iit::rbd Namespace Reference

Namespaces
	internal
	tpl

Classes
struct	Core
struct	DoubleTrait
struct	FloatTrait
class	HomogeneousTransformBase
class	JacobianBase
class	RotationTransformBase
class	SpatialTransformBase
class	StateDependentBase
class	StateDependentMatrix
class	Utils

Typedefs
using	InertiaMatrixDense = tpl::InertiaMatrixDense< double >
using	Velocity = typename Core< S >::VelocityVector
using	Force = typename Core< S >::ForceVector
using	Mat33 = typename Core< S >::Matrix33
using	Mat66 = typename Core< S >::Matrix66
using	Vec3 = typename Core< S >::Vector3
using	Vec6 = typename Core< S >::Vector6
using	InertiaMat = tpl::InertiaMatrixDense< S >
General matrix types
template<typename Derived >
using	MatrixBase = Eigen::MatrixBase< Derived >
template<typename Scalar , int R, int C>
using	PlainMatrix = Eigen::Matrix< Scalar, R, C >
template<typename XprType , int R, int C>
using	MatrixBlock = Eigen::Block< XprType, R, C >
template<typename Scalar >
using	SparseMatrix = Eigen::SparseMatrix< Scalar >
template<typename Scalar >
using	SparseVector = Eigen::SparseVector< Scalar >

Enumerations
Vector coordinates
Constants to index either 6D or 3D coordinate vectors.
enum	Coords3D { X =0, Y, Z }
	To be used with 6D vectors. 'A' stands for angular, 'L' for linear. More...
enum	Coords6D {   AX =0, AY, AZ, LX,   LY, LZ }
	To be used with 6D vectors. 'A' stands for angular, 'L' for linear. More...

Functions
template<typename Derived >
Force< DScalar >	vxIv (const Velocity< DScalar > &v, const MatrixBase< Derived > &I)
template<typename Derived >
Force< DScalar >	vxIv (const DScalar &omegaz, const MatrixBase< Derived > &I)
template<typename S = double>
void	motionCrossProductMx (const Velocity< S > &v, Mat66< S > &vx)
template<typename S = double>
void	forceCrossProductMx (const Velocity< S > &v, Mat66< S > &vx)
template<typename S = double>
void	fillInertia (S mass, const Vec3< S > &com, const internal::SymmMat3x3Coefficients< S > &I3x3, InertiaMat< S > &I)
template<typename Scalar = double>
void	transformInertia (const InertiaMat< Scalar > &I_A, const Mat66< Scalar > &XF, InertiaMat< Scalar > &I_B)
Articulated inertia - Coordinate transform
These functions perform the coordinate transform of a spatial articulated inertia, in the special case of a mass-less handle (see chapter 7 of the RBDA book, §7.2.2, equation 7.23) Two specialized functions are available for the two cases of revolute and prismatic joint (which connects the subtree with the mass-less handle), since the inertia exhibits two different sparsity patterns. Parameters Ia_A the articulated inertia in A coordinates XM a spatial coordinate transform for motion vectors, in the form A_XM_B (that is, mapping forces from A to B coordinates) [out] Ia_B_const the same articulated inertia, but expressed in B coordinates. Note that the constness is casted away (trick required with Eigen)
template<typename D1 , typename D2 , typename D3 >
void	ctransform_Ia_revolute (const MatrixBase< D1 > &Ia_A, const MatrixBase< D2 > &XM, const MatrixBase< D3 > &Ia_B_const)
template<typename D1 , typename D2 , typename D3 >
void	ctransform_Ia_prismatic (const MatrixBase< D1 > &Ia_A, const MatrixBase< D2 > &XM, const MatrixBase< D3 > &Ia_B_const)
Articulated inertia - Computation
These functions calculate the spatial articulated inertia of a subtree, in the special case of a mass-less handle (see chapter 7 of the RBDA book, §7.2.2, equation 7.23) Two specialized functions are available for the two cases of revolute and prismatic joint (which connects the subtree with the mass-less handle), since the inertia exhibits two different sparsity patterns. Parameters IA the regular articulated inertia of some subtree U the U term for the current joint (cfr. eq. 7.43 of RBDA) D the D term for the current joint (cfr. eq. 7.44 of RBDA) [out] Ia_const the articulated inertia for the same subtree, but propagated across the current joint. The matrix is assumed to be already initialized with zeros, at least in the row and column which is known to be zero. In other words, those elements are not computed nor assigned in this function. Note that the constness of the argument is casted away (trick required with Eigen), as this is an output argument.
template<typename D1 , typename D2 >
void	compute_Ia_revolute (const MatrixBase< D1 > &IA, const Vec6< typename D1::Scalar > &U, const typename D1::Scalar &D, const MatrixBase< D2 > &Ia_const)
template<typename D1 , typename D2 >
void	compute_Ia_prismatic (const MatrixBase< D1 > &IA, const Vec6< typename D1::Scalar > &U, const typename D1::Scalar &D, const MatrixBase< D2 > &Ia_const)

Types with 'double' as the scalar type.
Explicit instantiation of all the various matrix types using the standard double as the scalar type. See Core
typedef Core< double >	Cored
using	Matrix33d = Cored::Matrix33
using	Vector3d = Cored::Vector3
using	Matrix66d = Cored::Matrix66
using	Vector6d = Cored::Vector6
using	Vector6D = Cored::Vector6D
using	VelocityVector = Cored::VelocityVector
using	ForceVector = Cored::ForceVector
using	Part3D = Cored::Part3D
using	Part3DConst = Cored::Part3DConst
using	Column6d = Cored::Column6D
using	SparseMatrixd = SparseMatrix< double >
using	SparseColumnd = SparseVector< double >
Part3D	angularPart (Vector6D &f)
Part3D	linearPart (Vector6D &f)
Part3DConst	angularPart (const Vector6D &f)
Part3DConst	linearPart (const Vector6D &f)

Detailed Description

This namespace contains some basic types and functions related to spatial vectors and Rigid Body Dynamics (RBD).

This code has been developed to provide basic types and general utilities to be used in turn by the C++ classes generated by the Robotics Code Generator (RobCoGen). That is, the code is just meant to be a common, generic facility for all the robot-specific code that RobCoGen can generate.

In other words, the primary target of the iit_rbd library is not to provide a comprehensive object-oriented implementation of concepts of rigid-body dynamics and spatial vectors, for end-user applications. Some of such concepts do appear in this software, although the implementation is relatively simple. However, the library may very well be used in custom code that needs e.g. a type for spatial vectors or for the spatial 6x6 inertia tensor.

Typedef Documentation

InertiaMatrixDense

using iit::rbd::InertiaMatrixDense = typedef tpl::InertiaMatrixDense<double>

Velocity

using iit::rbd::Velocity = typedef typename Core<S>::VelocityVector

Force

using iit::rbd::Force = typedef typename Core<S>::ForceVector

Mat33

using iit::rbd::Mat33 = typedef typename Core<S>::Matrix33

Mat66

using iit::rbd::Mat66 = typedef typename Core<S>::Matrix66

Vec3

using iit::rbd::Vec3 = typedef typename Core<S>::Vector3

Vec6

using iit::rbd::Vec6 = typedef typename Core<S>::Vector6

InertiaMat

using iit::rbd::InertiaMat = typedef tpl::InertiaMatrixDense<S>