Template Struct SE3Base

Defined in File se3-base.hpp

Inheritance Relationships

Derived Types

public pinocchio::SE3Tpl< Scalar, Options > (Template Struct SE3Tpl)
public pinocchio::SE3Tpl< double, 0 > (Template Struct SE3Tpl)

Struct Documentation

template<class Derived> struct SE3Base

Base class for rigid transformation.

The rigid transform aMb can be seen in two ways:

given a point p expressed in frame B by its coordinate vector \( ^bp \), \( ^aM_b \) computes its coordinates in frame A by \( ^ap = {}^aM_b {}^bp \).
\( ^aM_b \) displaces a solid S centered at frame A into the solid centered in B. In particular, the origin of A is displaced at the origin of B: \(^aM_b {}^aA = {}^aB \).

The rigid displacement is stored as a rotation matrix and translation vector by: \( ^aM_b x = {}^aR_b x + {}^aAB \) where \(^aAB\) is the vector from origin A to origin B expressed in coordinates A.

\cheatsheet \( {}^aM_c = {}^aM_b {}^bM_c \)

Subclassed by pinocchio::SE3Tpl< Scalar, Options >, pinocchio::SE3Tpl< double, 0 >

Public Functions

PINOCCHIO_SE3_TYPEDEF_TPL(Derived)

inline Derived &derived()

inline const Derived &derived() const

inline ConstAngularRef rotation() const

inline ConstLinearRef translation() const

inline AngularRef rotation()

inline LinearRef translation()

inline void rotation(const AngularType &R)

inline void translation(const LinearType &t)

inline HomogeneousMatrixType toHomogeneousMatrix() const

inline operator HomogeneousMatrixType() const

inline ActionMatrixType toActionMatrix() const

The action matrix \( {}^aX_b \) of \( {}^aM_b \).

With \( {}^aM_b = \left( \begin{array}{cc} R & t \\ 0 & 1 \\ \end{array} \right) \),

\[\begin{split} {}^aX_b = \left( \begin{array}{cc} R & \hat{t} R \\ 0 & R \\ \end{array} \right) \end{split}\]

\cheatsheet \( {}^a\nu_c = {}^aX_b {}^b\nu_c \)

inline operator ActionMatrixType() const

inline ActionMatrixType toActionMatrixInverse() const

The action matrix \( {}^bX_a \) of \( {}^aM_b \).