Represents a Cubic-Hermite-Polynomial. More...

#include <polynomial.h>

Inheritance diagram for towr::CubicHermitePolynomial:

Public Member Functions
	CubicHermitePolynomial (int dim)

VectorXd	GetDerivativeOfPosWrtDuration (double t) const
	How the total duration affect the value ("pos") of the polynomial. More...

double	GetDerivativeWrtEndNode (Dx dfdt, Dx node_deriv, double t) const
	The derivative of the polynomial when changing the end node. More...

double	GetDerivativeWrtStartNode (Dx dfdt, Dx node_deriv, double t) const
	The derivative of the polynomial when changing the start node. More...

const double	GetDuration () const

void	SetDuration (double duration)
	sets the total duration of the polynomial. More...

void	SetNodes (const Node &n0, const Node &n1)
	Fully defines the polynomial by the node values using current duration. More...

void	UpdateCoeff ()
	updates the coefficients using current nodes and durations. More...

virtual	~CubicHermitePolynomial ()=default

Public Member Functions inherited from towr::Polynomial
double	GetDerivativeWrtCoeff (double t, Dx poly_deriv, Coefficients coeff) const
	The derivative of the polynomial with respect to the coefficients. More...

State	GetPoint (double t) const

	Polynomial (int poly_order, int poly_dim)
	Constructs a polynomial with zero coefficient values. More...

virtual	~Polynomial ()=default

Private Member Functions
double	GetDerivativeOfAccWrtEndNode (Dx node_deriv, double t_local) const

double	GetDerivativeOfAccWrtStartNode (Dx node_deriv, double t_local) const

double	GetDerivativeOfPosWrtEndNode (Dx node_deriv, double t_local) const

double	GetDerivativeOfPosWrtStartNode (Dx node_deriv, double t_local) const

double	GetDerivativeOfVelWrtEndNode (Dx node_deriv, double t_local) const

double	GetDerivativeOfVelWrtStartNode (Dx node_deriv, double t_local) const

Private Attributes
Node	n0_

Node	n1_
	the start and final node comprising the polynomial. More...

double	T_
	the total duration of the polynomial. More...

Additional Inherited Members
Public Types inherited from towr::Polynomial
enum	Coefficients { A =0, B, C, D, E, F, G, H, I, J }

using	CoeffIDVec = std::vector< Coefficients >

using	VectorXd = Eigen::VectorXd

Protected Attributes inherited from towr::Polynomial
std::vector< VectorXd >	coeff_

Detailed Description

Represents a Cubic-Hermite-Polynomial.

This class is a third-order ("cubic") polynomial, so: f(t) = Dt^3 + Ct^2 + Bt + A fd(t) = 3Dt^2 + 2Ct + B fdd(t) = 6Dt + 2C

Instead of setting the polynomial coefficients directly, a third-order polynomial is also fully defined by the value and first-derivative of the start and end of the polynomial as well as the duration. This way of specifying a polynomial is called "Hermite".

Three Cubic-Hermite-Polynomials

See also matlab/cubic_hermite_polynomial.m for generation of derivatives.

Definition at line 109 of file polynomial.h.

Constructor & Destructor Documentation

◆ CubicHermitePolynomial()

towr::CubicHermitePolynomial::CubicHermitePolynomial ( int dim )

Definition at line 76 of file polynomial.cc.

◆ ~CubicHermitePolynomial()

virtual towr::CubicHermitePolynomial::~CubicHermitePolynomial ( )

virtualdefault

Member Function Documentation

◆ GetDerivativeOfAccWrtEndNode()

double towr::CubicHermitePolynomial::GetDerivativeOfAccWrtEndNode	(	Dx	node_deriv,
		double	t_local
	)		const

private

Definition at line 222 of file polynomial.cc.

◆ GetDerivativeOfAccWrtStartNode()

double towr::CubicHermitePolynomial::GetDerivativeOfAccWrtStartNode	(	Dx	node_deriv,
		double	t_local
	)		const

private

Definition at line 174 of file polynomial.cc.

◆ GetDerivativeOfPosWrtDuration()

Eigen::VectorXd towr::CubicHermitePolynomial::GetDerivativeOfPosWrtDuration ( double t ) const

How the total duration affect the value ("pos") of the polynomial.

Parameters

t	The time [0,T] at which the change in value should be observed.

Definition at line 237 of file polynomial.cc.

◆ GetDerivativeOfPosWrtEndNode()

double towr::CubicHermitePolynomial::GetDerivativeOfPosWrtEndNode	(	Dx	node_deriv,
		double	t_local
	)		const

private

Definition at line 189 of file polynomial.cc.

◆ GetDerivativeOfPosWrtStartNode()

double towr::CubicHermitePolynomial::GetDerivativeOfPosWrtStartNode	(	Dx	node_deriv,
		double	t_local
	)		const

private

Definition at line 141 of file polynomial.cc.

◆ GetDerivativeOfVelWrtEndNode()

double towr::CubicHermitePolynomial::GetDerivativeOfVelWrtEndNode	(	Dx	node_deriv,
		double	t_local
	)		const

private

Definition at line 206 of file polynomial.cc.

◆ GetDerivativeOfVelWrtStartNode()

double towr::CubicHermitePolynomial::GetDerivativeOfVelWrtStartNode	(	Dx	node_deriv,
		double	t_local
	)		const

private

Definition at line 158 of file polynomial.cc.

◆ GetDerivativeWrtEndNode()

double towr::CubicHermitePolynomial::GetDerivativeWrtEndNode	(	Dx	dfdt,
		Dx	node_deriv,
		double	t
	)		const

The derivative of the polynomial when changing the end node.

Parameters

dxdt	Which polynomial derivative f(t), fd(t) function to use.
node_deriv	Whether derivative should be w.r.t end-node position or velocity.
t	The time along the polynomial.

Definition at line 124 of file polynomial.cc.

◆ GetDerivativeWrtStartNode()

double towr::CubicHermitePolynomial::GetDerivativeWrtStartNode	(	Dx	dfdt,
		Dx	node_deriv,
		double	t
	)		const

The derivative of the polynomial when changing the start node.

Parameters

dxdt	Which polynomial derivative f(t), fd(t) function to use.
node_deriv	Whether derivative should be w.r.t start-node position or velocity.
t	The time along the polynomial.

Definition at line 107 of file polynomial.cc.

◆ GetDuration()

const double towr::CubicHermitePolynomial::GetDuration ( ) const

inline

Returns: the total duration of the polynomial.

Definition at line 157 of file polynomial.h.

◆ SetDuration()

void towr::CubicHermitePolynomial::SetDuration ( double duration )

sets the total duration of the polynomial.

Definition at line 92 of file polynomial.cc.

◆ SetNodes()

void towr::CubicHermitePolynomial::SetNodes	(	const Node &	n0,
		const Node &	n1
	)

Fully defines the polynomial by the node values using current duration.

Parameters

n0	The value and derivative at the start of the polynomial.
n1	The value and derivative at the end of the polynomial.

Definition at line 85 of file polynomial.cc.

◆ UpdateCoeff()

void towr::CubicHermitePolynomial::UpdateCoeff ( )

updates the coefficients using current nodes and durations.

Definition at line 98 of file polynomial.cc.

Member Data Documentation

◆ n0_

Node towr::CubicHermitePolynomial::n0_

private

Definition at line 161 of file polynomial.h.

◆ n1_

Node towr::CubicHermitePolynomial::n1_

private

the start and final node comprising the polynomial.

Definition at line 161 of file polynomial.h.

◆ T_

double towr::CubicHermitePolynomial::T_

private

the total duration of the polynomial.

Definition at line 157 of file polynomial.h.

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

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CubicHermitePolynomial()

◆ ~CubicHermitePolynomial()

Member Function Documentation

◆ GetDerivativeOfAccWrtEndNode()

◆ GetDerivativeOfAccWrtStartNode()

◆ GetDerivativeOfPosWrtDuration()

◆ GetDerivativeOfPosWrtEndNode()

◆ GetDerivativeOfPosWrtStartNode()

◆ GetDerivativeOfVelWrtEndNode()

◆ GetDerivativeOfVelWrtStartNode()

◆ GetDerivativeWrtEndNode()

◆ GetDerivativeWrtStartNode()

◆ GetDuration()

◆ SetDuration()

◆ SetNodes()

◆ UpdateCoeff()

Member Data Documentation

◆ n0_

◆ n1_

◆ T_