An articulated body inertia (ABI) matrix P(q) contains the spatial inertia properties that a body appears to have when it is the free base body of an articulated multibody tree in a given configuration q. More...

#include <MassProperties.h>

Public Member Functions
	ArticulatedInertia_ ()
	Default contruction produces uninitialized junk at zero cost; be sure to fill this in before referencing it. More...

	ArticulatedInertia_ (const SymMat33P &mass, const Mat33P &massMoment, const SymMat33P &inertia)
	Construct an ArticulatedInertia from the mass, first moment, and inertia matrices it contains. More...

	ArticulatedInertia_ (const SpatialInertia_< P > &rbi)
	Construct an articulated body inertia (ABI) from a rigid body spatial inertia (RBI). More...

ArticulatedInertia_ &	setMass (const SymMat33P &mass)
	Set the mass distribution matrix M in this ArticulatedInertia (symmetric). More...

ArticulatedInertia_ &	setMassMoment (const Mat33P &massMoment)
	Set the mass first moment distribution matrix F in this ArticulatedInertia (full). More...

ArticulatedInertia_ &	setInertia (const SymMat33P &inertia)
	Set the mass second moment (inertia) matrix J in this ArticulatedInertia (symmetric). More...

const SymMat33P &	getMass () const
	Get the mass distribution matrix M from this ArticulatedInertia (symmetric). More...

const Mat33P &	getMassMoment () const
	Get the mass first moment distribution matrix F from this ArticulatedInertia (full). More...

const SymMat33P &	getInertia () const
	Get the mass second moment (inertia) matrix J from this ArticulatedInertia (symmetric). More...

ArticulatedInertia_ &	operator+= (const ArticulatedInertia_ &src)
	Add in a compatible ArticulatedInertia to this one. More...

ArticulatedInertia_ &	operator-= (const ArticulatedInertia_ &src)
	Subtract a compatible ArticulatedInertia from this one. More...

SpatialVecP	operator* (const SpatialVecP &v) const
	Multiply an ArticulatedIneria by a SpatialVec (66 flops). More...

template<int N>
Mat< 2, N, Vec3P >	operator* (const Mat< 2, N, Vec3P > &m) const
	Multiply an ArticulatedInertia by a row of SpatialVecs (66*N flops). More...

ArticulatedInertia_	shift (const Vec3P &s) const
	Rigid-shift the origin of this Articulated Body Inertia P by a shift vector s to produce a new ABI P'. More...

ArticulatedInertia_ &	shiftInPlace (const Vec3P &s)
	Rigid-shift this ABI in place. More...

const SpatialMatP	toSpatialMat () const
	Convert the compactly-stored ArticulatedInertia (21 elements) into a full SpatialMat with 36 elements. More...

Related Functions
(Note that these are not member functions.)
template<class P >
ArticulatedInertia_< P >	operator+ (const ArticulatedInertia_< P > &l, const ArticulatedInertia_< P > &r)
	Add two compatible articulated inertias. More...

template<class P >
ArticulatedInertia_< P >	operator- (const ArticulatedInertia_< P > &l, const ArticulatedInertia_< P > &r)
	Subtract one compatible articulated inertia from another. More...

Detailed Description

template<class P>
class SimTK::ArticulatedInertia_

An articulated body inertia (ABI) matrix P(q) contains the spatial inertia properties that a body appears to have when it is the free base body of an articulated multibody tree in a given configuration q.

Despite the complex relative motion that occurs within a multibody tree, at any given configuration q there is still a linear relationship between a spatial force F applied to a point of the base body and the resulting acceleration A of that body and that point: F = P(q)*A + c, where c is a velocity- dependent inertial bias force. P is thus analogous to a rigid body spatial inertia (RBI), but for a body which has other bodies connected to it by joints which are free to move.

An ABI P is a symmetric 6x6 spatial matrix, consisting of 2x2 blocks of 3x3 matrices, similar to the RBI. However, unlike the RBI which has only 10 independent elements, all 21 elements of P's lower triangle are significant. For example, the apparent mass of an articulated body depends on which way you push it, and in general there is no well-defined center of mass. This is a much more expensive matrix to manipulate than an RBI. In Simbody's formulation, we only work with ABIs in the Ground frame, so there is never a need to rotate or re-express them. (That is done by rotating RBIs prior to using them to construct the ABIs.) Thus only shifting operations need be performed when transforming ABIs from body to body. Cheap rigid body shifting is done when moving an ABI within a body or across a prescribed mobilizer; otherwise we have to perform an articulated shift operation which is quite expensive.

For a full discussion of the properties of articulated body inertias, see Section 7.1 (pp. 119-123) of Roy Featherstone's excellent 2008 book, Rigid Body Dynamics Algorithms.

In spatial matrix form, an ABI P may be considered to consist of the following 3x3 subblocks:

         P =  [ J  F ]
              [~F  M ]

Here M is a (symmetric) mass distribution, F is a full matrix giving the first mass moment distribution, and J is a (symmetric) inertia matrix.

Abbreviations

Typedefs exist for the most common invocations of ArticulatedInertia_:

ArticulatedInertia for default Real precision (this is almost always used)
fArticulatedInertia for single (float) precision
dArticulatedInertia for double precision

Constructor & Destructor Documentation

template<class P>

SimTK::ArticulatedInertia_::ArticulatedInertia_ ( )

inline

Default contruction produces uninitialized junk at zero cost; be sure to fill this in before referencing it.

template<class P>

SimTK::ArticulatedInertia_< P >::ArticulatedInertia_	(	const SymMat33P &	mass,
		const Mat33P &	massMoment,
		const SymMat33P &	inertia
	)

inline

Construct an ArticulatedInertia from the mass, first moment, and inertia matrices it contains.

template<class P>

SimTK::ArticulatedInertia_::ArticulatedInertia_ ( const SpatialInertia_ & rbi )

inlineexplicit

Construct an articulated body inertia (ABI) from a rigid body spatial inertia (RBI).

Every RBI is also the ABI for that (unarticulated) rigid body. 12 flops.

Member Function Documentation

template<class P>

ArticulatedInertia_& SimTK::ArticulatedInertia_::setMass ( const SymMat33P & mass )

inline

Set the mass distribution matrix M in this ArticulatedInertia (symmetric).

template<class P>

ArticulatedInertia_& SimTK::ArticulatedInertia_::setMassMoment ( const Mat33P & massMoment )

inline

Set the mass first moment distribution matrix F in this ArticulatedInertia (full).

template<class P>

ArticulatedInertia_& SimTK::ArticulatedInertia_::setInertia ( const SymMat33P & inertia )

inline

Set the mass second moment (inertia) matrix J in this ArticulatedInertia (symmetric).

template<class P>

const SymMat33P& SimTK::ArticulatedInertia_::getMass ( ) const

inline

Get the mass distribution matrix M from this ArticulatedInertia (symmetric).

template<class P>

const Mat33P& SimTK::ArticulatedInertia_::getMassMoment ( ) const

inline

Get the mass first moment distribution matrix F from this ArticulatedInertia (full).

template<class P>

const SymMat33P& SimTK::ArticulatedInertia_::getInertia ( ) const

inline

Get the mass second moment (inertia) matrix J from this ArticulatedInertia (symmetric).

template<class P>

ArticulatedInertia_& SimTK::ArticulatedInertia_::operator+= ( const ArticulatedInertia_ & src )

inline

Add in a compatible ArticulatedInertia to this one.

Both inertias must be expressed in the same frame and measured about the same point. 21 flops.

template<class P>

ArticulatedInertia_& SimTK::ArticulatedInertia_::operator-= ( const ArticulatedInertia_ & src )

inline

Subtract a compatible ArticulatedInertia from this one.

Both inertias must be expressed in the same frame and measured about the same point. 21 flops.

template<class P>

SpatialVecP SimTK::ArticulatedInertia_::operator* ( const SpatialVecP & v ) const

inline

Multiply an ArticulatedIneria by a SpatialVec (66 flops).

template<class P>

template<int N>

Mat<2,N,Vec3P> SimTK::ArticulatedInertia_::operator* ( const Mat< 2, N, Vec3P > & m ) const

inline

Multiply an ArticulatedInertia by a row of SpatialVecs (66*N flops).

template<class P>

ArticulatedInertia_ SimTK::ArticulatedInertia_::shift ( const Vec3P & s ) const

Rigid-shift the origin of this Articulated Body Inertia P by a shift vector s to produce a new ABI P'.

The calculation is

P' =  [ J'  F' ]  =  [ 1  sx ] [ J  F ] [ 1  0 ]
      [~F'  M  ]     [ 0  1  ] [~F  M ] [-sx 1 ]

where sx is the cross product matrix of s. Cost is 72 flops.

template<class P>

ArticulatedInertia_& SimTK::ArticulatedInertia_::shiftInPlace ( const Vec3P & s )

Rigid-shift this ABI in place.

72 flops.

See Also: shift() for details

template<class P>

const SpatialMatP SimTK::ArticulatedInertia_::toSpatialMat ( ) const

inline

Convert the compactly-stored ArticulatedInertia (21 elements) into a full SpatialMat with 36 elements.

Friends And Related Function Documentation

template<class P >

ArticulatedInertia_< P > operator+	(	const ArticulatedInertia_< P > &	l,
		const ArticulatedInertia_< P > &	r
	)

Cost is 21 flops.

template<class P >

ArticulatedInertia_< P > operator-	(	const ArticulatedInertia_< P > &	l,
		const ArticulatedInertia_< P > &	r
	)

Cost is 21 flops.

The documentation for this class was generated from the following file:

MassProperties.h

Public Member Functions

Related Functions

Detailed Description

template<class P> class SimTK::ArticulatedInertia_< P >

Abbreviations

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<class P>
class SimTK::ArticulatedInertia_< P >