#include <vpServo.h>

Public Types
enum	vpServoType { NONE, EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fVe_eJe, EYETOHAND_L_cVf_fJe }

enum	vpServoIteractionMatrixType { CURRENT, DESIRED, MEAN, USER_DEFINED }

enum	vpServoInversionType { TRANSPOSE, PSEUDO_INVERSE }

enum	vpServoPrintType { ALL, CONTROLLER, ERROR_VECTOR, FEATURE_CURRENT, FEATURE_DESIRED, GAIN, INTERACTION_MATRIX, MINIMUM }

Public Member Functions
	vpServo ()

	vpServo (vpServoType servoType)

virtual	~vpServo ()

void	addFeature (vpBasicFeature &s, vpBasicFeature &s_star, unsigned int select=vpBasicFeature::FEATURE_ALL)

void	addFeature (vpBasicFeature &s, unsigned int select=vpBasicFeature::FEATURE_ALL)

vpColVector	computeControlLaw ()

vpColVector	computeControlLaw (double t)

vpColVector	computeControlLaw (double t, const vpColVector &e_dot_init)

vpColVector	computeError ()

vpMatrix	computeInteractionMatrix ()

unsigned int	getDimension () const

vpColVector	getError () const

vpMatrix	getInteractionMatrix () const

vpMatrix	getI_WpW () const

vpServoType	getServoType () const

vpMatrix	getLargeP () const

vpMatrix	getTaskJacobian () const

vpMatrix	getTaskJacobianPseudoInverse () const

unsigned int	getTaskRank () const

vpColVector	getTaskSingularValues () const

vpMatrix	getWpW () const

vpVelocityTwistMatrix	get_cVe () const

vpVelocityTwistMatrix	get_cVf () const

vpVelocityTwistMatrix	get_fVe () const

vpMatrix	get_eJe () const

vpMatrix	get_fJe () const

double	getPseudoInverseThreshold () const

void	kill ()

void	print (const vpServo::vpServoPrintType display_level=ALL, std::ostream &os=std::cout)

vpColVector	secondaryTask (const vpColVector &de2dt, const bool &useLargeProjectionOperator=false)

vpColVector	secondaryTask (const vpColVector &e2, const vpColVector &de2dt, const bool &useLargeProjectionOperator=false)

vpColVector	secondaryTaskJointLimitAvoidance (const vpColVector &q, const vpColVector &dq, const vpColVector &jointMin, const vpColVector &jointMax, const double &rho=0.1, const double &rho1=0.3, const double &lambda_tune=0.7)

void	setCameraDoF (const vpColVector &dof)

void	setForceInteractionMatrixComputation (bool force_computation)

void	setInteractionMatrixType (const vpServoIteractionMatrixType &interactionMatrixType, const vpServoInversionType &interactionMatrixInversion=PSEUDO_INVERSE)

void	setLambda (double c)

void	setLambda (double gain_at_zero, double gain_at_infinity, double slope_at_zero)

void	setLambda (const vpAdaptiveGain &l)

void	setMu (double mu_)

void	setServo (const vpServoType &servo_type)

void	set_cVe (const vpVelocityTwistMatrix &cVe_)

void	set_cVe (const vpHomogeneousMatrix &cMe)

void	set_cVf (const vpVelocityTwistMatrix &cVf_)

void	set_cVf (const vpHomogeneousMatrix &cMf)

void	set_fVe (const vpVelocityTwistMatrix &fVe_)

void	set_fVe (const vpHomogeneousMatrix &fMe)

void	set_eJe (const vpMatrix &eJe_)

void	set_fJe (const vpMatrix &fJe_)

void	setPseudoInverseThreshold (double pseudo_inverse_threshold)

bool	testInitialization ()

bool	testUpdated ()

Public Attributes
vpMatrix	L

vpColVector	error

vpMatrix	J1

vpMatrix	J1p

vpColVector	s

vpColVector	sStar

vpColVector	e1

vpColVector	e

vpColVector	q_dot

vpColVector	v

vpServoType	servoType

unsigned int	rankJ1

std::list< vpBasicFeature * >	featureList

std::list< vpBasicFeature * >	desiredFeatureList

std::list< unsigned int >	featureSelectionList

vpAdaptiveGain	lambda

int	signInteractionMatrix

vpServoIteractionMatrixType	interactionMatrixType

vpServoInversionType	inversionType

Protected Member Functions
void	init ()

void	computeProjectionOperators (const vpMatrix &J1_, const vpMatrix &I_, const vpMatrix &I_WpW_, const vpColVector &error_, vpMatrix &P_) const

Protected Attributes
vpVelocityTwistMatrix	cVe

bool	init_cVe

vpVelocityTwistMatrix	cVf

bool	init_cVf

vpVelocityTwistMatrix	fVe

bool	init_fVe

vpMatrix	eJe

bool	init_eJe

vpMatrix	fJe

bool	init_fJe

bool	errorComputed

bool	interactionMatrixComputed

unsigned int	dim_task

bool	taskWasKilled

bool	forceInteractionMatrixComputation

vpMatrix	I

vpMatrix	WpW

vpMatrix	I_WpW

vpMatrix	P

vpColVector	sv

double	mu

vpColVector	e1_initial

bool	iscJcIdentity

vpMatrix	cJc

bool	m_first_iteration

double	m_pseudo_inverse_threshold

Detailed Description

Class required to compute the visual servoing control law descbribed in [2] and [3].

Warning: To avoid potential memory leaks, it is mendatory to call explicitly the kill() function to destroy the task. Otherwise, the destructor ~vpServo() launch an exception vpServoException::notKilledProperly.

To learn how to use this class, we suggest first to follow the Tutorial: Image-based visual servo. The Tutorial: Visual servo simulation on a pioneer-like unicycle robot and Tutorial: How to boost your visual servo control law are also useful for advanced usage of this class.

The example below shows how to build a position-based visual servo from 3D visual features $s=({^{c^*}}t_c,\theta u)$ . In that case, we have $s^* = 0$ . Let us denote $\theta u$ the angle/axis parametrization of the rotation ${^{c^*}}R_c$ . Moreover, ${^{c^*}}t_c$ and ${^{c^*}}R_c$ represent respectively the translation and the rotation between the desired camera frame and the current one obtained by pose estimation (see vpPose class).

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpHomogeneousMatrix.h>
#include <visp3/core/vpMatrix.h>
#include <visp3/visual_features/vpFeatureThetaU.h>
#include <visp3/visual_features/vpFeatureTranslation.h>
#include <visp3/vs/vpServo.h>
int main()
{
  // Creation of an homogeneous matrix that represent the displacement
  // the camera has to achieve to move from the desired camera frame
  // and the current one
  vpHomogeneousMatrix cdMc;
  // ... cdMc is here the result of a pose estimation
  // Creation of the current visual feature s = (c*_t_c, ThetaU)
  vpFeatureTranslation s_t(vpFeatureTranslation::cdMc);
  vpFeatureThetaU s_tu(vpFeatureThetaU::cdRc);
  // Set the initial values of the current visual feature s = (c*_t_c, ThetaU)
  s_t.buildFrom(cdMc);
  s_tu.buildFrom(cdMc);
  // Build the desired visual feature s* = (0,0)
  vpFeatureTranslation s_star_t(vpFeatureTranslation::cdMc); // Default initialization to zero
  vpFeatureThetaU s_star_tu(vpFeatureThetaU::cdRc); // Default initialization to zero
  vpColVector v; // Camera velocity
  double error;  // Task error
  // Creation of the visual servo task.
  vpServo task;
  // Visual servo task initialization
  // - Camera is monted on the robot end-effector and velocities are
  //   computed in the camera frame
  task.setServo(vpServo::EYEINHAND_CAMERA);
  // - Interaction matrix is computed with the current visual features s
  task.setInteractionMatrixType(vpServo::CURRENT);
  // - Set the contant gain to 1
  task.setLambda(1);
  // - Add current and desired translation feature
  task.addFeature(s_t, s_star_t);
  // - Add current and desired ThetaU feature for the rotation
  task.addFeature(s_tu, s_star_tu);
  // Visual servoing loop. The objective is here to update the visual
  // features s = (c*_t_c, ThetaU), compute the control law and apply
  // it to the robot
  do {
    // ... cdMc is here the result of a pose estimation
    // Update the current visual feature s
    s_t.buildFrom(cdMc);  // Update translation visual feature
    s_tu.buildFrom(cdMc); // Update ThetaU visual feature
    v = task.computeControlLaw(); // Compute camera velocity skew
    error =  ( task.getError() ).sumSquare(); // error = s^2 - s_star^2
  } while (error > 0.0001); // Stop the task when current and desired visual features are close
}

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma4Point2DCamVelocityKalman.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, servoViper850Point2DCamVelocityKalman.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeature.cpp, testFeatureSegment.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 146 of file vpServo.h.

Member Enumeration Documentation

enum vpServo::vpServoInversionType

Enumerator
TRANSPOSE	In the control law (see vpServo::vpServoType), uses the transpose instead of the pseudo inverse.
PSEUDO_INVERSE	In the control law (see vpServo::vpServoType), uses the pseudo inverse.

Definition at line 199 of file vpServo.h.

enum vpServo::vpServoIteractionMatrixType

Enumerator
CURRENT	In the control law (see vpServo::vpServoType), uses the interaction matrix ${\widehat {\bf L}}_s$ computed using the current features $\bf s$ .
DESIRED	In the control law (see vpServo::vpServoType), uses the interaction matrix ${\widehat {\bf L}}_{s^}$ computed using the desired features ${\bf s}^$ .
MEAN	In the control law (see vpServo::vpServoType), uses the interaction matrix ${\widehat {\bf L}} = \left({\widehat {\bf L}}_s + {\widehat {\bf L}}_{s^*}\right)/2$ .
USER_DEFINED	In the control law (see vpServo::vpServoType), uses an interaction matrix set by the user.

Definition at line 181 of file vpServo.h.

enum vpServo::vpServoPrintType

Enumerator
ALL	Print all the task information.
CONTROLLER	Print the type of controller law.
ERROR_VECTOR	Print the error vector $\bf e = (s-s^*)$ .
FEATURE_CURRENT	Print the current features $\bf s$ .
FEATURE_DESIRED	Print the desired features ${\bf s}^*$ .
GAIN	Print the gain $\lambda$ .
INTERACTION_MATRIX	Print the interaction matrix.
MINIMUM	Same as vpServo::vpServoPrintType::ERROR_VECTOR.

Definition at line 206 of file vpServo.h.

enum vpServo::vpServoType

Enumerator
NONE	No control law is specified.
EYEINHAND_CAMERA	Eye in hand visual servoing with the following control law ${\bf v}_c = -\lambda {\widehat {\bf L}}^{+}_{e} {\bf e}$ where camera velocities are computed.
EYEINHAND_L_cVe_eJe	Eye in hand visual servoing with the following control law ${\dot {\bf q}} = -\lambda \left( {{\widehat {\bf L}}_{e} {^c}{\bf V}_e {^e}{\bf J}_e} \right)^{+} {\bf e}$ where joint velocities are computed.
EYETOHAND_L_cVe_eJe	Eye to hand visual servoing with the following control law ${\dot {\bf q}} = \lambda \left( {{\widehat {\bf L}}_{e} {^c}{\bf V}_e {^e}{\bf J}_e} \right)^{+} {\bf e}$ where joint velocities are computed.
EYETOHAND_L_cVf_fVe_eJe	Eye to hand visual servoing with the following control law ${\dot {\bf q}} = \lambda \left( {{\widehat {\bf L}}_{e} {^c}{\bf V}_f {^f}{\bf V}_e {^e}{\bf J}_e} \right)^{+} {\bf e}$ where joint velocities are computed.
EYETOHAND_L_cVf_fJe	Eye to hand visual servoing with the following control law ${\dot {\bf q}} = \lambda \left( {{\widehat {\bf L}}_{e} {^c}{\bf V}_f {^f}{\bf J}_e} \right)^{+} {\bf e}$ where joint velocities are computed.

Definition at line 152 of file vpServo.h.

Constructor & Destructor Documentation

vpServo::vpServo ( )

Default constructor that initializes the following settings:

No control law is specified. The user has to call setServo() to specify the control law.
In the control law, the interaction matrix ${\widehat {\bf L}}_e$ is computed with the desired features ${\bf s}^*$ . Using setInteractionMatrixType() you can also compute the interaction matrix with the current visual features, or from the mean $\left({\widehat {\bf L}}_s + {\widehat {\bf L}}_{s^*}\right)/2$ .
In the control law the pseudo inverse will be used. The method setInteractionMatrixType() allows to use the transpose instead.

Warning: By default the threshold used to compute the pseudo-inverse is set to 1e-6. Advanced user can modify this value using setPseudoInverseThreshold().

Definition at line 72 of file vpServo.cpp.

References cJc, and vpMatrix::eye().

vpServo::vpServo ( vpServoType servo_type )

explicit

Constructor that allows to choose the visual servoing control law.

Parameters

servo_type : Visual servoing control law.

The other settings are the following:

In the control law, the interaction matrix ${\widehat {\bf L}}_e$ is computed with the desired features ${\bf s}^*$ . Using setInteractionMatrixType() you can also compute the interaction matrix with the current visual features, or from the mean $\left({\widehat {\bf L}}_s + {\widehat {\bf L}}_{s^*}\right)/2$ .
In the control law the pseudo inverse will be used. The method setInteractionMatrixType() allows to use the transpose instead.

Definition at line 98 of file vpServo.cpp.

References cJc, and vpMatrix::eye().

vpServo::~vpServo ( )

virtual

Destructor.

Since ViSP > 3.3.0 calls kill() to destroy the current and desired feature lists.

See also: kill()

Definition at line 116 of file vpServo.cpp.

References kill().

Member Function Documentation

void vpServo::addFeature	(	vpBasicFeature &	s_cur,
		vpBasicFeature &	s_star,
		unsigned int	select = `vpBasicFeature::FEATURE_ALL`
	)

Add a new set of 2 features $\bf s$ and ${\bf s}^*$ in the task.

Parameters

s_cur	: Current visual feature denoted $\bf s$ .
s_star	: Desired visual feature denoted ${\bf s}^*$ .
select	: Feature selector. By default all the features in s and s_star are used, but is is possible to specify which one is used in case of multiple features.

The following sample code explain how to use this method to add a visual feature point $(x,y)$ :

vpFeaturePoint s, s_star;
...
vpServo task;
task.addFeature(s, s_star);

For example to use only the $x$ visual feature, the previous code becomes:

vpFeaturePoint s, s_star;
...
vpServo task;
task.addFeature(s, s_star, vpFeaturePoint::selectX());

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeature.cpp, testFeatureSegment.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 490 of file vpServo.cpp.

References desiredFeatureList, featureList, and featureSelectionList.

Referenced by vpVirtualGrabber::acquire().

void vpServo::addFeature	(	vpBasicFeature &	s_cur,
		unsigned int	select = `vpBasicFeature::FEATURE_ALL`
	)

Add a new features $\bf s$ in the task. The desired visual feature denoted ${\bf s}^*$ is equal to zero.

Parameters

s_cur	: Current visual feature denoted $\bf s$ .
select	: Feature selector. By default all the features in s are used, but is is possible to specify which one is used in case of multiple features.

The following sample code explain how to use this method to add a $\theta {\bf u} =(\theta u_x, \theta u_y, \theta u_z)$ feature:

vpFeatureThetaU s(vpFeatureThetaU::cRcd);
...
vpServo task;
task.addFeature(s);

For example to use only the $\theta u_x$ feature, the previous code becomes:

vpFeatureThetaU s(vpFeatureThetaU::cRcd);
...
vpServo task;
task.addFeature(s, vpFeatureThetaU::selectTUx);

Definition at line 524 of file vpServo.cpp.

References desiredFeatureList, vpBasicFeature::duplicate(), featureList, featureSelectionList, vpBasicFeature::init(), vpBasicFeature::setDeallocate(), and vpBasicFeature::vpServo.

vpColVector vpServo::computeControlLaw ( )

Compute the control law specified using setServo(). See vpServo::vpServoType for more details concerning the control laws that are available. The Tutorial: Image-based visual servo and Tutorial: How to boost your visual servo control law are also useful to illustrate the usage of this function.

The general form of the control law is the following:

${\bf \dot q} = \pm \lambda {{\bf \widehat J}_e}^+ {\bf e}$

where :

${\bf \dot q}$ is the resulting velocity command to apply to the robot.
the sign of the control law depends on the eye in hand or eye to hand configuration.
$\bf J$ is the Jacobian of the task. It is function of the interaction matrix and of the robot Jacobian.
$\bf e = (s-s^*)$ is the error to regulate.

To ensure continuous sequencing the computeControlLaw(double) function can be used. It will ensure that the velocities that are computed are continuous.

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeatureSegment.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 929 of file vpServo.cpp.

References vpMatrix::AAt(), cJc, computeError(), computeInteractionMatrix(), cVe, cVf, e, e1, eJe, error, vpMatrix::eye(), EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fJe, EYETOHAND_L_cVf_fVe_eJe, fJe, fVe, vpArray2D< Type >::getCols(), I, I_WpW, init_cVe, init_eJe, init_fJe, init_fVe, inversionType, iscJcIdentity, J1, J1p, lambda, m_first_iteration, m_pseudo_inverse_threshold, NONE, vpMatrix::print(), PSEUDO_INVERSE, vpMatrix::pseudoInverse(), rankJ1, vpServoException::servoError, servoType, signInteractionMatrix, sv, vpMatrix::t(), testInitialization(), testUpdated(), vpERROR_TRACE, and WpW.

Referenced by vpVirtualGrabber::acquire().

vpColVector vpServo::computeControlLaw ( double t )

Compute the control law specified using setServo(). See vpServo::vpServoType for more details concerning the control laws that are available. The Tutorial: How to boost your visual servo control law is also useful to illustrate the usage of this function.

To the general form of the control law given in computeControlLaw(), we add here an additional term that comes from the task sequencing approach described in [27] equation (17). This additional term allows to compute continuous velocities by avoiding abrupt changes in the command.

The form of the control law considered here is the following:

${\bf \dot q} = \pm \lambda {{\bf \widehat J}_e}^+ {\bf e} \mp \lambda {{\bf \widehat J}_{e(0)}}^+ {{\bf e}(0)} \exp(-\mu t)$

where :

${\bf \dot q}$ is the resulting continuous velocity command to apply to the robot.
the sign of the control law depends on the eye in hand or eye to hand configuration.
$\bf J$ is the Jacobian of the task. It is function of the interaction matrix and of the robot Jacobian.
$\bf e = (s-s^*)$ is the error to regulate.
is the time given as parameter of this method.
$\mu$ is a gain that is set by default to 4 and that could be modified using setMu().
${\bf \widehat J}_{e(0)}^+ {\bf e}(0)$ is the value of ${\bf \widehat J}_e^+ {\bf e}$ when . This value is internally stored either at the first call of this method, or when t parameter is set to 0.

Parameters

t	: Time in second. When set to zero, ${{\bf \widehat J}_{e(0)}}^+ {{\bf e}(0)}$ is refreshed internally.

Definition at line 1073 of file vpServo.cpp.

References vpMatrix::AAt(), computeError(), computeInteractionMatrix(), cVe, cVf, e, e1, e1_initial, eJe, error, vpMatrix::eye(), EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fJe, EYETOHAND_L_cVf_fVe_eJe, fJe, fVe, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), I, I_WpW, init_cVe, init_eJe, init_fJe, init_fVe, inversionType, J1, J1p, lambda, m_first_iteration, m_pseudo_inverse_threshold, mu, NONE, PSEUDO_INVERSE, vpMatrix::pseudoInverse(), rankJ1, vpServoException::servoError, servoType, signInteractionMatrix, sv, vpMatrix::t(), testInitialization(), testUpdated(), vpERROR_TRACE, and WpW.

vpColVector vpServo::computeControlLaw	(	double	t,
		const vpColVector &	e_dot_init
	)

Compute the control law specified using setServo(). See vpServo::vpServoType for more details concerning the control laws that are available.

To the general form of the control law given in computeControlLaw(), we add here an additional term that comes from the task sequencing approach described in [27] equation (17). This additional term allows to compute continuous velocities by avoiding abrupt changes in the command.

The form of the control law considered here is the following:

${\bf \dot q} = \pm \lambda {{\bf \widehat J}_e}^+ {\bf e} + \left({\bf \dot e}(0) \mp \lambda {{\bf \widehat J}_{e(0)}}^+ {{\bf e}(0)}\right) \exp(-\mu t)$

where :

${\bf \dot q}$ is the resulting continuous velocity command to apply to the robot.
the sign of the control law depends on the eye in hand or eye to hand configuration.
$\bf J$ is the Jacobian of the task. It is function of the interaction matrix and of the robot Jacobian.
$\bf e = (s-s^*)$ is the error to regulate.
is the time given as parameter of this method.
$\mu$ is a gain that is set by default to 4 and that could be modified using setMu().
${\bf \widehat J}_{e(0)}^+ {\bf e}(0)$ is the value of ${\bf \widehat J}_e^+ {\bf e}$ when . This value is internally stored either at the first call of this method, or when t parameter is set to 0.

Parameters

t	: Time in second. When set to zero, ${{\bf \widehat J}_{e(0)}}^+ {{\bf e}(0)}$ is refreshed internally.
e_dot_init	: Initial value of ${\bf \dot e}(0)$ .

Definition at line 1226 of file vpServo.cpp.

References vpMatrix::AAt(), computeError(), computeInteractionMatrix(), cVe, cVf, e, e1, e1_initial, eJe, error, vpMatrix::eye(), EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fJe, EYETOHAND_L_cVf_fVe_eJe, fJe, fVe, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), I, I_WpW, init_cVe, init_eJe, init_fJe, init_fVe, inversionType, J1, J1p, lambda, m_first_iteration, m_pseudo_inverse_threshold, mu, NONE, PSEUDO_INVERSE, vpMatrix::pseudoInverse(), rankJ1, vpServoException::servoError, servoType, signInteractionMatrix, sv, vpMatrix::t(), testInitialization(), testUpdated(), vpERROR_TRACE, and WpW.

vpColVector vpServo::computeError ( )

Compute the error $\bf e =(s - s^*)$ between the current set of visual features $\bf s$ and the desired set of visual features $\bf s^*$ .

Returns: The error vector $\bf e$ .

Definition at line 709 of file vpServo.cpp.

References desiredFeatureList, dim_task, vpBasicFeature::error(), error, errorComputed, featureList, featureSelectionList, vpBasicFeature::get_s(), vpArray2D< Type >::getRows(), vpServoException::noFeatureError, vpColVector::resize(), s, sStar, vpDEBUG_TRACE, and vpERROR_TRACE.

Referenced by computeControlLaw().

vpMatrix vpServo::computeInteractionMatrix ( )

Compute and return the interaction matrix related to the set of visual features.

Returns: The interaction matrix ${\widehat {\bf L}}_e$ used in the control law specified using setServo().

Definition at line 647 of file vpServo.cpp.

References CURRENT, DESIRED, desiredFeatureList, dim_task, featureList, featureSelectionList, forceInteractionMatrixComputation, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), interactionMatrixComputed, interactionMatrixType, L, MEAN, and USER_DEFINED.

Referenced by computeControlLaw().

void vpServo::computeProjectionOperators	(	const vpMatrix &	J1_,
		const vpMatrix &	I_,
		const vpMatrix &	I_WpW_,
		const vpColVector &	error_,
		vpMatrix &	P_
	)		const

protected

Compute the classic projetion operator and the large projection operator.

Definition at line 1344 of file vpServo.cpp.

References vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::frobeniusNorm(), vpArray2D< Type >::getCols(), vpArray2D< Type >::resize(), and vpColVector::t().

Referenced by secondaryTask(), and secondaryTaskJointLimitAvoidance().

vpVelocityTwistMatrix vpServo::get_cVe ( ) const

inline

Return the velocity twist matrix used to transform a velocity skew vector from end-effector frame into the camera frame.

Definition at line 321 of file vpServo.h.

vpVelocityTwistMatrix vpServo::get_cVf ( ) const

inline

Return the velocity twist matrix used to transform a velocity skew vector from robot fixed frame (also called world or base frame) into the camera frame.

Definition at line 327 of file vpServo.h.

vpMatrix vpServo::get_eJe ( ) const

inline

Return the robot jacobian expressed in the end-effector frame.

Definition at line 337 of file vpServo.h.

vpMatrix vpServo::get_fJe ( ) const

inline

Return the robot jacobian expressed in the robot fixed frame (also called world or base frame).

Definition at line 342 of file vpServo.h.

vpVelocityTwistMatrix vpServo::get_fVe ( ) const

inline

Return the velocity twist matrix used to transform a velocity skew vector from robot end-effector frame into the fixed frame (also called world or base frame).

Definition at line 333 of file vpServo.h.

unsigned int vpServo::getDimension ( ) const

Return the task dimension.

Examples:: servoSimuCylinder.cpp, and servoSimuSphere.cpp.

Definition at line 553 of file vpServo.cpp.

References featureList, and featureSelectionList.

vpColVector vpServo::getError ( ) const

inline

Return the error $\bf e = (s - s^*)$ between the current set of visual features $\bf s$ and the desired set of visual features $\bf s^*$ . The error vector is updated after a call of computeError() or computeControlLaw().

vpServo task;
...
vpColVector v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing
vpColVector e = task.getError(); // Get the error vector

Examples:: manServoMomentsSimple.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, testFeatureSegment.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 278 of file vpServo.h.

Referenced by vpServoData::save().

vpMatrix vpServo::getI_WpW ( ) const

Return the projection operator ${\bf I}-{\bf W}^+{\bf W}$ . This operator is updated after a call of computeControlLaw().

vpServo task;
...
vpColVector  v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing
vpMatrix I_WpW = task.getI_WpW(); // Get the projection operator

See also: getWpW()

Definition at line 1725 of file vpServo.cpp.

References I_WpW.

vpMatrix vpServo::getInteractionMatrix ( ) const

inline

Definition at line 294 of file vpServo.h.

vpMatrix vpServo::getLargeP ( ) const

Return the large projection operator. This operator is updated after a call of computeControlLaw().

vpServo task;
...
vpColVector  v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing
vpMatrix P = task.getP();          // Get the large projection operator

See also: getP()

Definition at line 1739 of file vpServo.cpp.

References P.

double vpServo::getPseudoInverseThreshold ( ) const

Return pseudo-inverse threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

See also: setPseudoInverseThreshold()

Definition at line 1812 of file vpServo.cpp.

References m_pseudo_inverse_threshold.

vpServoType vpServo::getServoType ( ) const

inline

Return the visual servo type.

Definition at line 300 of file vpServo.h.

vpMatrix vpServo::getTaskJacobian ( ) const

Return the task jacobian $J$ . The task jacobian is updated after a call of computeControlLaw().

In the general case, the task jacobian is given by ${\bf J} = {\widehat {\bf L}} {^c}{\bf V}_a {^a}{\bf J}_e$ .

vpServo task;
...
vpColVector v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing vpMatrix
J = task.getTaskJacobian(); // Get the task jacobian used to compute v

See also: getTaskJacobianPseudoInverse(), getInteractionMatrix()

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp.

Definition at line 1755 of file vpServo.cpp.

References J1.

vpMatrix vpServo::getTaskJacobianPseudoInverse ( ) const

Return the pseudo inverse of the task jacobian $J$ .

In the general case, the task jacobian is given by ${\bf J} = {\widehat {\bf L}} {^c}{\bf V}_a {^a}{\bf J}_e$ .

The task jacobian and its pseudo inverse are updated after a call of computeControlLaw().

Returns: Pseudo inverse ${J}^{+}$ of the task jacobian.
vpServo task;
...
vpColVector v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing
vpMatrix Jp = task.getTaskJacobianPseudoInverse(); // Get the pseudo inverse of task jacobian used to compute v

See also: getTaskJacobian()

Definition at line 1775 of file vpServo.cpp.

References J1p.

unsigned int vpServo::getTaskRank ( ) const

Return the rank of the task jacobian. The rank is updated after a call of computeControlLaw().

vpServo task;
...
vpColVector v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing
unsigned int rank = task.getTaskRank();   // Get the rank of the task jacobian

Examples:: servoAfma6Ellipse2DCamVelocity.cpp, servoPioneerPanSegment3D.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, and simulateCircle2DCamVelocity.cpp.

Definition at line 1786 of file vpServo.cpp.

References rankJ1.

vpColVector vpServo::getTaskSingularValues ( ) const

inline

Get task singular values.

Returns: Singular values that relies on the task jacobian pseudo inverse.

Definition at line 313 of file vpServo.h.

vpMatrix vpServo::getWpW ( ) const

Return the projection operator ${\bf W}^+{\bf W}$ . This operator is updated after a call of computeControlLaw().

When the dimension of the task is equal to the number of degrees of freedom available ${\bf W^+W = I}$ .

vpServo task;
...
vpColVector v = task.computeControlLaw(); // Compute the velocity corresponding to the visual servoing
vpMatrix  WpW = task.getWpW(); // Get the projection operator

See also: getI_WpW()

Definition at line 1803 of file vpServo.cpp.

References WpW.

void vpServo::init ( void )

protected

Basic initialization.

Initialize the servo with the following settings:

No control law is specified. The user has to call setServo() to specify the control law.
In the control law, the interaction matrix ${\widehat {\bf L}}_e$ is computed with the desired features ${\bf s}^*$ . Using setInteractionMatrixType() you can also compute the interaction matrix with the current visual features, or from the mean $\left({\widehat {\bf L}}_s + {\widehat {\bf L}}_{s^*}\right)/2$ .
In the control law the pseudo inverse will be used. The method setInteractionMatrixType() allows to use the transpose instead.

Definition at line 135 of file vpServo.cpp.

References DESIRED, desiredFeatureList, dim_task, errorComputed, featureList, featureSelectionList, forceInteractionMatrixComputation, init_cVe, init_cVf, init_eJe, init_fJe, init_fVe, interactionMatrixComputed, interactionMatrixType, inversionType, m_first_iteration, NONE, PSEUDO_INVERSE, rankJ1, servoType, signInteractionMatrix, and taskWasKilled.

void vpServo::kill ( )

Task destruction. Kill the current and desired visual feature lists.

This function is called in the destructor. Since ViSP > 3.3.0 it is no more mandatory to call explicitely kill().

vpServo task ;
vpFeatureThetaU s;
...
task.addFeature(s); // Add current ThetaU feature
task.kill(); // This call is no more mandatory since achieved in the destructor

Definition at line 187 of file vpServo.cpp.

References desiredFeatureList, featureList, taskWasKilled, and vpBasicFeature::vpServo.

Referenced by ~vpServo().

void vpServo::print	(	const vpServo::vpServoPrintType	displayLevel = `ALL`,
		std::ostream &	os = `std::cout`
	)

Prints on os stream information about the task:

Parameters

displayLevel	: Indicates which are the task information to print. See vpServo::vpServoPrintType for more details.
os	: Output stream.

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 306 of file vpServo.cpp.

References ALL, CONTROLLER, desiredFeatureList, error, ERROR_VECTOR, errorComputed, EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fJe, EYETOHAND_L_cVf_fVe_eJe, FEATURE_CURRENT, FEATURE_DESIRED, featureList, featureSelectionList, GAIN, INTERACTION_MATRIX, interactionMatrixComputed, L, lambda, MINIMUM, NONE, servoType, and vpColVector::t().

vpColVector vpServo::secondaryTask	(	const vpColVector &	de2dt,
		const bool &	useLargeProjectionOperator = `false`
	)

Compute and return the secondary task vector according to the classic projection operator ${\bf I-W^+W}$ (see equation(7) in the paper [30]) or the new large projection operator (see equation(24) in the paper [32]).

Parameters

de2dt	: Value of $\frac{\partial {\bf e_2}}{\partial t}$ the derivative of the secondary task ${\bf e}_2$ .
useLargeProjectionOperator	: if true will be use the large projection operator, if false the classic one (default).

Returns: The secondary task vector.

If the classic projection operator is used ( useLargeProjectionOperator = false (default value)) this function return:

$({\bf I-W^+W})\frac{\partial {\bf e_2}}{\partial t}$

Note that the secondary task vector need than to be added to the primary task which can be in the general case written as:

$-\lambda {\bf W^+W {\widehat {\bf J}}_e^+({\bf s-s^*})}$

Otherwise if the new large projection operator is used ( useLargeProjectionOperator = true ) this function return:

${\bf P}\frac{\partial {\bf e_2}}{\partial t}$

where

${\bf P} =\bar{\lambda }\left ( \left \| {\bf e} \right \| \right ){\bf P}_{ \left \| {\bf e } \right \| } \left ( 1 - \bar{\lambda }\left ( \left \| {\bf e } \right \| \right ) \right ) \left ( {\bf I-W^+W}\right )$

with

${\bf P}_{\left \| {\bf e } \right \| } = I_{n} - \frac{1}{{\bf e }^\top {\bf J_{{\bf e }} } {\bf J_{{\bf e }}^\top }{\bf e }}{\bf J_{{\bf e }}^\top }{\bf e }{\bf e }^\top{\bf J_{{\bf e }} }$

Warning: computeControlLaw() must be call prior to this function since it updates the projection operators.

The following sample code shows how to use this method to compute a secondary task using the classic projection operator:

vpColVector v;
// Velocity applied to the robot vpColVector de2dt; vpServo task;
...
v  = task.computeControlLaw(); // Compute the primary task
v += task.secondaryTask(de2dt) // Compute and add the secondary task using the classical projection operator

The following sample code shows how to use this method to compute a secondary task using the large projection operator:

vpColVector v;
// Velocity applied to the robot vpColVector de2dt; vpServo task;
...
v  = task.computeControlLaw(); // Compute the primary task
v += task.secondaryTask(de2dt, true) // Compute and add the secondary task using the large projection operator

See also: computeControlLaw()

Examples:: servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, and servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp.

Definition at line 1446 of file vpServo.cpp.

References computeProjectionOperators(), error, vpArray2D< Type >::getCols(), I, I_WpW, J1, vpServoException::noDofFree, P, rankJ1, vpArray2D< Type >::resize(), vpMatrix::setIdentity(), vpERROR_TRACE, and WpW.

vpColVector vpServo::secondaryTask	(	const vpColVector &	e2,
		const vpColVector &	de2dt,
		const bool &	useLargeProjectionOperator = `false`
	)

Compute and return the secondary task vector according to the classic projection operator ${\bf I-W^+W}$ (see equation(7) in the paper [30]) or the new large projection operator (see equation(24) in the paper [32]).

Parameters

e2	: Value of the secondary task ${\bf e}_2$ .
de2dt	: Value of $\frac{\partial {\bf e_2}}{\partial t}$ the derivative of the secondary task ${\bf e}_2$ .
useLargeProjectionOperator	if true will be use the large projection operator, if false the classic one (default).

Returns: The secondary task vector.

If the classic projection operator is used ( useLargeProjectionOperator = false (default value)) this function return:

$-\lambda ({\bf I-W^+W}) {\bf e_2} + ({\bf I-W^+W})\frac{\partial {\bf e_2}}{\partial t}$

Note that the secondary task vector need than to be added to the primary task which can be in the general case written as:

$-\lambda {\bf W^+W {\widehat {\bf J}}_e^+({\bf s-s^*})}$

Otherwise if the new large projection operator is used ( useLargeProjectionOperator = true ) this function return:

$-\lambda {\bf P} {\bf e_2} + {\bf P}\frac{\partial {\bf e_2}}{\partial t}$

where

${\bf P} =\bar{\lambda }\left ( \left \| {\bf e} \right \| \right ){\bf P}_{ \left \| {\bf e } \right \| } \left ( 1 - \bar{\lambda }\left ( \left \| {\bf e } \right \| \right ) \right ) \left ( {\bf I-W^+W}\right )$

with

${\bf P}_{\left \| {\bf e } \right \| } = I_{n} - \frac{1}{{\bf e }^\top {\bf J_{{\bf e }} } {\bf J_{{\bf e }}^\top }{\bf e }}{\bf J_{{\bf e }}^\top }{\bf e }{\bf e }^\top{\bf J_{{\bf e }} }$

Warning: computeControlLaw() must be call prior to this function since it updates the projection operators.

The following sample code shows how to use this method to compute a secondary task using the classical projection operator:

vpColVector v;
// Velocity applied to the robot vpColVector e2; vpColVector de2dt; vpServo
task;
...
v  = task.computeControlLaw();     // Compute the primary task
v += task.secondaryTask(e2, de2dt) // Compute and add the secondary task using the classical projection operator

The following sample code shows how to use this method to compute a secondary task using the large projection operator:

vpColVector v;
// Velocity applied to the robot vpColVector e2; vpColVector de2dt; vpServo
task;
...
v  = task.computeControlLaw();     // Compute the primary task
v += task.secondaryTask(e2, de2dt, true) // Compute and add the secondary task using the large projection operator

See also: computeControlLaw()

Definition at line 1552 of file vpServo.cpp.

References computeProjectionOperators(), e1, error, vpArray2D< Type >::getCols(), I, I_WpW, J1, lambda, vpServoException::noDofFree, P, rankJ1, vpArray2D< Type >::resize(), vpMatrix::setIdentity(), vpERROR_TRACE, and WpW.

vpColVector vpServo::secondaryTaskJointLimitAvoidance	(	const vpColVector &	q,
		const vpColVector &	dq,
		const vpColVector &	qmin,
		const vpColVector &	qmax,
		const double &	rho = `0.1`,
		const double &	rho1 = `0.3`,
		const double &	lambda_tune = `0.7`
	)

Compute and return the secondary task vector for joint limit avoidance [33] using the new large projection operator (see equation(24) in the paper [32]). The robot avoids the joint limits very smoothly even when the main task constrains all the robot degrees of freedom.

Parameters

q	: Actual joint positions vector
dq	: Actual joint velocities vector
qmin	: Vector containing the low limit value of each joint in the chain.
qmax	: Vector containing the high limit value of each joint in the chain.
rho	: tuning paramenter ${\left [ 0,\frac{1}{2} \right]}$ used to define the safe configuration for the joint. When the joint angle value cross the max or min boundaries ( ${ q_{l_{0}}^{max} }$ and ${q_{l_{0}}^{min}}$ ) the secondary task is actived gradually.
rho1	: tuning paramenter ${\left ] 0,1 \right ]}$ to compute the external boundaries ( ${q_{l_{1}}^{max}}$ and ${q_{l_{1}}^{min}}$ ) for the joint limits. Here the secondary task it completely activated with the highest gain.
lambda_tune	: value ${\left [ 0,1 \right ]}$ used to tune the difference in magnitude between the absolute value of the elements of the primary task and the elements of the secondary task. (See equation (17) [33] )

vpServo task;
vpColVector qmin;
vpColVector qmax;
vpColVector q;
vpColVector dq;
// Fill vector qmin and qmax with min and max limits of the joints (same joint order than vector q).
// Update vector of joint position q and velocities dq;
...
// Compute the velocity corresponding to the visual servoing
vpColVector  v = task.computeControlLaw();
// Compute and add the secondary task for the joint limit avoidance
// using the large projection operator
v += task.secondaryTaskJointLimitAvoidance(q, dq, qmin, qmax)

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-large.cpp.

Definition at line 1630 of file vpServo.cpp.

References vpMath::abs(), computeProjectionOperators(), vpException::dimensionError, error, vpMatrix::getCol(), vpArray2D< Type >::getCols(), I, I_WpW, J1, P, vpArray2D< Type >::size(), and vpERROR_TRACE.

void vpServo::set_cVe ( const vpVelocityTwistMatrix & cVe_ )

inline

Set the velocity twist matrix used to transform a velocity skew vector from end-effector frame into the camera frame.

Examples:: manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuSphere.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 448 of file vpServo.h.

Referenced by setServo().

void vpServo::set_cVe ( const vpHomogeneousMatrix & cMe )

inline

Set the velocity twist matrix used to transform a velocity skew vector from end-effector frame into the camera frame.

Definition at line 457 of file vpServo.h.

void vpServo::set_cVf ( const vpVelocityTwistMatrix & cVf_ )

inline

Set the velocity twist matrix used to transform a velocity skew vector from robot fixed frame (also called world or base frame) into the camera frame.

Definition at line 467 of file vpServo.h.

void vpServo::set_cVf ( const vpHomogeneousMatrix & cMf )

inline

Set the velocity twist matrix used to transform a velocity skew vector from robot fixed frame (also called world or base frame) into the camera frame.

Definition at line 477 of file vpServo.h.

void vpServo::set_eJe ( const vpMatrix & eJe_ )

inline

Set the robot jacobian expressed in the end-effector frame.

Examples:: manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuSphere.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 506 of file vpServo.h.

Referenced by setServo().

void vpServo::set_fJe ( const vpMatrix & fJe_ )

inline

Set the robot jacobian expressed in the robot fixed frame (also called world or base frame).

Definition at line 515 of file vpServo.h.

void vpServo::set_fVe ( const vpVelocityTwistMatrix & fVe_ )

inline

Set the velocity twist matrix used to transform a velocity skew vector from robot end-effector frame into the fixed frame (also called world or base frame).

Definition at line 487 of file vpServo.h.

void vpServo::set_fVe ( const vpHomogeneousMatrix & fMe )

inline

Set the velocity twist matrix used to transform a velocity skew vector from robot end-effector frame into the fixed frame (also called world or base frame).

Definition at line 497 of file vpServo.h.

void vpServo::setCameraDoF ( const vpColVector & dof )

Set a 6-dim column vector representing the degrees of freedom that are controlled in the camera frame. When set to 1, all the 6 dof are controlled.

Parameters

dof

: Degrees of freedom to control in the camera frame. Below we give the correspondance between the index of the vector and the considered dof:

dof[0] = 1 if translation along X is controled, 0 otherwise;
dof[1] = 1 if translation along Y is controled, 0 otherwise;
dof[2] = 1 if translation along Z is controled, 0 otherwise;
dof[3] = 1 if rotation along X is controled, 0 otherwise;
dof[4] = 1 if rotation along Y is controled, 0 otherwise;
dof[5] = 1 if rotation along Z is controled, 0 otherwise;

The following example shows how to use this function to control only wx, wy like a pan/tilt:

#include <visp3/visual_features/vpFeaturePoint.h>
#include <visp3/vs/vpServo.h>
int main()
{
  vpServo servo;
  servo.setServo(vpServo::EYEINHAND_CAMERA);
  vpFeaturePoint s, sd;
  servo.addFeature(s, sd);
  vpColVector dof(6, 1);
  dof[0] = 0; // turn off vx
  dof[1] = 0; // turn off vy
  dof[2] = 0; // turn off vz
  dof[5] = 0; // turn off wz
  servo.setCameraDoF(dof);
  while(1) {
    // vpFeatureBuilder::create(s, ...);       // update current feature
    vpColVector v = servo.computeControlLaw(); // compute control law
    // only v[3] and v[4] corresponding to wx and wy are different from 0
  }
}

Definition at line 282 of file vpServo.cpp.

References cJc, iscJcIdentity, and vpArray2D< Type >::size().

void vpServo::setForceInteractionMatrixComputation ( bool force_computation )

inline

Set a variable which enables to compute the interaction matrix at each iteration.

When the interaction matrix is computed from the desired features ${\bf s}^*$ which are in general constant, the interaction matrix ${\widehat {\bf L}}_{s^*}$ is computed just at the first iteration of the servo loop. Sometimes, when the desired features are time dependent ${{\bf s}(t)}^*$ or varying, the interaction matrix need to be computed at each iteration of the servo loop. This method allows to force the computation of ${\widehat {\bf L}}$ in this particular case.

Parameters

force_computation : If true it forces the interaction matrix computation even if it is already done.

Definition at line 379 of file vpServo.h.

void vpServo::setInteractionMatrixType	(	const vpServoIteractionMatrixType &	interactionMatrixType,
		const vpServoInversionType &	interactionMatrixInversion = `PSEUDO_INVERSE`
	)

Set the interaction matrix type (current, desired, mean or user defined) and how its inverse is computed.

Parameters

interactionMatrixType	: The interaction matrix type. See vpServo::vpServoIteractionMatrixType for more details.
interactionMatrixInversion	: How is the inverse computed. See vpServo::vpServoInversionType for more details.

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuSphere.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeatureSegment.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 567 of file vpServo.cpp.

References featureList, featureSelectionList, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), interactionMatrixType, inversionType, L, vpServoException::noFeatureError, vpArray2D< Type >::resize(), vpDEBUG_TRACE, and vpERROR_TRACE.

Referenced by vpVirtualGrabber::acquire().

void vpServo::setLambda ( double c )

inline

Set the gain $\lambda$ used in the control law (see vpServo::vpServoType) as constant.

The usage of an adaptive gain allows to reduce the convergence time, see setLambda(const vpAdaptiveGain&).

Parameters

c	: Constant gain. Values are in general between 0.1 and 1. Higher is the gain, higher are the velocities that may be applied to the robot.

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeatureSegment.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 404 of file vpServo.h.

Referenced by vpVirtualGrabber::acquire().

void vpServo::setLambda	(	double	gain_at_zero,
		double	gain_at_infinity,
		double	slope_at_zero
	)

inline

Set the gain $\lambda$ used in the control law (see vpServo::vpServoType) as adaptive. Value of $\lambda$ that is used in computeControlLaw() depend on the infinity norm of the task Jacobian.

The usage of an adaptive gain rather than a constant gain allows to reduce the convergence time.

Parameters

gain_at_zero	: the expected gain when : $\lambda(0)$ .
gain_at_infinity	: the expected gain when $x=\infty$ : $\lambda(\infty)$ .
slope_at_zero	: the expected slope of $\lambda(x)$ when : ${\dot \lambda}(0)$ .

For more details on these parameters see vpAdaptiveGain class.

Definition at line 421 of file vpServo.h.

void vpServo::setLambda ( const vpAdaptiveGain & l )

inline

Set the gain $\lambda$ used in the control law (see vpServo::vpServoType) as adaptive. Value of $\lambda$ that is used in computeControlLaw() depend on the infinity norm of the task Jacobian.

The usage of an adaptive gain rather than a constant gain allows to reduce the convergence time.

See also: vpAdaptiveGain

Definition at line 433 of file vpServo.h.

void vpServo::setMu ( double mu_ )

inline

Set the value of the parameter $\mu$ used to ensure the continuity of the velocities computed using computeControlLaw(double).

A recommended value is 4.

Definition at line 440 of file vpServo.h.

void vpServo::setPseudoInverseThreshold ( double pseudo_inverse_threshold )

Set the pseudo-inverse threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

Parameters

pseudo_inverse_threshold : Value to use. Default value is set to 1e-6.

See also: getPseudoInverseThreshold()

Definition at line 1824 of file vpServo.cpp.

References m_pseudo_inverse_threshold.

void vpServo::setServo ( const vpServoType & servo_type )

Set the visual servoing control law.

Parameters

servo_type : Control law that will be considered. See vpServo::vpServoType to see the possible values.

Examples:: manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper650FourPoints2DCamVelocityLs_cur-SR300.cpp, servoViper650FourPoints2DCamVelocityLs_cur.cpp, servoViper650Point2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850FourPoints2DCamVelocityLs_cur.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeatureSegment.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 218 of file vpServo.cpp.

References vpMatrix::eye(), EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, servoType, set_cVe(), set_eJe(), and signInteractionMatrix.

Referenced by vpVirtualGrabber::acquire().

bool vpServo::testInitialization ( )

Test if all the initialization are correct. If true, the control law can be computed.

Definition at line 825 of file vpServo.cpp.

References EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fJe, EYETOHAND_L_cVf_fVe_eJe, init_cVe, init_cVf, init_eJe, init_fJe, init_fVe, NONE, vpServoException::servoError, servoType, and vpERROR_TRACE.

Referenced by computeControlLaw().

bool vpServo::testUpdated ( )

Test if all the update are correct. If true control law can be computed.

Definition at line 865 of file vpServo.cpp.

References EYEINHAND_CAMERA, EYEINHAND_L_cVe_eJe, EYETOHAND_L_cVe_eJe, EYETOHAND_L_cVf_fJe, EYETOHAND_L_cVf_fVe_eJe, init_cVe, init_eJe, init_fJe, init_fVe, NONE, vpServoException::servoError, servoType, and vpERROR_TRACE.

Referenced by computeControlLaw().

Member Data Documentation

vpMatrix vpServo::cJc

protected

A diag matrix used to determine which are the degrees of freedom that are controlled in the camera frame

Definition at line 678 of file vpServo.h.

Referenced by computeControlLaw(), setCameraDoF(), and vpServo().

vpVelocityTwistMatrix vpServo::cVe

protected

Twist transformation matrix between Re and Rc.

Definition at line 606 of file vpServo.h.

Referenced by computeControlLaw().

vpVelocityTwistMatrix vpServo::cVf

protected

Twist transformation matrix between Rf and Rc.

Definition at line 609 of file vpServo.h.

Referenced by computeControlLaw().

std::list<vpBasicFeature *> vpServo::desiredFeatureList

List of desired visual features $\bf s^*$ .

Definition at line 583 of file vpServo.h.

Referenced by addFeature(), computeError(), computeInteractionMatrix(), vpServoDisplay::display(), init(), kill(), and print().

unsigned int vpServo::dim_task

protected

Dimension of the task updated during computeControlLaw().

Definition at line 635 of file vpServo.h.

Referenced by computeError(), computeInteractionMatrix(), and init().

vpColVector vpServo::e

Task $e = e_1 + (I-{J_1}^{+} J_1) e_2$ .

Definition at line 567 of file vpServo.h.

Referenced by computeControlLaw().

vpColVector vpServo::e1

Primary task $e_1 = {J_1}^{+}(s-s*)$ .

Definition at line 565 of file vpServo.h.

Referenced by computeControlLaw(), and secondaryTask().

vpColVector vpServo::e1_initial

protected

Definition at line 671 of file vpServo.h.

Referenced by computeControlLaw().

vpMatrix vpServo::eJe

protected

Jacobian expressed in the end-effector frame.

Definition at line 620 of file vpServo.h.

Referenced by computeControlLaw().

vpColVector vpServo::error

Error $(s - s^*)$ between the current set of visual features $s$ and the desired set of visual features $s^*$ . This vector is updated after a call of computeError() or computeControlLaw().

Definition at line 549 of file vpServo.h.

Referenced by computeControlLaw(), computeError(), print(), secondaryTask(), and secondaryTaskJointLimitAvoidance().

bool vpServo::errorComputed

protected

true if the error has been computed.

Definition at line 631 of file vpServo.h.

Referenced by computeError(), init(), and print().

std::list<vpBasicFeature *> vpServo::featureList

List of current visual features $\bf s$ .

Definition at line 581 of file vpServo.h.

Referenced by addFeature(), computeError(), computeInteractionMatrix(), vpServoDisplay::display(), getDimension(), init(), kill(), print(), and setInteractionMatrixType().

std::list<unsigned int> vpServo::featureSelectionList

List of selection among visual features used for selection of a subset of each visual feature if required.

Definition at line 586 of file vpServo.h.

Referenced by addFeature(), computeError(), computeInteractionMatrix(), getDimension(), init(), print(), and setInteractionMatrixType().

vpMatrix vpServo::fJe

protected

Jacobian expressed in the robot reference frame.

Definition at line 623 of file vpServo.h.

Referenced by computeControlLaw().

bool vpServo::forceInteractionMatrixComputation

protected

Force the interaction matrix computation even if it is already done.

Definition at line 639 of file vpServo.h.

Referenced by computeInteractionMatrix(), and init().

vpVelocityTwistMatrix vpServo::fVe

protected

Twist transformation matrix between Re and Rf.

Definition at line 612 of file vpServo.h.

Referenced by computeControlLaw().

vpMatrix vpServo::I

protected

Identity matrix.

Definition at line 642 of file vpServo.h.

Referenced by computeControlLaw(), secondaryTask(), and secondaryTaskJointLimitAvoidance().

vpMatrix vpServo::I_WpW

protected

Projection operators $\bf I-WpW$ .

Definition at line 646 of file vpServo.h.

Referenced by computeControlLaw(), getI_WpW(), secondaryTask(), and secondaryTaskJointLimitAvoidance().

bool vpServo::init_cVe

protected

Definition at line 607 of file vpServo.h.

Referenced by computeControlLaw(), init(), testInitialization(), and testUpdated().

bool vpServo::init_cVf

protected

Definition at line 610 of file vpServo.h.

Referenced by init(), and testInitialization().

bool vpServo::init_eJe

protected

Definition at line 621 of file vpServo.h.

Referenced by computeControlLaw(), init(), testInitialization(), and testUpdated().

bool vpServo::init_fJe

protected

Definition at line 624 of file vpServo.h.

Referenced by computeControlLaw(), init(), testInitialization(), and testUpdated().

bool vpServo::init_fVe

protected

Definition at line 613 of file vpServo.h.

Referenced by computeControlLaw(), init(), testInitialization(), and testUpdated().

bool vpServo::interactionMatrixComputed

protected

true if the interaction matrix has been computed.

Definition at line 633 of file vpServo.h.

Referenced by computeInteractionMatrix(), init(), and print().

vpServoIteractionMatrixType vpServo::interactionMatrixType

Type of the interaction matrox (current, mean, desired, user)

Definition at line 595 of file vpServo.h.

Referenced by computeInteractionMatrix(), init(), and setInteractionMatrixType().

vpServoInversionType vpServo::inversionType

Indicates if the transpose or the pseudo inverse of the interaction matrix should be used to compute the task.

Definition at line 598 of file vpServo.h.

Referenced by computeControlLaw(), init(), and setInteractionMatrixType().

bool vpServo::iscJcIdentity

protected

Boolean to know if cJc is identity (for fast computation)

Definition at line 674 of file vpServo.h.

Referenced by computeControlLaw(), and setCameraDoF().

vpMatrix vpServo::J1

Task Jacobian $J_1 = L {^c}V_a {^a}J_e$ .

Definition at line 551 of file vpServo.h.

Referenced by computeControlLaw(), getTaskJacobian(), secondaryTask(), and secondaryTaskJointLimitAvoidance().

vpMatrix vpServo::J1p

Pseudo inverse ${J_1}^{+}$ of the task Jacobian.

Definition at line 553 of file vpServo.h.

Referenced by computeControlLaw(), and getTaskJacobianPseudoInverse().

vpMatrix vpServo::L

Interaction matrix.

Definition at line 544 of file vpServo.h.

Referenced by computeInteractionMatrix(), print(), and setInteractionMatrixType().

vpAdaptiveGain vpServo::lambda

Gain used in the control law.

Definition at line 589 of file vpServo.h.

Referenced by computeControlLaw(), print(), and secondaryTask().

bool vpServo::m_first_iteration

protected

True until first call of computeControlLaw() is achieved.

Definition at line 680 of file vpServo.h.

Referenced by computeControlLaw(), and init().

double vpServo::m_pseudo_inverse_threshold

protected

Threshold used in the pseudo inverse.

Definition at line 682 of file vpServo.h.

Referenced by computeControlLaw(), getPseudoInverseThreshold(), and setPseudoInverseThreshold().

double vpServo::mu

protected

Definition at line 669 of file vpServo.h.

Referenced by computeControlLaw().

vpMatrix vpServo::P

protected

New Large projection operator (see equation(24) in the paper [32]). This projection operator allows performing secondary task even when the main task is full rank.

${\bf P} =\bar{\lambda }\left ( \left \| {\bf e} \right \| \right ){\bf P}_{ \left \| {\bf e } \right \| } \left ( 1 - \bar{\lambda }\left ( \left \| {\bf e } \right \| \right ) \right ) \left ( {\bf I-W^+W}\right )$

with

${\bf P}_{\left \| {\bf e } \right \| } = I_{n} - \frac{1}{{\bf e }^\top {\bf J_{{\bf e }} } {\bf J_{{\bf e }}^\top } {\bf e }}{\bf J_{{\bf e }}^\top }{\bf e }{\bf e }^\top{\bf J_{{\bf e }} }$