Classes
class	TypeIIRMLPolynomial
	This class realizes polynomials of degree three as required for the Type II On-Line Trajectory Generation algorithm. More...
struct	MotionPolynomials
	Three arrays of TypeIIRMLMath::TypeIIRMLPolynomial. More...
Enumerations
enum	Step1_Profile { Step1_Undefined = 0, Step1_Profile_PosLinHldNegLin = 1, Step1_Profile_PosLinNegLin = 2, Step1_Profile_PosTriNegLin = 3, Step1_Profile_PosTrapNegLin = 4, Step1_Profile_NegLinHldPosLin = 5, Step1_Profile_NegLinPosLin = 6, Step1_Profile_NegTriPosLin = 7, Step1_Profile_NegTrapPosLin = 8 }
	Enumeration of all possible profiles of Step 1 (A, B, and C). More...
enum	Step2_Profile { Step2_Undefined = 0, Step2_Profile_PosLinHldNegLin = 1, Step2_Profile_PosLinHldPosLin = 2, Step2_Profile_NegLinHldPosLin = 3, Step2_Profile_NegLinHldNegLin = 4, Step2_Profile_PosTrapNegLin = 5, Step2_Profile_NegLinHldNegLinNegLin = 6 }
	Enumeration of all possible profiles of Step 2. More...
Functions
bool	Decision_1A__001 (const double &CurrentVelocity)
	Is (vi >= 0)?
bool	Decision_1A__002 (const double &CurrentVelocity, const double &MaxVelocity)
	Is (vi <= +vmax)?
bool	Decision_1A__003 (const double &CurrentVelocity, const double &TargetVelocity)
	Is (vi <= vtrgt)?
bool	Decision_1A__004 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->vtrgt, is p<=ptrgt?
bool	Decision_1A__005 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	If v->vmax->vtrgt, is p<=ptrgt?
bool	Decision_1A__006 (const double &TargetVelocity)
	Is (vtrgt >= 0)?
bool	Decision_1A__007 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->vtrgt, is p>=ptrgt?
bool	Decision_1A__008 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->0->vtrgt, is p>=ptrgt?
bool	Decision_1A__009 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	If v->vmax->0->vtrgt, is p>=ptrgt?
bool	Decision_1B__001 (const double &CurrentVelocity)
	Is (vi >= 0)?
bool	Decision_1B__002 (const double &CurrentVelocity, const double &MaxVelocity)
	Is (vi <= +vmax)?
bool	Decision_1B__003 (const double &TargetVelocity)
	Is (vtrgt >= 0)?
bool	Decision_1B__004 (const double &CurrentVelocity, const double &TargetVelocity)
	Is (vi <= vtrgt)?
bool	Decision_1B__005 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->vtrgt, is p<=ptrgt?
bool	Decision_1B__006 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->0->vtrgt, is p<=ptrgt?
bool	Decision_1B__007 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->vtrgt, is p>=ptrgt?
bool	Decision_1C__001 (const double &CurrentVelocity)
	Is (vi >= 0)?
bool	Decision_1C__002 (const double &CurrentVelocity, const double &MaxVelocity)
	Is (vi <= +vmax)?
bool	Decision_1C__003 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	If v->vmax->0->vtrgt, is p>=ptrgt?
bool	Decision_2___001 (const double &CurrentVelocity)
	Is (vi >= 0)?
bool	Decision_2___002 (const double &CurrentVelocity, const double &MaxVelocity)
	Is (vi <= +vmax)?
bool	Decision_2___003 (const double &CurrentVelocity, const double &TargetVelocity)
	Is (vi <= vtrgt)?
bool	Decision_2___004 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, const double &CurrentTime, const double &SynchronizationTime)
	If v->vtrgt->hold, so that t=tsync, is p<=ptrgt?
bool	Decision_2___005 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, const double &CurrentTime, const double &SynchronizationTime)
	If v->hold->vtrgt, so that t=tsync, is p<=ptrgt?
bool	Decision_2___006 (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If (v->0->vtrgt, is p<=ptrgt \|\| t > tsync)?
bool	Decision_2___007 (const double &TargetVelocity)
	Is (vtrgt >= 0)?
bool	Decision_2___008 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, const double &CurrentTime, const double &SynchronizationTime)
	If v->hold->vtrgt, so that t=tsync, is p<=ptrgt?
bool	Decision_2___009 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, const double &CurrentTime, const double &SynchronizationTime)
	If v->vtrgt->hold, so that t=tsync, is p<=ptrgt?
bool	Decision_2___010 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	If v->0->vtrgt, is p>=ptrgt?
bool	Decision_2___011 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, const double &CurrentTime, const double &SynchronizationTime)
	If v->vtrgt->hold, so that t=tsync, is p<=ptrgt?
bool	Decision_2___012 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, const double &CurrentTime, const double &SynchronizationTime)
	If v->hold->0->vtrgt, so that t=tsync, is p<=ptrgt?
bool	Decision_V___001 (const double &CurrentVelocity, const double &TargetVelocity)
	Is (vi <= vtrgt)?
void	TypeIIRMLDecisionTree1A (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration, Step1_Profile AppliedProfile, double MinimalExecutionTime)
	This function contains the decision tree 1A of the Step 1 of the Type II On-Line Trajectory Generation algorithm.
void	TypeIIRMLDecisionTree1B (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration, double *MaximalExecutionTime)
	This function contains the decision tree 1B of the Step 1 of the Type II On-Line Trajectory Generation algorithm.
void	TypeIIRMLDecisionTree1C (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration, double *AlternativeExecutionTime)
	This function contains the decision tree 1C of the Step 1 of the Type II On-Line Trajectory Generation algorithm.
void	TypeIIRMLDecisionTree2 (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration, const double &SynchronizationTime, MotionPolynomials *PolynomialsInternal)
	This function contains the decision tree of the Step 2 of the Type II On-Line Trajectory Generation algorithm.
double	RMLSqrt (const double &Value)
	Calculates the real square root of a given value. If the value is negative a value of almost zero will be returned.
bool	IsEpsilonEquality (const double &Value1, const double &Value2, const double &Epsilon)
	Checks epsilon equality for two values.
void	Quicksort (const int &LeftBound, const int &RightBound, double *ArrayOfValues)
	Standard implementation of the Quicksort algorithm for `double` values.
void	NegateStep1 (double ThisCurrentPosition, double ThisCurrentVelocity, double ThisTargetPosition, double ThisTargetVelocity)
	Negate input values during Step 1.
void	VToVMaxStep1 (double TotalTime, double ThisCurrentPosition, double *ThisCurrentVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	One intermediate Step 1 trajectory segment: v -> +vmax (NegLin)
void	VToZeroStep1 (double TotalTime, double ThisCurrentPosition, double *ThisCurrentVelocity, const double &MaxAcceleration)
	One intermediate Step 1 trajectory segment: v -> 0 (NegLin)
double	ProfileStep1PosLinHldNegLin (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	Calculates the execution time of the PosLinHldNegLin velocity profile.
double	ProfileStep1PosLinNegLin (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	Calculates the execution time of the PosLinNegLin velocity profile.
double	ProfileStep1PosTriNegLin (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	Calculates the execution time of the PosTriNegLin velocity profile.
double	ProfileStep1PosTrapNegLin (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	Calculates the execution time of the PosTrapNegLin velocity profile.
double	ProfileStep1NegLinPosLin (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration)
	Calculates the execution time of the NegLinPosLin velocity profile.
bool	IsSolutionForProfile_PosLinHldNegLin_Possible (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	Checks whether a valid solution for the PosLinHldNegLin velocity profile would be possible.
bool	IsSolutionForProfile_PosLinNegLin_Possible (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	Checks whether a valid solution for the PosLinNegLin velocity profile would be possible.
bool	IsSolutionForProfile_PosTriNegLin_Possible (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	Checks whether a valid solution for the PosTriNegLin velocity profile would be possible.
bool	IsSolutionForProfile_PosTrapNegLin_Possible (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration)
	Checks whether a valid solution for the PosTrapNegLin velocity profile would be possible.
void	NegateStep2 (double ThisCurrentPosition, double ThisCurrentVelocity, double ThisTargetPosition, double ThisTargetVelocity, bool *Inverted)
	Negate input values.
void	VToVMaxStep2 (double ThisCurrentTime, double ThisCurrentPosition, double ThisCurrentVelocity, const double &MaxVelocity, const double &MaxAcceleration, MotionPolynomials PolynomialsLocal, const bool &Inverted)
	One intermediate Step 2 trajectory segment: v -> vmax (NegLin)
void	VToZeroStep2 (double ThisCurrentTime, double ThisCurrentPosition, double ThisCurrentVelocity, const double &MaxAcceleration, MotionPolynomials PolynomialsLocal, const bool &Inverted)
	One intermediate Step 2 trajectory segment: v -> 0 (NegLin)
void	ProfileStep2PosLinHldNegLin (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, MotionPolynomials *PolynomialsLocal, const bool &Inverted)
	Parameterization of the Step 2 velocity profile PosLinHldNegLin (leaf of the Step 2 decision tree)
void	ProfileStep2PosLinHldPosLin (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, MotionPolynomials *PolynomialsLocal, const bool &Inverted)
	Parameterization of the Step 2 velocity profile PosLinHldNegLin (leaf of the Step 2 decision tree)
void	ProfileStep2NegLinHldPosLin (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, MotionPolynomials *PolynomialsLocal, const bool &Inverted)
	Parameterization of the Step 2 velocity profile NegLinHldPosLin (leaf of the Step 2 decision tree)
void	ProfileStep2NegLinHldNegLin (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, MotionPolynomials *PolynomialsLocal, const bool &Inverted)
	Parameterization of the Step 2 velocity profile NegLinHldNegLin (leaf of the Step 2 decision tree)
void	ProfileStep2PosTrapNegLin (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, MotionPolynomials *PolynomialsLocal, const bool &Inverted)
	Parameterization of the Step 2 velocity profile PosTrapNegLin (leaf of the Step 2 decision tree)
void	ProfileStep2NegLinHldNegLinNegLin (const double &CurrentTime, const double &SynchronizationTime, const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxAcceleration, MotionPolynomials *PolynomialsLocal, const bool &Inverted)
	Parameterization of the Step 2 velocity profile NegLinHldNegLinNegLin (leaf of the Step 2 decision tree)
void	Step2WithoutSynchronization (const double &CurrentPosition, const double &CurrentVelocity, const double &TargetPosition, const double &TargetVelocity, const double &MaxVelocity, const double &MaxAcceleration, const TypeIIRMLMath::Step1_Profile &UsedProfile, const double &MinimumExecutionTime, MotionPolynomials *PolynomialsInternal)
	This function contains sets of trajectory parameters (i.e., all polynomial coefficients) in the case of non-synchronized trajectories.

Enumeration Type Documentation

enum TypeIIRMLMath::Step1_Profile

Enumeration of all possible profiles of Step 1 (A, B, and C).

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

Enumerator:

Step1_Undefined	The profile is undefined.
Step1_Profile_PosLinHldNegLin	The profile is PosLinHldNegLin.
Step1_Profile_PosLinNegLin	The profile is PosLinNegLin.
Step1_Profile_PosTriNegLin	The profile is PosTriNegLin.
Step1_Profile_PosTrapNegLin	The profile is PosTrapNegLin.
Step1_Profile_NegLinHldPosLin	The profile is NegLinHldPosLin.
Step1_Profile_NegLinPosLin	The profile is NegLinPosLin.
Step1_Profile_NegTriPosLin	The profile is NegTriPosLin.
Step1_Profile_NegTrapPosLin	The profile is NegTrapPosLin.

enum TypeIIRMLMath::Step2_Profile

Enumeration of all possible profiles of Step 2.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

Enumerator:

Step2_Undefined	The profile is undefined.
Step2_Profile_PosLinHldNegLin	The profile is PosLinHldNegLin.
Step2_Profile_PosLinHldPosLin	The profile is PosLinHldPosLin.
Step2_Profile_NegLinHldPosLin	The profile is NegLinHldPosLin.
Step2_Profile_NegLinHldNegLin	The profile is NegLinHldNegLin.
Step2_Profile_PosTrapNegLin	The profile is PosTrapNegLin.
Step2_Profile_NegLinHldNegLinNegLin	The profile is NegLinHldNegLinNegLin.

Function Documentation

bool TypeIIRMLMath::Decision_1A__001 ( const double & CurrentVelocity )

Is (vi >= 0)?

bool TypeIIRMLMath::Decision_1A__002	(	const double &	CurrentVelocity,
		const double &	MaxVelocity
	)

Is (vi <= +vmax)?

bool TypeIIRMLMath::Decision_1A__003	(	const double &	CurrentVelocity,
		const double &	TargetVelocity
	)

Is (vi <= vtrgt)?

bool TypeIIRMLMath::Decision_1A__004	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->vtrgt, is p<=ptrgt?

bool TypeIIRMLMath::Decision_1A__005	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

If v->vmax->vtrgt, is p<=ptrgt?

bool TypeIIRMLMath::Decision_1A__006 ( const double & TargetVelocity )

Is (vtrgt >= 0)?

bool TypeIIRMLMath::Decision_1A__007	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->vtrgt, is p>=ptrgt?

bool TypeIIRMLMath::Decision_1A__008	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->0->vtrgt, is p>=ptrgt?

bool TypeIIRMLMath::Decision_1A__009	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

If v->vmax->0->vtrgt, is p>=ptrgt?

bool TypeIIRMLMath::Decision_1B__001 ( const double & CurrentVelocity )

Is (vi >= 0)?

bool TypeIIRMLMath::Decision_1B__002	(	const double &	CurrentVelocity,
		const double &	MaxVelocity
	)

Is (vi <= +vmax)?

bool TypeIIRMLMath::Decision_1B__003 ( const double & TargetVelocity )

Is (vtrgt >= 0)?

bool TypeIIRMLMath::Decision_1B__004	(	const double &	CurrentVelocity,
		const double &	TargetVelocity
	)

Is (vi <= vtrgt)?

bool TypeIIRMLMath::Decision_1B__005	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->vtrgt, is p<=ptrgt?

bool TypeIIRMLMath::Decision_1B__006	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->0->vtrgt, is p<=ptrgt?

bool TypeIIRMLMath::Decision_1B__007	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->vtrgt, is p>=ptrgt?

bool TypeIIRMLMath::Decision_1C__001 ( const double & CurrentVelocity )

Is (vi >= 0)?

bool TypeIIRMLMath::Decision_1C__002	(	const double &	CurrentVelocity,
		const double &	MaxVelocity
	)

Is (vi <= +vmax)?

bool TypeIIRMLMath::Decision_1C__003	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

If v->vmax->0->vtrgt, is p>=ptrgt?

bool TypeIIRMLMath::Decision_2___001 ( const double & CurrentVelocity )

Is (vi >= 0)?

bool TypeIIRMLMath::Decision_2___002	(	const double &	CurrentVelocity,
		const double &	MaxVelocity
	)

Is (vi <= +vmax)?

bool TypeIIRMLMath::Decision_2___003	(	const double &	CurrentVelocity,
		const double &	TargetVelocity
	)

Is (vi <= vtrgt)?

bool TypeIIRMLMath::Decision_2___004	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		const double &	CurrentTime,
		const double &	SynchronizationTime
	)

If v->vtrgt->hold, so that t=tsync, is p<=ptrgt?

bool TypeIIRMLMath::Decision_2___005	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		const double &	CurrentTime,
		const double &	SynchronizationTime
	)

If v->hold->vtrgt, so that t=tsync, is p<=ptrgt?

bool TypeIIRMLMath::Decision_2___006	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If (v->0->vtrgt, is p<=ptrgt || t > tsync)?

bool TypeIIRMLMath::Decision_2___007 ( const double & TargetVelocity )

Is (vtrgt >= 0)?

bool TypeIIRMLMath::Decision_2___008	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		const double &	CurrentTime,
		const double &	SynchronizationTime
	)

If v->hold->vtrgt, so that t=tsync, is p<=ptrgt?

bool TypeIIRMLMath::Decision_2___009	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		const double &	CurrentTime,
		const double &	SynchronizationTime
	)

If v->vtrgt->hold, so that t=tsync, is p<=ptrgt?

bool TypeIIRMLMath::Decision_2___010	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

If v->0->vtrgt, is p>=ptrgt?

bool TypeIIRMLMath::Decision_2___011	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		const double &	CurrentTime,
		const double &	SynchronizationTime
	)

If v->vtrgt->hold, so that t=tsync, is p<=ptrgt?

bool TypeIIRMLMath::Decision_2___012	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		const double &	CurrentTime,
		const double &	SynchronizationTime
	)

If v->hold->0->vtrgt, so that t=tsync, is p<=ptrgt?

bool TypeIIRMLMath::Decision_V___001	(	const double &	CurrentVelocity,
		const double &	TargetVelocity
	)

Is (vi <= vtrgt)?

bool TypeIIRMLMath::IsEpsilonEquality	(	const double &	Value1,
		const double &	Value2,
		const double &	Epsilon
	)		`[inline]`

Checks epsilon equality for two values.

Returns $\left(\left|Value1\,-\,Value2\right|\ <=\ Epsilon\right)$ , that if epsilon quality holds, true will be returned, otherwise false.

Parameters:

Value1	First value to be compared
Value2	Second value to be compared
Epsilon	Value for Epsilon

Returns:: true if both values are epsilon equal, otherwise false

bool TypeIIRMLMath::IsSolutionForProfile_PosLinHldNegLin_Possible	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

Checks whether a valid solution for the PosLinHldNegLin velocity profile would be possible.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:

true if a valid solution would be possible
false otherwise

See also:: TypeIIRMLPosition::Step1()

bool TypeIIRMLMath::IsSolutionForProfile_PosLinNegLin_Possible	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

Checks whether a valid solution for the PosLinNegLin velocity profile would be possible.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:

true if a valid solution would be possible
false otherwise

See also:: TypeIIRMLPosition::Step1()

bool TypeIIRMLMath::IsSolutionForProfile_PosTrapNegLin_Possible	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

Checks whether a valid solution for the PosTrapNegLin velocity profile would be possible.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:

true if a valid solution would be possible
false otherwise

See also:: TypeIIRMLPosition::Step1()

bool TypeIIRMLMath::IsSolutionForProfile_PosTriNegLin_Possible	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

Checks whether a valid solution for the PosTriNegLin velocity profile would be possible.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:

true if a valid solution would be possible
false otherwise

See also:: TypeIIRMLPosition::Step1()

void TypeIIRMLMath::NegateStep1	(	double *	ThisCurrentPosition,
		double *	ThisCurrentVelocity,
		double *	ThisTargetPosition,
		double *	ThisTargetVelocity
	)

Negate input values during Step 1.

Parameters:

ThisCurrentPosition	Pointer to a `double` value: Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$ . The sign of this value will be flipped.
ThisCurrentVelocity	Pointer to a `double` value: Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$ The sign of this value will be flipped.
ThisTargetPosition	Pointer to a `double` value: Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$ The sign of this value will be flipped.
ThisTargetVelocity	Pointer to a `double` value: Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$ The sign of this value will be flipped.

Note:: This function is used in the Step 1 decision trees 1A, 1B, and 1C.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C(); TypeIIRMLMath::NegateStep2()

void TypeIIRMLMath::NegateStep2	(	double *	ThisCurrentPosition,
		double *	ThisCurrentVelocity,
		double *	ThisTargetPosition,
		double *	ThisTargetVelocity,
		bool *	Inverted
	)

Negate input values.

Parameters:

ThisCurrentPosition	Pointer to a `double` value: Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$ . The sign of this value will be flipped.
ThisCurrentVelocity	Pointer to a `double` value: Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$ The sign of this value will be flipped.
ThisTargetPosition	Pointer to a `double` value: Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$ The sign of this value will be flipped.
ThisTargetVelocity	Pointer to a `double` value: Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$ The sign of this value will be flipped.
Inverted	Pointer to `bool` value: This bit will be flipped; it indicates, whether the input values have been flipped even or odd times, such that succeeding functions can set-up the trajectory parameters correspondingly.

Note:: This function is used in the Step 2 decision tree.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2(); TypeIIRMLMath::NegateStep1()

double TypeIIRMLMath::ProfileStep1NegLinPosLin	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

Calculates the execution time of the NegLinPosLin velocity profile.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:: Execution time for this profile in seconds

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

double TypeIIRMLMath::ProfileStep1PosLinHldNegLin	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

Calculates the execution time of the PosLinHldNegLin velocity profile.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:: Execution time for this profile in seconds

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

double TypeIIRMLMath::ProfileStep1PosLinNegLin	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

Calculates the execution time of the PosLinNegLin velocity profile.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:: Execution time for this profile in seconds

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

double TypeIIRMLMath::ProfileStep1PosTrapNegLin	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

Calculates the execution time of the PosTrapNegLin velocity profile.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:: Execution time for this profile in seconds

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

double TypeIIRMLMath::ProfileStep1PosTriNegLin	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration
	)

Calculates the execution time of the PosTriNegLin velocity profile.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$

Returns:: Execution time for this profile in seconds

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

void TypeIIRMLMath::ProfileStep2NegLinHldNegLin	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

Parameterization of the Step 2 velocity profile NegLinHldNegLin (leaf of the Step 2 decision tree)

Parameters:

CurrentTime	Time in seconds required for preceding intermediate trajectory segments, $^{\left(\Lambda+1\right)}_{\ \ \ \ \ k}t_i$ , where $\Lambda$ is the number of preceding trajectory segments.
SynchronizationTime	Synchronization time in seconds, $t_i^{\,sync}$
CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will set-up all remaining trajectory parameters.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegateStep2()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::ProfileStep2NegLinHldNegLinNegLin	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

Parameterization of the Step 2 velocity profile NegLinHldNegLinNegLin (leaf of the Step 2 decision tree)

Parameters:

CurrentTime	Time in seconds required for preceding intermediate trajectory segments, $^{\left(\Lambda+1\right)}_{\ \ \ \ \ k}t_i$ , where $\Lambda$ is the number of preceding trajectory segments.
SynchronizationTime	Synchronization time in seconds, $t_i^{\,sync}$
CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will set-up all remaining trajectory parameters.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegateStep2()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::ProfileStep2NegLinHldPosLin	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

Parameterization of the Step 2 velocity profile NegLinHldPosLin (leaf of the Step 2 decision tree)

Parameters:

CurrentTime	Time in seconds required for preceding intermediate trajectory segments, $^{\left(\Lambda+1\right)}_{\ \ \ \ \ k}t_i$ , where $\Lambda$ is the number of preceding trajectory segments.
SynchronizationTime	Synchronization time in seconds, $t_i^{\,sync}$
CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will set-up all remaining trajectory parameters.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegateStep2()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::ProfileStep2PosLinHldNegLin	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

Parameterization of the Step 2 velocity profile PosLinHldNegLin (leaf of the Step 2 decision tree)

Parameters:

CurrentTime	Time in seconds required for preceding intermediate trajectory segments, $^{\left(\Lambda+1\right)}_{\ \ \ \ \ k}t_i$ , where $\Lambda$ is the number of preceding trajectory segments.
SynchronizationTime	Synchronization time in seconds, $t_i^{\,sync}$
CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will set-up all remaining trajectory parameters.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegateStep2()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::ProfileStep2PosLinHldPosLin	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

Parameterization of the Step 2 velocity profile PosLinHldNegLin (leaf of the Step 2 decision tree)

Parameters:

CurrentTime	Time in seconds required for preceding intermediate trajectory segments, $^{\left(\Lambda+1\right)}_{\ \ \ \ \ k}t_i$ , where $\Lambda$ is the number of preceding trajectory segments.
SynchronizationTime	Synchronization time in seconds, $t_i^{\,sync}$
CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will set-up all remaining trajectory parameters.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegateStep2()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::ProfileStep2PosTrapNegLin	(	const double &	CurrentTime,
		const double &	SynchronizationTime,
		const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

Parameterization of the Step 2 velocity profile PosTrapNegLin (leaf of the Step 2 decision tree)

Parameters:

CurrentTime	Time in seconds required for preceding intermediate trajectory segments, $^{\left(\Lambda+1\right)}_{\ \ \ \ \ k}t_i$ , where $\Lambda$ is the number of preceding trajectory segments.
SynchronizationTime	Synchronization time in seconds, $t_i^{\,sync}$
CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will set-up all remaining trajectory parameters.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegateStep2()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::Quicksort	(	const int &	LeftBound,
		const int &	RightBound,
		double *	ArrayOfValues
	)

Standard implementation of the Quicksort algorithm for double values.

This function is used to sort of time values that are calculated during Step 1

$_kt_i^{\,min},\,_kt_i^{\,begin},\,_kt_i^{\,end}\ \forall\ k\ \in\ \left\{1,\,\dots,\,K\right\}$

where $ K $ is the number of degrees of freedom.

Parameters:

LeftBound	Index value for the left border
RightBound	Index value for the right border
ArrayOfValues	A pointer to an array of double values to be sorted

See also:: TypeIIRMLPosition::Step1()

double TypeIIRMLMath::RMLSqrt ( const double & Value ) [inline]

Calculates the real square root of a given value. If the value is negative a value of almost zero will be returned.

Parameters:

Value Square root radicand

Returns:: Square root value (real).

See also:: POSITIVE_ZERO

void TypeIIRMLMath::Step2WithoutSynchronization	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration,
		const TypeIIRMLMath::Step1_Profile &	UsedProfile,
		const double &	MinimumExecutionTime,
		MotionPolynomials *	PolynomialsInternal
	)

This function contains sets of trajectory parameters (i.e., all polynomial coefficients) in the case of non-synchronized trajectories.

Based on all input values for one selected degree of freedom and on the velocity profile that was applied in Step 1A, all trajectory parameters, that is, all polynomial coefficients, are set-up. This method is only applied in the case of non-synchronized trajectories (cf. RMLFlags::NO_SYNCHRONIZATION).

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
UsedProfile	The ID of the used acceleration profile in Step 1A (cf. RMLMath::Step1_Profile).
MinimumExecutionTime	Minimum execution time $t_{i}^{\,min}$ for the current degree of freedom (i.e., the result of profiles of the Step 1A 1A decision tree.
PolynomialsInternal	A pointer to a `MotionPolynomials` object (cf. TypeIIRMLMath::MotionPolynomials). All trajectory parameters of the synchronized Type II trajectory will be written into this object.

See also:: RMLFlags::NO_SYNCHRONIZATION

void TypeIIRMLMath::TypeIIRMLDecisionTree1A	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration,
		Step1_Profile *	AppliedProfile,
		double *	MinimalExecutionTime
	)

This function contains the decision tree 1A of the Step 1 of the Type II On-Line Trajectory Generation algorithm.

This function calculates the minimum possible trajectory execution time $\ _{k}t_{i}^{\,min}$ for DOF $ k $ at instant $T_{i}$ .

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
AppliedProfile	A pointer to an `int` value. The index of the motion profile, which is used to achieve the minimum execution time (cf. TypeIIRMLMath::Step1_Profile) will be copied to this variable.
MinimalExecutionTime	Pointer to a `double` value: The actual result of the of this function, that is, minimum possible execution time $\ _{k}t_{i}^{\,min}$ will be copied to this variable.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C(); TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::TypeIIRMLDecisionTree1B	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration,
		double *	MaximalExecutionTime
	)

This function contains the decision tree 1B of the Step 1 of the Type II On-Line Trajectory Generation algorithm.

This function calculates the beginning of possible inoperative time interval, that is, the time $\ _{k}t_{i}^{\,begin}$ for DOF $ k $ at instant $T_{i}$ .

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
MaximalExecutionTime	Pointer to a `double` value: The actual result of the of this function, that is, the value of the beginning of possible inoperative time interval, that is, the time $\ _{k}t_{i}^{\,begin}$ for DOF at instant $T_{i}$ . If no inoperative time interval is existent, a value of `RML_INFINITY` will be written to this variable.

Returns:: For the case, an error during the calculations of one motion profile happens, the return value will be true, otherwise false.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1C(); TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::TypeIIRMLDecisionTree1C	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration,
		double *	AlternativeExecutionTime
	)

This function contains the decision tree 1C of the Step 1 of the Type II On-Line Trajectory Generation algorithm.

This function calculates the end of an inoperative time interval, that is, the time $\ _{k}t_{i}^{\,end}$ for DOF $ k $ at instant $T_{i}$ .

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
AlternativeExecutionTime	Pointer to a `double` value: The actual result of the of this function, that is, the value of the end of the inoperative time interval, that is, the time $\ _{k}t_{i}^{\,end}$ for DOF at instant $T_{i}$ .

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree2()

void TypeIIRMLMath::TypeIIRMLDecisionTree2	(	const double &	CurrentPosition,
		const double &	CurrentVelocity,
		const double &	TargetPosition,
		const double &	TargetVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration,
		const double &	SynchronizationTime,
		MotionPolynomials *	PolynomialsInternal
	)

This function contains the decision tree of the Step 2 of the Type II On-Line Trajectory Generation algorithm.

This function synchronizes the trajectory for one single degree of freedom to the synchronization time $t_{i}^{\,sync}$ and calculates all trajectory parameters.

Parameters:

CurrentPosition	Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$
CurrentVelocity	Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$
TargetPosition	Target position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}^{\,trgt}$
TargetVelocity	Target velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,trgt}$
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$
SynchronizationTime	The synchronization time $t_{i}^{\,sync}$ that was calculated in Step 1 of the On-Line Trajectory Generation algorithm (in seconds).
PolynomialsInternal	A pointer to a `MotionPolynomials` object (cf. TypeIIRMLMath::MotionPolynomials). All trajectory parameters of the synchronized Type II trajectory will be written into this object.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C()

void TypeIIRMLMath::VToVMaxStep1	(	double *	TotalTime,
		double *	ThisCurrentPosition,
		double *	ThisCurrentVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration
	)

One intermediate Step 1 trajectory segment: v -> +vmax (NegLin)

Parameters:

TotalTime	Pointer to a `double` value: Time in seconds required for preceding trajectory segments. This value will be increased by the amount of time required time for this trajectory segment.
ThisCurrentPosition	Pointer to a `double` value: Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$ . This value will be changed by the function in order to intermediately reach an acceleration value of zero.
ThisCurrentVelocity	Pointer to a `double` value: Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$ This value will be increased in order to intermediately reach an acceleration value of $\ _{k}A_{i}^{\,max}$ .
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$ .
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$ .

Note:: This function is used in the Step 1 decision trees 1A, 1B, and 1C.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C(); TypeIIRMLMath::VToVMaxStep2()

void TypeIIRMLMath::VToVMaxStep2	(	double *	ThisCurrentTime,
		double *	ThisCurrentPosition,
		double *	ThisCurrentVelocity,
		const double &	MaxVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

One intermediate Step 2 trajectory segment: v -> vmax (NegLin)

Parameters:

ThisCurrentTime	Pointer to a `double` value: Time in seconds required for preceding trajectory segments. This value will be increased by the amount of time required time for this trajectory segment.
ThisCurrentPosition	Pointer to a `double` value: Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$ . This value will be changed by the function in order to intermediately reach the maximum velocity value, $\ _{k}V_{i}^{\,max}$ .
ThisCurrentVelocity	Pointer to a `double` value: Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$ This value will be increased in order to intermediately reach the maximum velocity value, $\ _{k}V_{i}^{\,max}$ .
MaxVelocity	Maximum allowed velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}^{\,max}$ .
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$ .
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will add one further trajectory segment to this object.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegatePink()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

Note:: This function is used in the Step 2 decision tree.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2(); TypeIIRMLMath::VToVMaxStep1()

void TypeIIRMLMath::VToZeroStep1	(	double *	TotalTime,
		double *	ThisCurrentPosition,
		double *	ThisCurrentVelocity,
		const double &	MaxAcceleration
	)

One intermediate Step 1 trajectory segment: v -> 0 (NegLin)

Parameters:

TotalTime	Pointer to a `double` value: Time in seconds required for preceding trajectory segments. This value will be increased by the amount of time required time for this trajectory segment.
ThisCurrentPosition	Pointer to a `double` value: Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$ . This value will be changed by the function in order to intermediately reach an acceleration value of zero.
ThisCurrentVelocity	Pointer to a `double` value: Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$ This value will be increased in order to intermediately reach an acceleration value of $\ _{k}A_{i}^{\,max}$ .
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$ .

Note:: This function is used in the Step 1 decision trees 1A, 1B, and 1C.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree1A(); TypeIIRMLMath::TypeIIRMLDecisionTree1B(); TypeIIRMLMath::TypeIIRMLDecisionTree1C(); TypeIIRMLMath::VToZeroStep2()

void TypeIIRMLMath::VToZeroStep2	(	double *	ThisCurrentTime,
		double *	ThisCurrentPosition,
		double *	ThisCurrentVelocity,
		const double &	MaxAcceleration,
		MotionPolynomials *	PolynomialsLocal,
		const bool &	Inverted
	)

One intermediate Step 2 trajectory segment: v -> 0 (NegLin)

Parameters:

ThisCurrentTime	Pointer to a `double` value: Time in seconds required for preceding trajectory segments. This value will be increased by the amount of time required time for this trajectory segment.
ThisCurrentPosition	Pointer to a `double` value: Current position value for DOF at instant $T_{i}$ , $\ _{k}P_{i}$ . This value will be changed by the function in order to intermediately reach a velocity value of zero.
ThisCurrentVelocity	Pointer to a `double` value: Current velocity value for DOF at instant $T_{i}$ , $\ _{k}V_{i}$ This value will be increased in order to intermediately reach a velocity value of zero.
MaxAcceleration	Maximum allowed acceleration value for DOF at instant $T_{i}$ , $\ _{k}A_{i}^{\,max}$ .
PolynomialsLocal	Pointer to a `MotionPolynomials` object, which contains the complete trajectory for one single DOF at instant $T_{i}$ , $_k{\cal M}_{i}(t)$ . This function will add one further trajectory segment to this object.
Inverted	A `bool` value that indicates whether the input values have been flipped even or odd times prior to the execution of this function (cf. TypeIIRMLMath::NegatePink()). The trajectory parameters in `PolynomialsLocal` will be set-up correspondingly.

Note:: This function is used in the Step 2 decision tree.

See also:: TypeIIRMLMath::TypeIIRMLDecisionTree2(); TypeIIRMLMath::VToZeroStep1()

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