Cubic B-Spline trajectory. More...

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

Inheritance diagram for roboptim::trajectory::CubicBSpline:

Public Types
typedef std::vector < Polynomial3, Eigen::aligned_allocator < Polynomial3 > >	polynomials3vector_t
typedef std::vector < polynomials3vector_t >	polynomials3vectors_t
typedef std::vector< value_type >	knots_t
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.
	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.
	CubicBSpline (const CubicBSpline &spline)
	Copy constructor.
virtual	~CubicBSpline ()
virtual void	setParameters (const vector_t &)
	Modify spline parameters.
virtual jacobian_t	variationConfigWrtParam (double t) const
	Get the variation of a configuration with respect to parameter vector.
virtual jacobian_t	variationDerivWrtParam (double t, size_type order) const
	Get the variation of a derivative with respect to parameter vector.
virtual value_type	singularPointAtRank (size_type rank) const
	Get singular point at given rank.
virtual vector_t	derivBeforeSingularPoint (size_type rank, size_type order) const
	Get left limit value of derivative at given singular point.
virtual vector_t	derivAfterSingularPoint (size_type rank, size_type order) const
	Get right limit value of derivative at given singular point.
virtual Trajectory < derivabilityOrder > *	resize (interval_t timeRange) const
	Clone and resize a trajectory.
virtual std::ostream &	print (std::ostream &o) const
	Display the function on the specified output stream.
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.
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.
value_type	Dt () const ROBOPTIM_TRAJECTORY_DEPRECATED
	Regular spacing between B-spline knots.
void	translateBasisPolynomials (double t1)
	Translate the basis polynomials to a given time t1.
void	toPolynomials (polynomials3vector_t &res) const
	Return the polynomial expression of the cubic B-spline on each time interval.
const polynomials3vectors_t &	basisPolynomials () const
	Constant getter for the basis polynomials of the cubic B-spline.
size_type	interval (value_type t) const
	Find the index of the interval in which t is.
size_type	getNumberControlPoints () const
	Get the number of control points of the spline.
const knots_t &	knotVector () const
	Return the knot vector of the spline.
CubicBSpline	operator+ (const CubicBSpline &s) const
	Add two cubic B-splines, supposing they have the same dimensions.
void	operator+= (const CubicBSpline &s)
	Add a second B-spline to this B-spline.
Protected Member Functions
void	impl_compute (result_ref, double) const
void	impl_derivative (derivative_ref g, double 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.
vector_t	basisFunctions (value_type t, size_type order) const ROBOPTIM_TRAJECTORY_DEPRECATED
	Compute the basis functions for a given instant t.

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<value_type> roboptim::trajectory::CubicBSpline::knots_t

typedef std::vector< Polynomial3, Eigen::aligned_allocator<Polynomial3> > roboptim::trajectory::CubicBSpline::polynomials3vector_t

typedef std::vector<polynomials3vector_t> roboptim::trajectory::CubicBSpline::polynomials3vectors_t

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: $
dimension	spline dimension:
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:
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< DerivabilityOrder >::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 polynomials3vectors_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	derivative,
		double	t
	)		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,
		double	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 `[protected, virtual]`

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(), impl_derivative(), and variationDerivWrtParam().

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

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 [inline, virtual]

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_t & 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 ( polynomials3vector_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 ( double 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).

CubicBSpline::jacobian_t roboptim::trajectory::CubicBSpline::variationConfigWrtParam ( double t ) const [virtual]

Get the variation of a configuration with respect to parameter vector.

Parameters:

t	value in the definition interval.

Returns:: Jacobian:
$\frac{\partial\Gamma_{\textbf{p}}(t)}{\partial\textbf{p}}$

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

Examples:: spline-optimization.cc.

References variationDerivWrtParam().

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().

CubicBSpline::jacobian_t roboptim::trajectory::CubicBSpline::variationDerivWrtParam	(	double	t,
		size_type	order
	)		const `[virtual]`

Get the variation of a derivative with respect to parameter vector.

Parameters:

t	value in the definition interval.
order	order of the derivative.

Returns:: jacobian
$\frac{\partial}{\partial\textbf{p}} \left(\frac{d^r\Gamma_{\textbf{p}}}{dt^r}(t)\right)$

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

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

Referenced by variationConfigWrtParam(), and 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().

Public Types

Public Member Functions

Protected Member Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation