Cubic B-Spline trajectory. More...

#include <roboptim/trajectory/cubic-b-spline.hh>

Inheritance diagram for roboptim::trajectory::CubicBSpline:

Public Types
typedef Polynomial3	polynomial_t
	Polynomial type. More...

typedef std::vector < polynomial_t, Eigen::aligned_allocator < polynomial_t > >	basisPolynomials_t
	Basis polynomials type. More...

typedef std::vector < basisPolynomials_t >	basisPolynomialsVector_t
	Basis polynomials vector type. More...

typedef basisPolynomials_t polynomials3vector_t	ROBOPTIM_TRAJECTORY_DEPRECATED
	Legacy typedef. More...

typedef basisPolynomialsVector_t polynomials3vectors_t	ROBOPTIM_TRAJECTORY_DEPRECATED
	Legacy typedef. More...

typedef vector_t	knots_t
	Knot vector type. More...

Public Types inherited from roboptim::trajectory::Trajectory< 3 >
typedef parent_t::interval_t	interval_t
	Import interval type. More...

Public Member Functions
	CubicBSpline (interval_t timeRange, size_type dimension, const vector_t &parameters, const std::string name="cubic B-Spline", bool clamped=false)
	Instantiate a uniform cubic B-Spline from its definition. More...

	CubicBSpline (size_type dimension, const knots_t &knots, const vector_t &parameters, const std::string name="cubic B-Spline")
	Instantiate a cubic B-Spline from its definition. More...

	CubicBSpline (const CubicBSpline &spline)
	Copy constructor. More...

virtual	~CubicBSpline ()

virtual void	setParameters (const_vector_ref)
	Modify spline parameters. More...

virtual jacobian_t	variationConfigWrtParam (value_type t) const

virtual jacobian_t	variationDerivWrtParam (value_type t, size_type order) const

virtual value_type	singularPointAtRank (size_type rank) const
	Get singular point at given rank. More...

virtual vector_t	derivBeforeSingularPoint (size_type rank, size_type order) const
	Get left limit value of derivative at given singular point. More...

virtual vector_t	derivAfterSingularPoint (size_type rank, size_type order) const
	Get right limit value of derivative at given singular point. More...

virtual Trajectory < derivabilityOrder > *	resize (interval_t timeRange) const
	Clone and resize a trajectory. More...

virtual std::ostream &	print (std::ostream &o) const
	Display the function on the specified output stream. More...

jacobian_t	variationConfigWrtParam (StableTimePoint tp) const

jacobian_t	variationDerivWrtParam (StableTimePoint tp, size_type order) const

template<typename P >
void	freezeCurveStart (P &problem, size_type offset=0) const
	Add a constraint to a problem in order to freeze the B-spline at its start. More...

template<typename P >
void	freezeCurveEnd (P &problem, size_type offset=0) const
	Add a constraint to a problem in order to freeze the B-spline at its end. More...

value_type	Dt () const ROBOPTIM_TRAJECTORY_DEPRECATED
	Regular spacing between B-spline knots. More...

void	translateBasisPolynomials (value_type t1)
	Translate the basis polynomials to a given time t1. More...

void	toPolynomials (basisPolynomials_t &res) const
	Return the polynomial expression of the cubic B-spline on each time interval. More...

const basisPolynomialsVector_t &	basisPolynomials () const
	Constant getter for the basis polynomials of the cubic B-spline. More...

size_type	interval (value_type t) const
	Find the index of the interval in which t is. More...

size_type	getNumberControlPoints () const
	Get the number of control points of the spline. More...

const knots_t &	knotVector () const
	Return the knot vector of the spline. More...

CubicBSpline	operator+ (const CubicBSpline &s) const
	Add two cubic B-splines, supposing they have the same dimensions. More...

void	operator+= (const CubicBSpline &s)
	Add a second B-spline to this B-spline. More...

int	order () const
	Retrieve the order of the spline. More...

Public Member Functions inherited from roboptim::trajectory::Trajectory< 3 >
	ROBOPTIM_NTIMES_DERIVABLE_FUNCTION_FWD_TYPEDEFS_ (NTimesDerivableFunction< DerivabilityOrder >)
	Parent type and imports. More...

virtual	~Trajectory ()

result_t	operator() (StableTimePoint argument) const

void	operator() (result_ref result, StableTimePoint argument) const

derivative_t	derivative (StableTimePoint argument, size_type order=1) const

void	derivative (derivative_ref derivative, StableTimePoint argument, size_type order=1) const

bool	isValidTime (value_type t) const

virtual void	normalizeAngles (size_type index)
	Normalize angles in parameters array. More...

virtual Trajectory < DerivabilityOrder > *	clone () const =0

const vector_t &	parameters () const

interval_t	timeRange () const

value_type	length () const

virtual vector_t	state (double t, size_type order) const
	Get state along trajectory. More...

virtual vector_t	state (StableTimePoint t, size_type order) const

virtual jacobian_t	variationConfigWrtParam (double t) const =0
	Get the variation of a configuration with respect to parameter vector. More...

virtual jacobian_t	variationDerivWrtParam (double t, size_type order) const =0
	Get the variation of a derivative with respect to parameter vector. More...

jacobian_t	variationStateWrtParam (double t, size_type order) const
	Get the variation of the state with respect to parameter vector. More...

jacobian_t	variationStateWrtParam (StableTimePoint stp, size_type order) const

size_type	singularPoints () const
	Get number of singular points. More...

void	tolerance (const double &tolerance)

double	tolerance () const
	Get tolerance for inclusion of parameter in interval of definition. More...

Protected Member Functions
void	impl_compute (result_ref, value_type) const

void	impl_derivative (derivative_ref g, value_type x, size_type order) const

void	impl_derivative (derivative_ref g, StableTimePoint, size_type order) const

void	computeBasisPolynomials ()
	Compute the basis polynomials for the cubic B-spline. More...

vector_t	basisFunctions (value_type t, size_type order) const ROBOPTIM_TRAJECTORY_DEPRECATED
	Compute the basis functions for a given instant t. More...

Protected Member Functions inherited from roboptim::trajectory::Trajectory< 3 >
virtual void	normalizeAngles (size_type index, size_type offset)
	Internal version of normalizeAngles allowing an optional offset. More...

void	impl_compute (result_ref, StableTimePoint) const

	Trajectory (interval_t, size_type, const vector_t &, std::string name=std::string())

Additional Inherited Members
Protected Attributes inherited from roboptim::trajectory::Trajectory< 3 >
interval_t	timeRange_

vector_t	parameters_

size_type	singularPoints_

Detailed Description

Cubic B-Spline trajectory.

Implement a B-Spline as a trajectory as described in doc/cubic-b-spline.tex

Examples:: spline-optimization.cc, and spline-time-optimization.cc.

Member Typedef Documentation

typedef std::vector< polynomial_t, Eigen::aligned_allocator<polynomial_t> > roboptim::trajectory::CubicBSpline::basisPolynomials_t

Basis polynomials type.

typedef std::vector<basisPolynomials_t> roboptim::trajectory::CubicBSpline::basisPolynomialsVector_t

Basis polynomials vector type.

typedef vector_t roboptim::trajectory::CubicBSpline::knots_t

Knot vector type.

typedef Polynomial3 roboptim::trajectory::CubicBSpline::polynomial_t

Polynomial type.

typedef basisPolynomials_t polynomials3vector_t roboptim::trajectory::CubicBSpline::ROBOPTIM_TRAJECTORY_DEPRECATED

Legacy typedef.

typedef basisPolynomialsVector_t polynomials3vectors_t roboptim::trajectory::CubicBSpline::ROBOPTIM_TRAJECTORY_DEPRECATED

Legacy typedef.

Constructor & Destructor Documentation

roboptim::trajectory::CubicBSpline::CubicBSpline	(	interval_t	timeRange,
		size_type	dimension,
		const vector_t &	parameters,
		const std::string	name = `"cubic B-Spline"`,
		bool	clamped = `false`
	)

Instantiate a uniform cubic B-Spline from its definition.

Parameters

timeRange	spline time range: $ $[t_3,t_n]$
dimension	spline dimension: $n$
parameters	vector of parameters defining control points
name	function title
clamped	whether the spline should be clamped

The number of control points is inferred from the dimension of the parameter vector.

References computeBasisPolynomials(), roboptim::trajectory::Trajectory< 3 >::parameters_, and setParameters().

Referenced by resize().

roboptim::trajectory::CubicBSpline::CubicBSpline	(	size_type	dimension,
		const knots_t &	knots,
		const vector_t &	parameters,
		const std::string	name = `"cubic B-Spline"`
	)

Instantiate a cubic B-Spline from its definition.

Parameters

dimension	spline dimension: $n$
knots	vector of knots,
parameters	vector of parameters defining control points
name	function title

The number of control points is inferred from the dimension of the parameter vector.

References computeBasisPolynomials(), roboptim::trajectory::Trajectory< 3 >::parameters_, and setParameters().

roboptim::trajectory::CubicBSpline::CubicBSpline ( const CubicBSpline & spline )

Copy constructor.

Parameters

spline spline that will be copied

References roboptim::trajectory::Trajectory< dorder >::parameters(), roboptim::trajectory::Trajectory< 3 >::parameters_, and setParameters().

roboptim::trajectory::CubicBSpline::~CubicBSpline ( )

virtual

Member Function Documentation

CubicBSpline::vector_t roboptim::trajectory::CubicBSpline::basisFunctions	(	value_type	t,
		size_type	order
	)		const

protected

Compute the basis functions for a given instant t.

Parameters

t	instant considered.
order	order of the basis functions.

Returns: basis functions evaluated at t.

References Dt(), roboptim::trajectory::detail::fixTime(), interval(), roboptim::trajectory::Trajectory< 3 >::length(), roboptim::trajectory::Trajectory< 3 >::timeRange(), and roboptim::trajectory::Trajectory< 3 >::tolerance().

const basisPolynomialsVector_t& roboptim::trajectory::CubicBSpline::basisPolynomials ( ) const

inline

Constant getter for the basis polynomials of the cubic B-spline.

Returns: constant reference to the basis polynomials.

Note: computeBasisPolynomials() needs to be called beforehand (which is done in the CubicBSpline constructor).

void roboptim::trajectory::CubicBSpline::computeBasisPolynomials ( )

protected

Compute the basis polynomials for the cubic B-spline.

Referenced by CubicBSpline().

CubicBSpline::vector_t roboptim::trajectory::CubicBSpline::derivAfterSingularPoint	(	size_type	rank,
		size_type	order
	)		const

virtual

Get right limit value of derivative at given singular point.

Parameters

rank	rank of the singular points.
order	order of derivation.

Return values

derivative Limit of the derivative at singular point for decreasing parameter values.

Implements roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::Trajectory< 3 >::derivative(), and singularPointAtRank().

CubicBSpline::vector_t roboptim::trajectory::CubicBSpline::derivBeforeSingularPoint	(	size_type	rank,
		size_type	order
	)		const

virtual

Get left limit value of derivative at given singular point.

Parameters

rank	rank of the singular points.
order	order of derivation.

Returns: Limit of the derivative at singular point for increasing parameter values.

Implements roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::Trajectory< 3 >::derivative(), and singularPointAtRank().

CubicBSpline::value_type roboptim::trajectory::CubicBSpline::Dt ( ) const

Regular spacing between B-spline knots.

This is only valid for uniform B-splines.

Returns: regular spacing between B-spline knots.

References roboptim::trajectory::Trajectory< 3 >::length().

Referenced by basisFunctions().

template<typename P >

void roboptim::trajectory::CubicBSpline::freezeCurveEnd	(	P &	problem,
		size_type	offset = `0`
	)		const

Add a constraint to a problem in order to freeze the B-spline at its end.

Parameters

problem	problem to which the constraint will be added.
offset	offset of the B-spline parameters in the problem's parameter list.

Examples:: spline-optimization.cc.

References interval(), and roboptim::trajectory::Trajectory< 3 >::parameters().

template<typename P >

void roboptim::trajectory::CubicBSpline::freezeCurveStart	(	P &	problem,
		size_type	offset = `0`
	)		const

Add a constraint to a problem in order to freeze the B-spline at its start.

Parameters

problem	problem to which the constraint will be added.
offset	offset of the B-spline parameters in the problem's parameter list.

Examples:: spline-optimization.cc.

References interval(), and roboptim::trajectory::Trajectory< 3 >::parameters().

size_type roboptim::trajectory::CubicBSpline::getNumberControlPoints ( ) const

inline

Get the number of control points of the spline.

Returns: Number of control points of the spline.

Referenced by roboptim::trajectory::visualization::matplotlib::plot_spline().

void roboptim::trajectory::CubicBSpline::impl_compute	(	result_ref	,
		value_type
	)		const

protected

References roboptim::trajectory::Trajectory< 3 >::derivative(), roboptim::trajectory::detail::fixTime(), and roboptim::trajectory::Trajectory< 3 >::timeRange().

void roboptim::trajectory::CubicBSpline::impl_derivative	(	derivative_ref	g,
		value_type	x,
		size_type	order
	)		const

protected

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::trajectory::Polynomial< N >::derivative(), roboptim::trajectory::detail::fixTime(), interval(), and roboptim::trajectory::Trajectory< 3 >::parameters().

Referenced by impl_derivative().

void roboptim::trajectory::CubicBSpline::impl_derivative	(	derivative_ref	g,
		StableTimePoint	stp,
		size_type	order
	)		const

protectedvirtual

Implements roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::StableTimePoint::getTime(), and impl_derivative().

CubicBSpline::size_type roboptim::trajectory::CubicBSpline::interval ( value_type t ) const

Find the index of the interval in which t is.

Parameters

t	instant considered.

Returns: index of the interval in which t is.

References roboptim::trajectory::detail::fixTime(), and roboptim::trajectory::Trajectory< 3 >::timeRange().

Referenced by basisFunctions(), freezeCurveEnd(), freezeCurveStart(), and impl_derivative().

const knots_t& roboptim::trajectory::CubicBSpline::knotVector ( ) const

inline

Return the knot vector of the spline.

Returns: knot vector of the spline (const).

Referenced by roboptim::trajectory::visualization::matplotlib::plot_spline().

CubicBSpline roboptim::trajectory::CubicBSpline::operator+ ( const CubicBSpline & s ) const

Add two cubic B-splines, supposing they have the same dimensions.

Parameters

s	other B-spline with the same dimensions.

Returns: S2 = S0 + S1

Exceptions

std::runtime_error if splines do not have the same dimensions.

References roboptim::trajectory::Trajectory< 3 >::parameters(), roboptim::trajectory::Trajectory< dorder >::parameters(), roboptim::trajectory::Trajectory< 3 >::timeRange(), and roboptim::trajectory::Trajectory< dorder >::timeRange().

void roboptim::trajectory::CubicBSpline::operator+= ( const CubicBSpline & s )

Add a second B-spline to this B-spline.

Parameters

s	other B-spline with the same dimensions.

Exceptions

std::runtime_error if splines do not have the same dimensions.

References roboptim::trajectory::Trajectory< 3 >::parameters(), roboptim::trajectory::Trajectory< dorder >::parameters(), setParameters(), roboptim::trajectory::Trajectory< 3 >::timeRange(), and roboptim::trajectory::Trajectory< dorder >::timeRange().

int roboptim::trajectory::CubicBSpline::order ( ) const

Retrieve the order of the spline.

std::ostream & roboptim::trajectory::CubicBSpline::print ( std::ostream & o ) const

virtual

Display the function on the specified output stream.

Parameters

o	output stream used for display

Returns: output stream

Reimplemented from roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::Trajectory< 3 >::length(), and roboptim::trajectory::Trajectory< 3 >::parameters().

virtual Trajectory<derivabilityOrder>* roboptim::trajectory::CubicBSpline::resize ( interval_t timeRange ) const

inlinevirtual

Clone and resize a trajectory.

Implements roboptim::trajectory::Trajectory< 3 >.

References CubicBSpline(), and roboptim::trajectory::Trajectory< 3 >::parameters().

void roboptim::trajectory::CubicBSpline::setParameters ( const_vector_ref p )

virtual

Modify spline parameters.

Reimplemented from roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::Trajectory< 3 >::parameters_.

Referenced by CubicBSpline(), roboptim::trajectory::SplineLength::impl_compute(), roboptim::trajectory::SplineLength::impl_gradient(), and operator+=().

CubicBSpline::value_type roboptim::trajectory::CubicBSpline::singularPointAtRank ( size_type rank ) const

virtual

Get singular point at given rank.

Implements roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::Trajectory< 3 >::length().

Referenced by derivAfterSingularPoint(), and derivBeforeSingularPoint().

void roboptim::trajectory::CubicBSpline::toPolynomials ( basisPolynomials_t & res ) const

Return the polynomial expression of the cubic B-spline on each time interval.

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::trajectory::Trajectory< 3 >::parameters().

Referenced by roboptim::trajectory::visualization::matplotlib::plot_spline().

void roboptim::trajectory::CubicBSpline::translateBasisPolynomials ( value_type t1 )

Translate the basis polynomials to a given time t1.

Parameters

t1	new center time, i.e. P = sum(a_i*(t-t1)^i, i={0,3})

This method can be useful when one needs to have all the polynomials expressed in the same basis (e.g. t1 = 0).

virtual jacobian_t roboptim::trajectory::CubicBSpline::variationConfigWrtParam ( value_type t ) const

virtual

Examples:: spline-optimization.cc.

Referenced by variationConfigWrtParam().

CubicBSpline::jacobian_t roboptim::trajectory::CubicBSpline::variationConfigWrtParam ( StableTimePoint tp ) const

virtual

Implements roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::StableTimePoint::getTime(), and variationConfigWrtParam().

virtual jacobian_t roboptim::trajectory::CubicBSpline::variationDerivWrtParam	(	value_type	t,
		size_type	order
	)		const

virtual

Referenced by variationDerivWrtParam().

CubicBSpline::jacobian_t roboptim::trajectory::CubicBSpline::variationDerivWrtParam	(	StableTimePoint	tp,
		size_type	order
	)		const

virtual

Implements roboptim::trajectory::Trajectory< 3 >.

References roboptim::trajectory::StableTimePoint::getTime(), and variationDerivWrtParam().

timeRange	spline time range: $ \([t_3,t_n]\)
dimension	spline dimension: \(n\)
parameters	vector of parameters defining control points
name	function title
clamped	whether the spline should be clamped

Public Types

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation