math::SE3¶

rb::math::SE3 provides 3D rigid transform helpers. It is the natural companion to SO3 when controllers or planners need poses, twists, or adjoint operators between reference frames.

Header

#include <rby1-sdk/math/se3.h>

Declaration

Namespace	`rb::math`
Kind	`class`
Primary role	Provide static helpers for 3D rigid transforms and adjoint operations.

Member Types

Type	Purpose	Notes
`MatrixType`	Matrix representation used by the transform helpers.	Returned by the construction methods on this page.

Public Member Functions

Method group	Purpose	Notes
`Identity()`, `T(...)`, `Inverse(...)`	Create or invert rigid transforms.	`T(...)` builds transforms from position and rotation data.
`Exp(...)`, `Log(...)`, `Hat(...)`, `Vec(...)`	Move between transform matrices and twist-space representations.	Common in model-based control and estimation.
`Ad(...)`, `InvAd(...)`, `ad(...)`, `adTranspose(...)`	Apply adjoint and Lie-bracket operators.	Useful for wrench and twist transforms.
`GetPosition(...)`, `GetRotation(...)`, `Multiply(...)`	Extract components or apply a transform to a point.	Good for task-space utility code.
`Average(...)`	Average a set of rigid transforms.	Useful for pose filtering and alignment.

Detailed Reference

class SE3¶

Public Types

using MatrixType = Eigen::Matrix4d¶

Public Static Functions

static Eigen::Matrix<double, 6, 6> Ad(const MatrixType &T)¶

static se3v::MatrixType Ad(const MatrixType &T, const se3v::MatrixType &S)¶

static Eigen::Matrix<double, 6, 6> ad(const se3v::MatrixType &S)¶

static se3v::MatrixType ad(const se3v::MatrixType &S1, const se3v::MatrixType &S2)¶

static Eigen::Matrix<double, 6, 6> adTranspose(const se3v::MatrixType &S)¶

static se3v::MatrixType adTranspose(const se3v::MatrixType &S1, const se3v::MatrixType &S2)¶

template<typename Container, typename = std::enable_if_t<std::is_same_v<typename Container::value_type, MatrixType>>> static std::optional<MatrixType> Average(const Container &matrices, double eps, int max_iter = -1)¶

static MatrixType Exp(const se3v::MatrixType &S, double angle = 1.)¶

static MatrixType Exp(so3v::MatrixType w, Eigen::Vector3d v, double angle = 1.)¶

static Eigen::Vector3d GetPosition(const MatrixType &T)¶

static SO3::MatrixType GetRotation(const MatrixType &T)¶

static se3::MatrixType Hat(const se3v::MatrixType &v)¶

static MatrixType Identity()¶

static Eigen::Matrix<double, 6, 6> InvAd(const MatrixType &T)¶

static se3v::MatrixType InvAd(const MatrixType &T, const se3v::MatrixType &S)¶

static MatrixType Inverse(const MatrixType &T)¶

static se3v::MatrixType Log(const MatrixType &T)¶

static Eigen::Vector3d Multiply(const MatrixType &T, const Eigen::Vector3d &p)¶

static MatrixType T(const Eigen::Vector3d &p)¶

static MatrixType T(const SO3::MatrixType &R, const Eigen::Vector3d &p = Eigen::Vector3d::Zero())¶

static se3v::MatrixType Vec(const se3::MatrixType &s)¶

Related Types

Examples

dynamics/load_urdf.cpp and optimal_control.cpp are good places to see SE3 in context.