#include <hpp/core/fwd.hh>

Inheritance diagram for hpp::core::path::Spline< _PolynomeBasis, _Order >:

Collaboration diagram for hpp::core::path::Spline< _PolynomeBasis, _Order >:

Public Types
enum	{ PolynomeBasis = _PolynomeBasis, Order = _Order, NbCoeffs = _Order + 1, NbPowerOfT = 2 * NbCoeffs + 1 }

typedef internal::sbf_traits< PolynomeBasis, Order >	sbf_traits

typedef internal::spline_basis_function< PolynomeBasis, Order >	BasisFunction_t

typedef Eigen::Matrix< value_type, NbPowerOfT, 1 >	PowersOfT_t

typedef sbf_traits::Coeffs_t	BasisFunctionVector_t

typedef sbf_traits::IntegralCoeffs_t	BasisFunctionIntegralMatrix_t

typedef Eigen::Matrix< value_type, NbCoeffs, Eigen::Dynamic, Eigen::RowMajor >	ParameterMatrix_t

typedef Eigen::Map< const vector_t, Eigen::Aligned >	ConstParameterVector_t

typedef Eigen::Map< vector_t, Eigen::Aligned >	ParameterVector_t

typedef boost::shared_ptr< Spline >	Ptr_t

typedef boost::weak_ptr< Spline >	WkPtr_t

Public Member Functions
size_type	parameterSize () const

void	parameterDerivativeCoefficients (vectorOut_t res, const value_type &t) const

void	parameterIntegrate (vectorIn_t dParam)
	Adds dParam to the parameters. More...

value_type	squaredNormIntegral (const size_type order) const

void	squaredNormIntegralDerivative (const size_type order, vectorOut_t res) const

void	basisFunctionDerivative (const size_type order, const value_type &u, BasisFunctionVector_t &res) const

void	basisFunctionDerivative (const size_type order, const value_type &u, vectorOut_t res) const

void	maxVelocity (vectorOut_t res) const

void	squaredNormBasisFunctionIntegral (const size_type order, BasisFunctionIntegralMatrix_t &res) const

void	squaredNormBasisFunctionIntegral (const size_type order, matrixOut_t res) const

virtual Configuration_t	initial () const
	Get the initial configuration. More...

virtual Configuration_t	end () const
	Get the final configuration. More...

const Configuration_t &	base () const

void	base (const Configuration_t &q)

const ParameterMatrix_t &	parameters () const
	Each row corresponds to a velocity of the robot. More...

void	parameters (const ParameterMatrix_t &m)

ConstParameterVector_t	rowParameters () const
	Concatenate the parameters as one vector (P_0^T, ..., P_n^T). More...

void	rowParameters (vectorIn_t p)
	Set the parameters. More...

PathPtr_t	copy () const
	Return a shared pointer to a copy of this. More...

PathPtr_t	copy (const ConstraintSetPtr_t &constraints) const

virtual	~Spline ()

Public Member Functions inherited from hpp::core::Path
virtual	~Path ()
	Destructor. More...

template<class T >
boost::shared_ptr< T >	as (void)
	Static cast into a derived type. More...

template<class T >
boost::shared_ptr< const T >	as (void) const
	Static cast into a derived type. More...

PathPtr_t	extract (const interval_t &subInterval) const

PathPtr_t	extract (const value_type &tmin, const value_type &tmax) const

virtual PathPtr_t	reverse () const

Configuration_t	operator() (const value_type &time) const HPP_CORE_DEPRECATED

Configuration_t	operator() (const value_type &time, bool &success) const

bool	operator() (ConfigurationOut_t result, const value_type &time) const

Configuration_t	eval (const value_type &time, bool &success) const

bool	eval (ConfigurationOut_t result, const value_type &time) const

bool	at (const value_type &time, ConfigurationOut_t result) const
	Get the configuration at a parameter without applying the constraints. More...

void	derivative (vectorOut_t result, const value_type &time, size_type order) const

void	velocityBound (vectorOut_t result, const value_type &t0, const value_type &t1) const

size_type	outputSize () const
	Get size of configuration space. More...

size_type	outputDerivativeSize () const
	Get size of velocity. More...

const interval_t &	timeRange () const
	Get interval of definition. More...

virtual value_type	length () const
	Get length of definition interval. More...

const ConstraintSetPtr_t &	constraints () const
	Get constraints the path is subject to. More...

const interval_t &	paramRange () const

void	timeParameterization (const TimeParameterizationPtr_t &tp, const interval_t &tr)
	Set the time parameterization function. More...

Static Public Member Functions
static void	timeFreeBasisFunctionDerivative (const size_type order, const value_type &u, BasisFunctionVector_t &res)

static void	timeFreeBasisFunctionDerivative (const size_type order, const value_type &u, vectorOut_t res)

static Ptr_t	create (const DevicePtr_t &robot, const interval_t &interval, const ConstraintSetPtr_t &constraints)

static void	value (pinocchio::LiegroupElementConstRef base, Eigen::Ref< const ParameterMatrix_t > params, const value_type &u, ConfigurationOut_t config, vectorOut_t velocity)

Protected Member Functions
	Spline (const DevicePtr_t &robot, const interval_t &interval, const ConstraintSetPtr_t &constraints)

	Spline (const Spline &path)

	Spline (const Spline &path, const ConstraintSetPtr_t &constraints)

void	init (const Ptr_t &self)

std::ostream &	print (std::ostream &os) const

bool	impl_compute (ConfigurationOut_t configuration, value_type t) const
	Function evaluation without applying constraints. More...

void	impl_derivative (vectorOut_t res, const value_type &t, size_type order) const

void	impl_paramDerivative (vectorOut_t res, const value_type &t) const

void	impl_paramIntegrate (vectorIn_t dParam)

void	impl_velocityBound (vectorOut_t result, const value_type &t0, const value_type &t1) const

Protected Member Functions inherited from hpp::core::Path
	Path (const interval_t &interval, size_type outputSize, size_type outputDerivativeSize, const ConstraintSetPtr_t &constraints)

	Path (const interval_t &interval, size_type outputSize, size_type outputDerivativeSize)

	Path (const Path &path)
	Copy constructor. More...

	Path (const Path &path, const ConstraintSetPtr_t &constraints)
	Copy constructor with constraints. More...

void	init (const PathWkPtr_t &self)

void	constraints (const ConstraintSetPtr_t &constraint)

virtual void	checkPath () const
	Should be called by child classes after having init. More...

void	timeRange (const interval_t &timeRange)

const TimeParameterizationPtr_t &	timeParameterization () const

value_type	paramLength () const

Configuration_t	configAtParam (const value_type &param, bool &success) const

virtual PathPtr_t	impl_extract (const interval_t &paramInterval) const
	Virtual implementation of extract. More...

Protected Attributes
size_type	parameterSize_
	Robot number of degrees of freedom. More...

DevicePtr_t	robot_

LiegroupElement	base_

ParameterMatrix_t	parameters_

Protected Attributes inherited from hpp::core::Path
interval_t	paramRange_
	Interval of parameters. More...

Detailed Description

template<int _PolynomeBasis, int _Order>
class hpp::core::path::Spline< _PolynomeBasis, _Order >

Base class for spline paths

Splines are polynomials with various possible representations.

Parameters

_PolynomeBasis	basis of polynomials used among CanonicalPolynomeBasis for the canonical basis, BernsteinBasis for Bernstein basis
_Order	degree of the polynomial representation.

See also: hpp::core::path::PolynomeBasisType.

Splines represent a curve in the tangent space of a given robot (hpp::core::Device) at a configuration called base.

\begin{eqnarray*} spline (u) &=& base + PM^{T} B (u) \end{eqnarray*}

where*

\(u\in [0,1]\),
operator "+" should be understood as Lie group integration,
\(PM\) is the matrix of parameters the rows of which are the spline control points. This matrix is accessible via setter and getter Spline::parameters,
\(B (t)\) is the vector containing the values of the basis functions at parameter \(t\).

The dimension of control points, corresponding to the robot number of degrees of freedom can be retrieved by getter Spline::parameterSize.

Member Typedef Documentation

◆ BasisFunction_t

template<int _PolynomeBasis, int _Order>

typedef internal::spline_basis_function<PolynomeBasis, Order> hpp::core::path::Spline< _PolynomeBasis, _Order >::BasisFunction_t

◆ BasisFunctionIntegralMatrix_t

template<int _PolynomeBasis, int _Order>

typedef sbf_traits::IntegralCoeffs_t hpp::core::path::Spline< _PolynomeBasis, _Order >::BasisFunctionIntegralMatrix_t

◆ BasisFunctionVector_t

template<int _PolynomeBasis, int _Order>

typedef sbf_traits::Coeffs_t hpp::core::path::Spline< _PolynomeBasis, _Order >::BasisFunctionVector_t

◆ ConstParameterVector_t

template<int _PolynomeBasis, int _Order>

typedef Eigen::Map<const vector_t, Eigen::Aligned> hpp::core::path::Spline< _PolynomeBasis, _Order >::ConstParameterVector_t

◆ ParameterMatrix_t

template<int _PolynomeBasis, int _Order>

typedef Eigen::Matrix<value_type, NbCoeffs, Eigen::Dynamic, Eigen::RowMajor> hpp::core::path::Spline< _PolynomeBasis, _Order >::ParameterMatrix_t

◆ ParameterVector_t

template<int _PolynomeBasis, int _Order>

typedef Eigen::Map< vector_t, Eigen::Aligned> hpp::core::path::Spline< _PolynomeBasis, _Order >::ParameterVector_t

◆ PowersOfT_t

template<int _PolynomeBasis, int _Order>

typedef Eigen::Matrix<value_type, NbPowerOfT, 1> hpp::core::path::Spline< _PolynomeBasis, _Order >::PowersOfT_t

◆ Ptr_t

template<int _PolynomeBasis, int _Order>

typedef boost::shared_ptr<Spline> hpp::core::path::Spline< _PolynomeBasis, _Order >::Ptr_t

◆ sbf_traits

template<int _PolynomeBasis, int _Order>

typedef internal::sbf_traits<PolynomeBasis, Order> hpp::core::path::Spline< _PolynomeBasis, _Order >::sbf_traits

◆ WkPtr_t

template<int _PolynomeBasis, int _Order>

typedef boost::weak_ptr<Spline> hpp::core::path::Spline< _PolynomeBasis, _Order >::WkPtr_t

Member Enumeration Documentation

◆ anonymous enum

template<int _PolynomeBasis, int _Order>

anonymous enum

Enumerator
PolynomeBasis
Order
NbCoeffs
NbPowerOfT

Constructor & Destructor Documentation

◆ ~Spline()

template<int _PolynomeBasis, int _Order>

virtual hpp::core::path::Spline< _PolynomeBasis, _Order >::~Spline ( )

inlinevirtual

◆ Spline() [1/3]

template<int _PolynomeBasis, int _Order>

hpp::core::path::Spline< _PolynomeBasis, _Order >::Spline	(	const DevicePtr_t &	robot,
		const interval_t &	interval,
		const ConstraintSetPtr_t &	constraints
	)

inlineprotected

◆ Spline() [2/3]

template<int _PolynomeBasis, int _Order>

hpp::core::path::Spline< _PolynomeBasis, _Order >::Spline ( const Spline< _PolynomeBasis, _Order > & path )

protected

◆ Spline() [3/3]

template<int _PolynomeBasis, int _Order>

hpp::core::path::Spline< _PolynomeBasis, _Order >::Spline	(	const Spline< _PolynomeBasis, _Order > &	path,
		const ConstraintSetPtr_t &	constraints
	)

protected

Member Function Documentation

◆ base() [1/2]

template<int _PolynomeBasis, int _Order>

const Configuration_t& hpp::core::path::Spline< _PolynomeBasis, _Order >::base ( ) const

inline

Get the base configuration. The parameters are velocities to be integrated from this configuration.

◆ base() [2/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::base ( const Configuration_t & q )

inline

See also: base() const

◆ basisFunctionDerivative() [1/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::basisFunctionDerivative	(	const size_type	order,
		const value_type &	u,
		BasisFunctionVector_t &	res
	)		const

Returns a vector \( (v_i) \) as

\[ v_i = T^{-k} b_i^{(k)}(u) \]

◆ basisFunctionDerivative() [2/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::basisFunctionDerivative	(	const size_type	order,
		const value_type &	u,
		vectorOut_t	res
	)		const

inline

◆ copy() [1/2]

template<int _PolynomeBasis, int _Order>

PathPtr_t hpp::core::path::Spline< _PolynomeBasis, _Order >::copy ( ) const

inlinevirtual

Return a shared pointer to a copy of this.

Implements hpp::core::Path.

◆ copy() [2/2]

template<int _PolynomeBasis, int _Order>

PathPtr_t hpp::core::path::Spline< _PolynomeBasis, _Order >::copy ( const ConstraintSetPtr_t & constraints ) const

inlinevirtual

Return a shared pointer to a copy of this and set constraints

Parameters

constraints constraints to apply to the copy

Precondition: *this should not have constraints.

Implements hpp::core::Path.

◆ create()

template<int _PolynomeBasis, int _Order>

static Ptr_t hpp::core::path::Spline< _PolynomeBasis, _Order >::create	(	const DevicePtr_t &	robot,
		const interval_t &	interval,
		const ConstraintSetPtr_t &	constraints
	)

inlinestatic

◆ end()

template<int _PolynomeBasis, int _Order>

virtual Configuration_t hpp::core::path::Spline< _PolynomeBasis, _Order >::end ( ) const

inlinevirtual

Get the final configuration.

Implements hpp::core::Path.

Reimplemented in hpp::core::path::Hermite.

◆ impl_compute()

template<int _PolynomeBasis, int _Order>

bool hpp::core::path::Spline< _PolynomeBasis, _Order >::impl_compute	(	ConfigurationOut_t	configuration,
		value_type	param
	)		const

protectedvirtual

Function evaluation without applying constraints.

Returns: true if everything went good.

Implements hpp::core::Path.

◆ impl_derivative()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::impl_derivative	(	vectorOut_t	derivative,
		const value_type &	param,
		size_type	order
	)		const

protectedvirtual

Virtual implementation of derivative

Parameters

param	parameter within paramRange
order	order of derivation.

Return values

derivative

Reimplemented from hpp::core::Path.

◆ impl_paramDerivative()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::impl_paramDerivative	(	vectorOut_t	res,
		const value_type &	t
	)		const

protected

◆ impl_paramIntegrate()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::impl_paramIntegrate ( vectorIn_t dParam )

protected

◆ impl_velocityBound()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::impl_velocityBound	(	vectorOut_t	bound,
		const value_type &	param0,
		const value_type &	param1
	)		const

protectedvirtual

Virtual implementation of velocityBound

Parameters

param0,param1 interval of parameter

Return values

bound

Reimplemented from hpp::core::Path.

◆ init()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::init ( const Ptr_t & self )

inlineprotected

◆ initial()

template<int _PolynomeBasis, int _Order>

virtual Configuration_t hpp::core::path::Spline< _PolynomeBasis, _Order >::initial ( ) const

inlinevirtual

Get the initial configuration.

Implements hpp::core::Path.

Reimplemented in hpp::core::path::Hermite.

◆ maxVelocity()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::maxVelocity ( vectorOut_t res ) const

Returns an upper bound of the velocity on the complete interval.

See also: Path::velocityBound

◆ parameterDerivativeCoefficients()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::parameterDerivativeCoefficients	(	vectorOut_t	res,
		const value_type &	t
	)		const

inline

The partial derivative with respects to the parameters is of the form

\begin{eqnarray*} \frac{\partial S}{\partial p_{k}} (q, p, t) &=& B_k(t) \times I \\ \frac{\partial S}{\partial q_{base}} (q, p, t) &=& I \end{eqnarray*}

This method returns the coefficients \( (B_k(t))_{k} \)

◆ parameterIntegrate()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::parameterIntegrate ( vectorIn_t dParam )

inline

Adds dParam to the parameters.

◆ parameters() [1/2]

template<int _PolynomeBasis, int _Order>

const ParameterMatrix_t& hpp::core::path::Spline< _PolynomeBasis, _Order >::parameters ( ) const

inline

Each row corresponds to a velocity of the robot.

◆ parameters() [2/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::parameters ( const ParameterMatrix_t & m )

inline

Returns the \( (P_i^T) \). Each row contains one parameter.

◆ parameterSize()

template<int _PolynomeBasis, int _Order>

size_type hpp::core::path::Spline< _PolynomeBasis, _Order >::parameterSize ( ) const

inline

◆ print()

template<int _PolynomeBasis, int _Order>

std::ostream& hpp::core::path::Spline< _PolynomeBasis, _Order >::print ( std::ostream & os ) const

protectedvirtual

Print interval of definition (and of parameters if relevant) in a stream

Reimplemented from hpp::core::Path.

◆ rowParameters() [1/2]

template<int _PolynomeBasis, int _Order>

ConstParameterVector_t hpp::core::path::Spline< _PolynomeBasis, _Order >::rowParameters ( ) const

inline

Concatenate the parameters as one vector (P_0^T, ..., P_n^T).

◆ rowParameters() [2/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::rowParameters ( vectorIn_t p )

inline

Set the parameters.

◆ squaredNormBasisFunctionIntegral() [1/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::squaredNormBasisFunctionIntegral	(	const size_type	order,
		BasisFunctionIntegralMatrix_t &	res
	)		const

Returns a matrix \( (m_{i,j}) \) as

\[ m_{i,j} = T^{1-2k} \int_0^1 b_i^{(k)}(u) b_j^{(k)}(u) du \]

◆ squaredNormBasisFunctionIntegral() [2/2]

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::squaredNormBasisFunctionIntegral	(	const size_type	order,
		matrixOut_t	res
	)		const

inline

◆ squaredNormIntegral()

template<int _PolynomeBasis, int _Order>

value_type hpp::core::path::Spline< _PolynomeBasis, _Order >::squaredNormIntegral ( const size_type order ) const

Returns \( \int S^{(k)}(t)^T \times S^{(k)}(t) dt \)

where k is the argument

◆ squaredNormIntegralDerivative()

template<int _PolynomeBasis, int _Order>

void hpp::core::path::Spline< _PolynomeBasis, _Order >::squaredNormIntegralDerivative	(	const size_type	order,
		vectorOut_t	res
	)		const

Returns the derivative of squaredNormIntegral wrt the parameters.

\[ res(j) \gets 2 \sum_i P_i^T \times m_{i,j} \]

◆ timeFreeBasisFunctionDerivative() [1/2]

template<int _PolynomeBasis, int _Order>

static void hpp::core::path::Spline< _PolynomeBasis, _Order >::timeFreeBasisFunctionDerivative	(	const size_type	order,
		const value_type &	u,
		BasisFunctionVector_t &	res
	)

static

Returns a vector \( (v_i) \) as

\[ v_i = b_i^{(k)}(u) \]

◆ timeFreeBasisFunctionDerivative() [2/2]

template<int _PolynomeBasis, int _Order>

static void hpp::core::path::Spline< _PolynomeBasis, _Order >::timeFreeBasisFunctionDerivative	(	const size_type	order,
		const value_type &	u,
		vectorOut_t	res
	)

inlinestatic

◆ value()

template<int _PolynomeBasis, int _Order>

static void hpp::core::path::Spline< _PolynomeBasis, _Order >::value	(	pinocchio::LiegroupElementConstRef	base,
		Eigen::Ref< const ParameterMatrix_t >	params,
		const value_type &	u,
		ConfigurationOut_t	config,
		vectorOut_t	velocity
	)

static

Evaluate a spline.

Parameters

base	the base configuration.
params	concatenation of row vectors representing the velocity interpolation points.
u	the ratio, between 0 and 1.

Return values

config	the output configuration
velocity	the interpolated velocity

Member Data Documentation

◆ base_

template<int _PolynomeBasis, int _Order>

LiegroupElement hpp::core::path::Spline< _PolynomeBasis, _Order >::base_

protected

Base of the spline path. The spline is a curve in the tangent space of the robot at this configuration.

◆ parameters_

template<int _PolynomeBasis, int _Order>

ParameterMatrix_t hpp::core::path::Spline< _PolynomeBasis, _Order >::parameters_

protected

Parameters of the spline are stored in a matrix number of rows = degree of polynomial + 1 number of columns = robot number of degrees of freedom.

◆ parameterSize_

template<int _PolynomeBasis, int _Order>

size_type hpp::core::path::Spline< _PolynomeBasis, _Order >::parameterSize_

protected

Robot number of degrees of freedom.

◆ robot_

template<int _PolynomeBasis, int _Order>

DevicePtr_t hpp::core::path::Spline< _PolynomeBasis, _Order >::robot_

protected

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

include/hpp/core/fwd.hh
include/hpp/core/path/spline.hh

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<int _PolynomeBasis, int _Order> class hpp::core::path::Spline< _PolynomeBasis, _Order >

Member Typedef Documentation

◆ BasisFunction_t

◆ BasisFunctionIntegralMatrix_t

◆ BasisFunctionVector_t

◆ ConstParameterVector_t

◆ ParameterMatrix_t

◆ ParameterVector_t

◆ PowersOfT_t

◆ Ptr_t

◆ sbf_traits

◆ WkPtr_t

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ~Spline()

◆ Spline() [1/3]

◆ Spline() [2/3]

◆ Spline() [3/3]

Member Function Documentation

◆ base() [1/2]

◆ base() [2/2]

◆ basisFunctionDerivative() [1/2]

◆ basisFunctionDerivative() [2/2]

◆ copy() [1/2]

◆ copy() [2/2]

◆ create()

◆ end()

◆ impl_compute()

◆ impl_derivative()

◆ impl_paramDerivative()

◆ impl_paramIntegrate()

◆ impl_velocityBound()

◆ init()

◆ initial()

◆ maxVelocity()

◆ parameterDerivativeCoefficients()

◆ parameterIntegrate()

◆ parameters() [1/2]

◆ parameters() [2/2]

◆ parameterSize()

◆ print()

◆ rowParameters() [1/2]

◆ rowParameters() [2/2]

◆ squaredNormBasisFunctionIntegral() [1/2]

◆ squaredNormBasisFunctionIntegral() [2/2]

◆ squaredNormIntegral()

◆ squaredNormIntegralDerivative()

◆ timeFreeBasisFunctionDerivative() [1/2]

◆ timeFreeBasisFunctionDerivative() [2/2]

◆ value()

Member Data Documentation

◆ base_

◆ parameters_

◆ parameterSize_

◆ robot_

template<int _PolynomeBasis, int _Order>
class hpp::core::path::Spline< _PolynomeBasis, _Order >