W)\).
◆ LiegroupType
Elementary Lie groups A boost variant with the following classes:
- \(\mathbf{R}^n\), where \(n\) is either 1, 2, 3 or dynamic,
- \(\mathbf{R}^n \times SO(n) \), where \(n\) is either 2 or 3,
- \(SO(n) \), where \(n\) is either 2 or 3,
- \(SE(n) \), where \(n\) is either 2 or 3.
- See also
- hpp::pinocchio::liegroup::VectorSpaceOperation, hpp::pinocchio::liegroup::CartesianProductOperation, hpp::pinocchio::liegroup::SpecialOrthogonalOperation, hpp::pinocchio::liegroup::SpecialEuclideanOperation,
◆ DerivativeProduct
Enumerator |
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DerivativeTimesInput | |
InputTimesDerivative | |
◆ operator*()
Cartesian product between Lie groups.
◆ operator+()
template<typename vector_type >
Integration of a velocity vector from a configuration
- Parameters
-
e | element of the Lie group, |
v | element of the tangent space of the Lie group. |
- Returns
- the element of the Lie group resulting from the integration
By extension of the vector space case, we represent the integration of a constant velocity during unit time by an addition
◆ operator-()
template<typename vector_type1 , typename vector_type2 >
Difference between two configurations
- Parameters
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e1,e2 | elements of the Lie group, |
- Returns
- the velocity that integrated from e2 yiels e1
By extension of the vector space case, we represent the integration of a constant velocity during unit time by an addition
◆ operator<<()
std::ostream& hpp::pinocchio::operator<< |
( |
std::ostream & |
os, |
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const LiegroupSpace & |
space |
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) |
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inline |
◆ operator^()
Cartesian power by an integer.