Detailed Description

template<template< typename > class SV, typename T>
class drake::multibody::SpatialVector< SV, T >

This class represents a spatial vector and has 6 elements, with a 3-element rotational vector on top of a 3-element translational vector.

Important subclasses of SpatialVector include SpatialVelocity, SpatialAcceleration, SpatialForce, and SpatialMomentum. Each of the 3-element vectors is assumed to be expressed in the same expressed-in frame E. This class only stores 6 elements and does not store the underlying expressed-in frame E or other information. The user is responsible for explicitly tracking the underlying frames with monogram notation. For example, Foo_E denotes an arbitrary spatial vector Foo expressed in a frame E. Details on spatial vectors and monogram notation are in sections Spatial Vectors and monogram notation.

Template Parameters

SV	The type of the more specialized spatial vector class. It must be a template on the scalar type T.
T	The scalar type, which must be one of the default scalars.

#include <drake/multibody/math/spatial_vector.h>

Public Types
enum	{ kSpatialVectorSize = 6, kRotationSize = 3, kTranslationSize = 3 }
	Sizes for spatial quantities and its components in 3D (three dimensions). More...

using	SpatialQuantity = SV< T >
	The more specialized spatial vector class templated on the scalar type T. More...

using	CoeffsEigenType = Vector6< T >
	The type of the underlying in-memory representation using an Eigen vector. More...

Public Member Functions
	SpatialVector ()
	Default constructor. More...

	SpatialVector (const Eigen::Ref< const Vector3< T >> &w, const Eigen::Ref< const Vector3< T >> &v)
	Constructs a spatial vector from a rotational component w and a translational component v. More...

template<typename OtherDerived >
	SpatialVector (const Eigen::MatrixBase< OtherDerived > &V)
	Constructs a spatial vector V from an Eigen expression that represents a 6-element vector (3-element rotational vector on top of a 3-element translational vector). More...

int	size () const
	For 3D (three-dimensional) analysis, the total size of the concatenated rotational vector (3 elements) and translational vector (3 elements) is six (6), which is known at compile time. More...

const T &	operator[] (int i) const
	Const access to the i-th element of this spatial vector. More...

T &	operator[] (int i)
	Mutable access to the i-th element of this spatial vector. More...

const Vector3< T > &	rotational () const
	Const access to the rotational component of this spatial vector. More...

Vector3< T > &	rotational ()
	Mutable access to the rotational component of this spatial vector. More...

const Vector3< T > &	translational () const
	Const access to the translational component of this spatial vector. More...

Vector3< T > &	translational ()
	Mutable access to the translational component of this spatial vector. More...

const T *	data () const
	Returns a (const) bare pointer to the underlying data. More...

T *	mutable_data ()
	Returns a (mutable) bare pointer to the underlying data. More...

std::tuple< const T, const T >	GetMaximumAbsoluteDifferences (const SpatialQuantity &other) const
	Returns the maximum absolute values of the differences in the rotational and translational components of `this` and `other` (i.e., the infinity norms of the difference in rotational and translational components). More...

decltype(T()< T())	IsNearlyEqualWithinAbsoluteTolerance (const SpatialQuantity &other, double rotational_tolerance, double translational_tolerance) const
	Compares the rotational and translational parts of `this` and `other` to check if they are the same to within specified absolute differences. More...

decltype(T()< T())	IsApprox (const SpatialQuantity &other, double tolerance=2 *std::numeric_limits< double >::epsilon()) const
	Determines whether all six corresponding elements of two spatial vectors are equal to each other to within a specified tolerance epsilon. More...

void	SetNaN ()
	Sets all the elements in `this` SpatialVector to NaN. More...

SpatialQuantity &	SetZero ()
	Sets both the rotational and translational components of `this` SpatialVector to zero. More...

CoeffsEigenType &	get_coeffs ()
	Returns a mutable reference to the underlying storage. More...

const CoeffsEigenType &	get_coeffs () const
	Returns a constant reference to the underlying storage. More...

SpatialQuantity	operator- () const
	Unary minus operator. More...

SpatialQuantity &	operator+= (const SpatialQuantity &V)
	Addition assignment operator. More...

SpatialQuantity &	operator-= (const SpatialQuantity &V)
	Subtraction assignment operator. More...

SpatialQuantity &	operator *= (const T &s)
	Multiplication assignment operator. More...

Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	SpatialVector (const SpatialVector &)=default

SpatialVector &	operator= (const SpatialVector &)=default

	SpatialVector (SpatialVector &&)=default

SpatialVector &	operator= (SpatialVector &&)=default

Static Public Member Functions
static SpatialQuantity	Zero ()
	Factory to create a zero spatial vector, i.e., a SpatialVector whose rotational and translational components are both zero. More...

Friends
SpatialQuantity	operator+ (const SpatialQuantity &V1_E, const SpatialQuantity &V2_E)
	Adds two spatial vectors by simply adding their 6 underlying elements. More...

SpatialQuantity	operator- (const SpatialQuantity &V1, const SpatialQuantity &V2)
	Subtracts two spatial vectors by simply subtracting their 6 underlying elements. More...

SpatialQuantity	operator * (const math::RotationMatrix< T > &R_FE, const SpatialQuantity &V_E)
	Expresses a spatial vector in another frame. More...

Related Functions
(Note that these are not member functions.)
SpatialQuantity	operator * (const T &s, const SpatialQuantity &V)
	Multiplication of a spatial vector V from the left by a scalar `s`. More...

SpatialQuantity	operator * (const SpatialQuantity &V, const T &s)
	Multiplication of a spatial vector V from the right by a scalar `s`. More...

template<template< typename > class SpatialQuantity, typename T >
std::ostream &	operator<< (std::ostream &o, const SpatialVector< SpatialQuantity, T > &V)
	Stream insertion operator to write SpatialVector objects into a `std::ostream`. More...

Member Typedef Documentation

◆ CoeffsEigenType

using CoeffsEigenType = Vector6<T>

The type of the underlying in-memory representation using an Eigen vector.

◆ SpatialQuantity

using SpatialQuantity = SV<T>

The more specialized spatial vector class templated on the scalar type T.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Sizes for spatial quantities and its components in 3D (three dimensions).

Enumerator
kSpatialVectorSize
kRotationSize
kTranslationSize

Constructor & Destructor Documentation

◆ SpatialVector() [1/5]

SpatialVector ( const SpatialVector< SV, T > & )

default

◆ SpatialVector() [2/5]

SpatialVector ( SpatialVector< SV, T > && )

default

◆ SpatialVector() [3/5]

SpatialVector ( )

Default constructor.

In Release builds, all 6 elements of a newly constructed spatial vector are uninitialized (for speed). In Debug builds, the 6 elements are set to NaN so that invalid operations on an uninitialized spatial vector fail fast (fast bug detection).

◆ SpatialVector() [4/5]

SpatialVector	(	const Eigen::Ref< const Vector3< T >> &	w,
		const Eigen::Ref< const Vector3< T >> &	v
	)

Constructs a spatial vector from a rotational component w and a translational component v.

◆ SpatialVector() [5/5]

SpatialVector ( const Eigen::MatrixBase< OtherDerived > & V )

explicit

Constructs a spatial vector V from an Eigen expression that represents a 6-element vector (3-element rotational vector on top of a 3-element translational vector).

This constructor asserts the size of V is six (6) either at compile-time for fixed sized Eigen expressions or at run-time for dynamic sized Eigen expressions.

Member Function Documentation

◆ data()

const T* data ( ) const

Returns a (const) bare pointer to the underlying data.

It is guaranteed that there will be six (6) T's densely packed at data[0], data[1], etc.

◆ get_coeffs() [1/2]

CoeffsEigenType& get_coeffs ( )

Returns a mutable reference to the underlying storage.

◆ get_coeffs() [2/2]

const CoeffsEigenType& get_coeffs ( ) const

Returns a constant reference to the underlying storage.

◆ GetMaximumAbsoluteDifferences()

std::tuple<const T, const T> GetMaximumAbsoluteDifferences ( const SpatialQuantity & other ) const

Returns the maximum absolute values of the differences in the rotational and translational components of this and other (i.e., the infinity norms of the difference in rotational and translational components).

Parameters

[in] other spatial vector to subtract from this spatial vector.

Returns

The following quantities in a tuple, in the order below.

std::tuple	Description
w_max_difference	Maximum absolute difference in rotation components
v_max_difference	Maximum absolute difference in translation components

◆ IsApprox()

decltype(T() < T()) IsApprox	(	const SpatialQuantity &	other,
		double	tolerance = `2 * std::numeric_limits<double>::epsilon()`
	)		const

Determines whether all six corresponding elements of two spatial vectors are equal to each other to within a specified tolerance epsilon.

Parameters

[in]	other	spatial vector to compare to `this` spatial vector.
[in]	epsilon	specified tolerance for this test.

Returns: true if ‖this - other‖∞ < epsilon, otherwise returns false. Note: the infinity norm ‖this - other‖∞ is simply the maximum of the six absolute values in (this - other).

◆ IsNearlyEqualWithinAbsoluteTolerance()

decltype(T() < T()) IsNearlyEqualWithinAbsoluteTolerance	(	const SpatialQuantity &	other,
		double	rotational_tolerance,
		double	translational_tolerance
	)		const

Compares the rotational and translational parts of this and other to check if they are the same to within specified absolute differences.

Parameters

[in]	other	spatial vector to compare to `this` spatial vector.
[in]	rotational_tolerance	maximum allowable absolute difference between the rotational parts of `this` and `other`. The units depend on the underlying class. For example, spatial velocity, acceleration, and force have units of rad/sec, rad/sec^2, and N*m, respectively.
[in]	translational_tolerance	maximum allowable absolute difference between the translational parts of `this` and `other`. The units depend on the underlying class. For example, spatial velocity, acceleration, and force have units of meter/sec, meter/sec^2, and Newton, respectively.

Returns: true if all three rotational elements of this and other are equal within rotational_tolerance and all three translational elements of this and other are equal within translational_tolerance.

◆ mutable_data()

T* mutable_data ( )

Returns a (mutable) bare pointer to the underlying data.

It is guaranteed that there will be six (6) T's densely packed at data[0], data[1], etc.

◆ operator *=()

SpatialQuantity& operator *= ( const T & s )

Multiplication assignment operator.

◆ operator+=()

SpatialQuantity& operator+= ( const SpatialQuantity & V )

Addition assignment operator.

◆ operator-()

SpatialQuantity operator- ( ) const

Unary minus operator.

◆ operator-=()

SpatialQuantity& operator-= ( const SpatialQuantity & V )

Subtraction assignment operator.

◆ operator=() [1/2]

SpatialVector& operator= ( SpatialVector< SV, T > && )

default

◆ operator=() [2/2]

SpatialVector& operator= ( const SpatialVector< SV, T > & )

default

◆ operator[]() [1/2]

const T& operator[] ( int i ) const

Const access to the i-th element of this spatial vector.

In Debug builds, this function asserts that i is in bounds whereas for release builds, no bounds-check on i is performed (for speed).

◆ operator[]() [2/2]

T& operator[] ( int i )

Mutable access to the i-th element of this spatial vector.

In Debug builds, this function asserts that i is in bounds whereas for release builds, no bounds-check on i is performed (for speed).

◆ rotational() [1/2]

const Vector3<T>& rotational ( ) const

Const access to the rotational component of this spatial vector.

◆ rotational() [2/2]

Vector3<T>& rotational ( )

Mutable access to the rotational component of this spatial vector.

◆ SetNaN()

void SetNaN ( )

Sets all the elements in this SpatialVector to NaN.

This is typically used to quickly detect uninitialized values since NaN will trigger a chain of invalid computations that can be tracked back to their source.

◆ SetZero()

SpatialQuantity& SetZero ( )

Sets both the rotational and translational components of this SpatialVector to zero.

◆ size()

int size ( ) const

For 3D (three-dimensional) analysis, the total size of the concatenated rotational vector (3 elements) and translational vector (3 elements) is six (6), which is known at compile time.

◆ translational() [1/2]

const Vector3<T>& translational ( ) const

Const access to the translational component of this spatial vector.

◆ translational() [2/2]

Vector3<T>& translational ( )

Mutable access to the translational component of this spatial vector.

◆ Zero()

static SpatialQuantity Zero ( )

static

Factory to create a zero spatial vector, i.e., a SpatialVector whose rotational and translational components are both zero.

Friends And Related Function Documentation

◆ operator * [1/3]

SpatialQuantity operator *	(	const T &	s,
		const SpatialQuantity &	V
	)

friend

Multiplication of a spatial vector V from the left by a scalar s.

◆ operator * [2/3]

SpatialQuantity operator *	(	const SpatialQuantity &	V,
		const T &	s
	)

friend

Multiplication of a spatial vector V from the right by a scalar s.

◆ operator * [3/3]

SpatialQuantity operator *	(	const math::RotationMatrix< T > &	R_FE,
		const SpatialQuantity &	V_E
	)

friend

Expresses a spatial vector in another frame.

Parameters

[in]	R_FE	RotationMatrix relating a frame F to a frame E.
[in]	V_E	spatial vector expressed in frame E.

Returns

V_F spatial vector expressed in frame F, calculated from:

  V_F.rotational()    = R_FE * V_E.rotational(),
  V_F.translational() = R_FE * V_E.translational()

◆ operator+

SpatialQuantity operator+	(	const SpatialQuantity &	V1_E,
		const SpatialQuantity &	V2_E
	)

friend

Adds two spatial vectors by simply adding their 6 underlying elements.

Parameters

[in]	V1_E	spatial vector expressed in the same frame E as V2_E.
[in]	V2_E	spatial vector expressed in the same frame E as V1_E.

Note: The general utility of this operator+() function is questionable and it should only be used if you are sure it makes sense. Please refer to documentation for the appropriate spatial quantity subclass (e.g., SpatialVelocity, SpatialAcceleration, SpatialForce, or SpatialMomentum).

◆ operator-

SpatialQuantity operator-	(	const SpatialQuantity &	V1,
		const SpatialQuantity &	V2
	)

friend

Subtracts two spatial vectors by simply subtracting their 6 underlying elements.

Parameters

[in]	V1_E	spatial vector expressed in the same frame E as V2_E.
[in]	V2_E	spatial vector expressed in the same frame E as V1_E.

Note: The general utility of this operator-() function is questionable and it should only be used if you are sure it makes sense. Please refer to documentation for the appropriate spatial quantity subclass (e.g., SpatialVelocity, SpatialAcceleration, SpatialForce, or SpatialMomentum).

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	o,
		const SpatialVector< SpatialQuantity, T > &	V
	)

Especially useful for debugging.

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

drake/multibody/math/spatial_vector.h

Detailed Description

template<template< typename > class SV, typename T> class drake::multibody::SpatialVector< SV, T >

Public Types

Public Member Functions

Static Public Member Functions

Friends

Related Functions

Member Typedef Documentation

◆ CoeffsEigenType

◆ SpatialQuantity

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ SpatialVector() [1/5]

◆ SpatialVector() [2/5]

◆ SpatialVector() [3/5]

◆ SpatialVector() [4/5]

◆ SpatialVector() [5/5]

Member Function Documentation

◆ data()

◆ get_coeffs() [1/2]

◆ get_coeffs() [2/2]

◆ GetMaximumAbsoluteDifferences()

◆ IsApprox()

◆ IsNearlyEqualWithinAbsoluteTolerance()

◆ mutable_data()

◆ operator *=()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ rotational() [1/2]

◆ rotational() [2/2]

◆ SetNaN()

◆ SetZero()

◆ size()

◆ translational() [1/2]

◆ translational() [2/2]

◆ Zero()

Friends And Related Function Documentation

◆ operator * [1/3]

◆ operator * [2/3]

◆ operator * [3/3]

◆ operator+

◆ operator-

◆ operator<<()

template<template< typename > class SV, typename T>
class drake::multibody::SpatialVector< SV, T >