Cubic B-Spline trajectory. More...

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

Inheritance diagram for roboptim::CubicBSpline:

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

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

virtual	~CubicBSpline () throw ()

virtual void	setParameters (const vector_t &) throw ()
	Modify spline parameters. More...

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

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

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 throw ()
	Clone and resize a trajectory. More...

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

jacobian_t	variationConfigWrtParam (StableTimePoint tp) const throw ()

jacobian_t	variationDerivWrtParam (StableTimePoint tp, size_type order) const throw ()

Public Member Functions inherited from roboptim::Trajectory< 3 >
virtual	~Trajectory () throw ()

result_t	operator() (StableTimePoint argument) const throw ()

void	operator() (result_t &result, StableTimePoint argument) const throw ()

gradient_t	derivative (StableTimePoint argument, size_type order=1) const throw ()

void	derivative (gradient_t &derivative, StableTimePoint argument, size_type order=1) const throw ()

bool	isValidTime (value_type t) const throw ()

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

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

const vector_t &	parameters () const throw ()

interval_t	timeRange () const throw ()

value_type	length () const throw ()

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

virtual vector_t	state (StableTimePoint t, size_type order) const throw ()

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

jacobian_t	variationStateWrtParam (StableTimePoint stp, size_type order) const throw ()

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

Protected Member Functions
void	impl_compute (result_t &, double) const throw ()

void	impl_derivative (gradient_t &g, double x, size_type order) const throw ()

void	impl_derivative (gradient_t &g, StableTimePoint, size_type order) const throw ()

value_type	Dt () const

size_type	interval (value_type t) const

vector_t	basisFunctions (value_type t, size_type order) const

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

void	impl_compute (result_t &, StableTimePoint) const throw ()

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

Additional Inherited Members
Public Types inherited from roboptim::Trajectory< 3 >
typedef NTimesDerivableFunction < DerivabilityOrder >	parent_t
	Parent type. More...

typedef parent_t::value_type	value_type
	Import value type. More...

typedef parent_t::size_type	size_type
	Import size type. More...

typedef parent_t::vector_t	vector_t
	Import vector type. More...

typedef parent_t::result_t	result_t
	Import result type. More...

typedef parent_t::gradient_t	gradient_t
	Import gradient type. More...

typedef parent_t::jacobian_t	jacobian_t
	Import jacobian type. More...

typedef parent_t::interval_t	interval_t
	Import interval type. More...

Protected Attributes inherited from roboptim::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 below: given

a number $m\geq 4$ of control points,
regularly spaced time points: $t_0 < t_1 < \cdots < t_{m}$ , $\forall i\in\{0,...,m-1\}$ , $t_{i+1}-t_i = \Delta t$
control points $P_0,\cdots, P_{m-1}$ in $\textbf{R}^n$ , the cubic B-spline of control points $P_0,\cdots, P_{m-1}$ is defined over $[t_3,t_{m}]$ by
$B(t) = \sum_{i=0}^{m-1} P_i b_{i,3}(t)$
where basis functions $b_{i,3}$ are defined by:
$\begin{eqnarray*} b_{i,3}(t)=& \frac{(t-t_i)^3}{6\Delta t^3} & \mbox{ if } t_{i} \leq t < t_{i+1} \\ & \frac{(t-t_i)^2(t_{i+2}-t)+(t-t_i)(t_{i+3}-t)(t-t_{i+1})+(t_{i+4}-t)(t-t_{i+1})^2}{6\Delta t^3}& \mbox{ if } t_{i+1} \leq t < t_{i+2} \\ & \frac{(t-t_i)(t_{i+3}-t)^2+(t_{i+4}-t)(t-t_{i+1})(t_{i+3}-t)+(t_{i+4}-t)^2(t-t_{i+2})}{6\Delta t^3}& \mbox{ if } t_{i+2} \leq t < t_{i+3} \\ & \frac{(t_{i+4}-t)^3}{6\Delta t^3}& \mbox{ if } t_{i+3} \leq t < t_{i+4} \end{eqnarray*}$

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

Constructor & Destructor Documentation

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

Instantiate a cubic B-Spline from its definition.

Parameters

timeRange	spline time range: $
dimension	spline dimension:
parameters	vector of parameters defining control points
name	function title

Number of control points is inferred from dimension of dimenion of parameter vector.

Referenced by resize().

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

Copy constructor.

Parameters

spline spline that will be copied

roboptim::CubicBSpline::~CubicBSpline	(	)
throw	(
	)

virtual

Member Function Documentation

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

protected

References Dt(), interval(), and roboptim::Trajectory< 3 >::timeRange().

CubicBSpline::vector_t roboptim::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< 3 >.

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

CubicBSpline::vector_t roboptim::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< 3 >.

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

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

protected

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

Referenced by basisFunctions(), and interval().

void roboptim::CubicBSpline::impl_compute	(	result_t &	derivative,
		double	t
	)		const
throw	(
	)

protected

void roboptim::CubicBSpline::impl_derivative	(	gradient_t &	g,
		double	x,
		size_type	order
	)		const
throw	(
	)

protected

void roboptim::CubicBSpline::impl_derivative	(	gradient_t &	g,
		StableTimePoint	stp,
		size_type	order
	)		const
throw	(
	)

protectedvirtual

Implements roboptim::Trajectory< 3 >.

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

protected

References Dt(), and roboptim::Trajectory< 3 >::timeRange().

Referenced by basisFunctions().

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

virtual

Display the function on the specified output stream.

Parameters

o	output stream used for display

Returns: output stream

Reimplemented from roboptim::Trajectory< 3 >.

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

inlinevirtual

Clone and resize a trajectory.

Implements roboptim::Trajectory< 3 >.

References CubicBSpline().

void roboptim::CubicBSpline::setParameters	(	const vector_t &	p)
throw	(
	)

virtual

Modify spline parameters.

Reimplemented from roboptim::Trajectory< 3 >.

Referenced by roboptim::SplineLength::impl_compute(), and roboptim::SplineLength::impl_gradient().

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

virtual

Get singular point at given rank.

Implements roboptim::Trajectory< 3 >.

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

Referenced by derivAfterSingularPoint(), and derivBeforeSingularPoint().

CubicBSpline::jacobian_t roboptim::CubicBSpline::variationConfigWrtParam	(	double	t)	const
throw	(
	)

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< 3 >.

Examples:: spline-optimization.cc.

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

virtual

Implements roboptim::Trajectory< 3 >.

CubicBSpline::jacobian_t roboptim::CubicBSpline::variationDerivWrtParam	(	double	t,
		size_type	order
	)		const
throw	(
	)

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< 3 >.

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

virtual

Implements roboptim::Trajectory< 3 >.

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation