ViSP  2.9.0

#include <vpViper.h>

+ Inheritance diagram for vpViper:

Public Member Functions

 vpViper ()
 
virtual ~vpViper ()
 
vpHomogeneousMatrix getForwardKinematics (const vpColVector &q) const
 
unsigned int getInverseKinematicsWrist (const vpHomogeneousMatrix &fMw, vpColVector &q, const bool &verbose=false) const
 
unsigned int getInverseKinematics (const vpHomogeneousMatrix &fMc, vpColVector &q, const bool &verbose=false) const
 
vpHomogeneousMatrix get_fMc (const vpColVector &q) const
 
void get_fMw (const vpColVector &q, vpHomogeneousMatrix &fMw) const
 
void get_wMe (vpHomogeneousMatrix &wMe) const
 
void get_eMc (vpHomogeneousMatrix &eMc) const
 
void get_fMe (const vpColVector &q, vpHomogeneousMatrix &fMe) const
 
void get_fMc (const vpColVector &q, vpHomogeneousMatrix &fMc) const
 
void get_cMe (vpHomogeneousMatrix &cMe) const
 
void get_cVe (vpVelocityTwistMatrix &cVe) const
 
void get_fJw (const vpColVector &q, vpMatrix &fJw) const
 
void get_fJe (const vpColVector &q, vpMatrix &fJe) const
 
void get_eJe (const vpColVector &q, vpMatrix &eJe) const
 
vpColVector getJointMin () const
 
vpColVector getJointMax () const
 
double getCoupl56 () const
 

Static Public Attributes

static const unsigned int njoint = 6
 

Protected Attributes

vpHomogeneousMatrix eMc
 
vpTranslationVector etc
 
vpRxyzVector erc
 
double a1
 
double d1
 
double a2
 
double a3
 
double d4
 
double d6
 
double c56
 
vpColVector joint_max
 
vpColVector joint_min
 

Friends

VISP_EXPORT std::ostream & operator<< (std::ostream &os, const vpViper &viper)
 

Detailed Description

Modelisation of the ADEPT Viper robot.

This robot has six degrees of freedom.

The non modified Denavit-Hartenberg representation of the robot is given in the table below, where $q_1^*, \ldots, q_6^*$ are the variable joint positions.

\[ \begin{tabular}{|c|c|c|c|c|} \hline Joint & $a_i$ & $d_i$ & $\alpha_i$ & $\theta_i$ \\ \hline 1 & $a_1$ & $d_1$ & $-\pi/2$ & $q_1^*$ \\ 2 & $a_2$ & 0 & 0 & $q_2^*$ \\ 3 & $a_3$ & 0 & $-\pi/2$ & $q_3^* - \pi$ \\ 4 & 0 & $d_4$ & $\pi/2$ & $q_4^*$ \\ 5 & 0 & 0 & $-\pi/2$ & $q_5^*$ \\ 6 & 0 & 0 & 0 & $q_6^*-\pi$ \\ 7 & 0 & $d_6$ & 0 & 0 \\ \hline \end{tabular} \]

In this modelisation, different frames have to be considered.

  • $ {\cal F}_f $: the reference frame, also called world frame,
  • $ {\cal F}_w $: the wrist frame located at the intersection of the last three rotations, with $ ^f{\bf M}_w = ^0{\bf M}_6 $,
  • $ {\cal F}_e $: the end-effector frame, with $^f{\bf M}_e = 0{\bf M}_7 $,
  • $ {\cal F}_c $: the camera frame, with $^f{\bf M}_c = ^f{\bf M}_e \; ^e{\bf M}_c $ where $ ^e{\bf M}_c $ is the result of a calibration stage.

The forward kinematics of the robot is implemented in get_fMw(), get_fMe() and get_fMc().

The robot forward jacobian used to compute the cartesian velocities from joint ones is given and implemented in get_fJw(), get_fJe() and get_eJe().

Definition at line 111 of file vpViper.h.

Constructor & Destructor Documentation

vpViper::vpViper ( )

Default constructor.

Definition at line 70 of file vpViper.cpp.

References a1, a2, a3, c56, d1, d4, d6, eMc, joint_max, joint_min, njoint, vpMath::rad(), vpColVector::resize(), and vpHomogeneousMatrix::setIdentity().

virtual vpViper::~vpViper ( )
inlinevirtual

Definition at line 115 of file vpViper.h.

Member Function Documentation

void vpViper::get_cMe ( vpHomogeneousMatrix cMe) const

Get the geometric transformation between the camera frame and the end-effector frame. This transformation is constant and correspond to the extrinsic camera parameters estimated by calibration.

Parameters
cMe: Transformation between the camera frame and the end-effector frame.
See also
get_eMc()

Definition at line 931 of file vpViper.cpp.

References eMc, and vpHomogeneousMatrix::inverse().

Referenced by vpSimulatorViper850::get_cMe(), vpRobotViper650::get_cMe(), vpRobotViper850::get_cMe(), get_cVe(), vpSimulatorViper850::get_cVe(), vpRobotViper650::get_cVe(), and vpRobotViper850::get_cVe().

void vpViper::get_cVe ( vpVelocityTwistMatrix cVe) const

Get the twist transformation $^c{\bf V}_e$ from camera frame to end-effector frame. This transformation allows to compute a velocity expressed in the end-effector frame into the camera frame.

\[ ^c{\bf V}_e = \left(\begin{array}{cc} ^c{\bf R}_e & [^c{\bf t}_e]_\times ^c{\bf R}_e\\ {\bf 0}_{3\times 3} & ^c{\bf R}_e \end{array} \right) \]

Parameters
cVe: Twist transformation $^c{\bf V}_e$.

Definition at line 952 of file vpViper.cpp.

References vpVelocityTwistMatrix::buildFrom(), and get_cMe().

void vpViper::get_eJe ( const vpColVector q,
vpMatrix eJe 
) const

Get the robot jacobian ${^e}{\bf J}_e$ which gives the velocity of the origin of the end-effector frame expressed in end-effector frame.

\[ {^e}{\bf J}_e = \left[\begin{array}{cc} {^w}{\bf R}_f & {[{^e}{\bf t}_w}]_\times \; {^w}{\bf R}_f \\ 0_{3\times3} & {^w}{\bf R}_f \end{array} \right] \; {^f}{\bf J}_w \]

Parameters
q: A six-dimension vector that contains the joint positions of the robot expressed in radians.
eJe: Robot jacobian ${^e}{\bf J}_e$ that express the velocity of the end-effector in the robot end-effector frame.
See also
get_fJw()

Definition at line 985 of file vpViper.cpp.

References vpHomogeneousMatrix::extract(), get_fJw(), get_fMw(), get_wMe(), vpRotationMatrix::inverse(), vpHomogeneousMatrix::inverse(), and vpTranslationVector::skew().

Referenced by vpSimulatorViper850::computeArticularVelocity(), vpSimulatorViper850::get_eJe(), vpRobotViper650::get_eJe(), vpRobotViper850::get_eJe(), and vpSimulatorViper850::getVelocity().

void vpViper::get_eMc ( vpHomogeneousMatrix eMc_) const

Get the geometric transformation between the end-effector frame and the camera frame. This transformation is constant and correspond to the extrinsic camera parameters estimated by calibration.

Parameters
eMc_: Transformation between the the end-effector frame and the camera frame.
See also
get_cMe()

Definition at line 914 of file vpViper.cpp.

References eMc.

Referenced by getInverseKinematics().

void vpViper::get_fJe ( const vpColVector q,
vpMatrix fJe 
) const

Get the robot jacobian ${^f}{\bf J}_e$ which gives the velocity of the origin of the end-effector frame expressed in the robot reference frame also called fix frame.

\[ {^f}{\bf J}_e = \left[\begin{array}{cc} I_{3\times3} & [{^f}{\bf R}_w \; {^e}{\bf t}_w]_\times \\ 0_{3\times3} & I_{3\times3} \end{array} \right] {^f}{\bf J}_w \]

Parameters
q: A six-dimension vector that contains the joint positions of the robot expressed in radians.
fJe: Robot jacobian ${^f}{\bf J}_e$ that express the velocity of the end-effector in the robot reference frame.
See also
get_fJw

Definition at line 1177 of file vpViper.cpp.

References vpHomogeneousMatrix::extract(), get_fJw(), get_fMw(), get_wMe(), and vpHomogeneousMatrix::inverse().

Referenced by vpSimulatorViper850::computeArticularVelocity(), vpSimulatorViper850::get_fJe(), vpRobotViper650::get_fJe(), vpRobotViper850::get_fJe(), and vpSimulatorViper850::getVelocity().

void vpViper::get_fJw ( const vpColVector q,
vpMatrix fJw 
) const

Get the robot jacobian ${^f}{\bf J}_w$ which express the velocity of the origin of the wrist frame in the robot reference frame also called fix frame.

\[ {^f}J_w = \left(\begin{array}{cccccc} J_{11} & J_{12} & J_{13} & 0 & 0 & 0 \\ J_{21} & J_{22} & J_{23} & 0 & 0 & 0 \\ 0 & J_{32} & J_{33} & 0 & 0 & 0 \\ 0 & -s1 & -s1 & c1s23 & J_{45} & J_{46} \\ 0 & c1 & c1 & s1s23 & J_{55} & J_{56} \\ 1 & 0 & 0 & c23 & s23s4 & J_{56} \\ \end{array} \right) \]

with

\[ \begin{array}{l} J_{11} = -s1(-c23a3+s23d4+a1+a2c2) \\ J_{21} = c1(-c23a3+s23d4+a1+a2c2) \\ J_{12} = c1(s23a3+c23d4-a2s2) \\ J_{22} = s1(s23a3+c23d4-a2s2) \\ J_{32} = c23a3-s23d4-a2c2 \\ J_{13} = c1(a3(s2c3+c2s3)+(-s2s3+c2c3)d4)\\ J_{23} = s1(a3(s2c3+c2s3)+(-s2s3+c2c3)d4)\\ J_{33} = -a3(s2s3-c2c3)-d4(s2c3+c2s3)\\ J_{45} = -c23c1s4-s1c4\\ J_{55} = c1c4-c23s1s4\\ J_{46} = (c1c23c4-s1s4)s5+c1s23c5\\ J_{56} = (s1c23c4+c1s4)s5+s1s23c5\\ J_{66} = -s23c4s5+c23c5\\ \end{array} \]

Parameters
q: A six-dimension vector that contains the joint positions of the robot expressed in radians.
fJw: Robot jacobian ${^f}{\bf J}_w$ that express the velocity of the point w (origin of the wrist frame) in the robot reference frame.
See also
get_fJe(), get_eJe()

Definition at line 1071 of file vpViper.cpp.

References a1, a2, a3, d4, and vpMatrix::resize().

Referenced by get_eJe(), and get_fJe().

vpHomogeneousMatrix vpViper::get_fMc ( const vpColVector q) const

Compute the forward kinematics (direct geometric model) as an homogeneous matrix.

By forward kinematics we mean here the position and the orientation of the camera relative to the base frame given the joint positions of all the six joints.

\[ ^f{\bf M}_c = ^f{\bf M}_e \; ^e{\bf M}_c \]

This method is the same than getForwardKinematics(const vpColVector & q).

Parameters
q: Vector of six joint positions expressed in radians.
Returns
The homogeneous matrix corresponding to the direct geometric model which expresses the transformation between the base frame and the camera frame (fMc).
See also
getForwardKinematics(const vpColVector & q), get_fMe(), get_eMc()
Examples:
testRobotViper850Pose.cpp.

Definition at line 615 of file vpViper.cpp.

Referenced by vpSimulatorViper850::compute_fMi(), getForwardKinematics(), vpSimulatorViper850::getPosition(), vpRobotViper650::getVelocity(), vpRobotViper850::getVelocity(), vpSimulatorViper850::setPosition(), vpRobotViper650::setPosition(), and vpRobotViper850::setPosition().

void vpViper::get_fMc ( const vpColVector q,
vpHomogeneousMatrix fMc 
) const

Compute the forward kinematics (direct geometric model) as an homogeneous matrix.

By forward kinematics we mean here the position and the orientation of the camera relative to the base frame given the six joint positions.

\[ ^f{\bf M}_c = ^f{\bf M}_e \; {^e}{\bf M}_c \]

Parameters
q: Vector of six joint positions expressed in radians.
fMcThe homogeneous matrix $^f{\bf M}_c$corresponding to the direct geometric model which expresses the transformation between the fix frame and the camera frame.
See also
get_fMe(), get_eMc()

Definition at line 645 of file vpViper.cpp.

References eMc, and get_fMe().

void vpViper::get_fMe ( const vpColVector q,
vpHomogeneousMatrix fMe 
) const

Compute the forward kinematics (direct geometric model) as an homogeneous matrix ${^f}{\bf M}_e$.

By forward kinematics we mean here the position and the orientation of the end effector with respect to the base frame given the motor positions of all the six joints.

\[ {^f}M_e = \left(\begin{array}{cccc} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ \end{array} \right) \]

with

\[ \begin{array}{l} r_{11} = c1(c23(c4c5c6-s4s6)-s23s5c6)-s1(s4c5c6+c4s6) \\ r_{21} = -s1(c23(-c4c5c6+s4s6)+s23s5c6)+c1(s4c5c6+c4s6) \\ r_{31} = s23(s4s6-c4c5c6)-c23s5c6 \\ \\ r_{12} = -c1(c23(c4c5s6+s4c6)-s23s5s6)+s1(s4c5s6-c4c6)\\ r_{22} = -s1(c23(c4c5s6+s4c6)-s23s5s6)-c1(s4c5s6-c4c6)\\ r_{32} = s23(c4c5s6+s4c6)+c23s5s6\\ \\ r_{13} = c1(c23c4s5+s23c5)-s1s4s5\\ r_{23} = s1(c23c4s5+s23c5)+c1s4s5\\ r_{33} = -s23c4s5+c23c5\\ \\ t_x = c1(c23(c4s5d6-a3)+s23(c5d6+d4)+a1+a2c2)-s1s4s5d6\\ t_y = s1(c23(c4s5d6-a3)+s23(c5d6+d4)+a1+a2c2)+c1s4s5d6\\ t_z = s23(a3-c4s5d6)+c23(c5d6+d4)-a2s2+d1\\ \end{array} \]

Parameters
q: A 6-dimension vector that contains the 6 joint positions expressed in radians.
fMeThe homogeneous matrix ${^f}{\bf M}_e$ corresponding to the direct geometric model which expresses the transformation between the fix frame and the end effector frame.

Note that this transformation can also be computed by considering the wrist frame ${^f}{\bf M}_e = {^f}{\bf M}_w *{^w}{\bf M}_e$.

#include <visp/vpViper.h>
int main()
{
vpViper robot;
vpColVector q(6); // The measured six joint positions
vpHomogeneousMatrix fMe; // Transformation from fix frame to end-effector
robot.get_fMe(q, fMe); // Get the forward kinematics
// The forward kinematics can also be computed by considering the wrist frame
vpHomogeneousMatrix fMw; // Transformation from fix frame to wrist frame
robot.get_fMw(q, fMw);
vpHomogeneousMatrix wMe; // Transformation from wrist frame to end-effector
robot.get_wMe(wMe); // Constant transformation
// Compute the forward kinematics
fMe = fMw * wMe;
}
Examples:
testRobotViper850.cpp, and testViper850.cpp.

Definition at line 732 of file vpViper.cpp.

References a1, a2, a3, d1, d4, and d6.

Referenced by get_fMc().

void vpViper::get_fMw ( const vpColVector q,
vpHomogeneousMatrix fMw 
) const

Compute the transformation between the fix frame and the wrist frame. The wrist frame is located on the intersection of the 3 last rotations.

Parameters
q: A 6-dimension vector that contains the 6 joint positions expressed in radians.
fMwThe homogeneous matrix corresponding to the transformation between the fix frame and the wrist frame (fMw).

\[ {^f}M_w = \left(\begin{array}{cccc} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ \end{array} \right) \]

with

\[ \begin{array}{l} r_{11} = c1(c23(c4c5c6-s4s6)-s23s5c6)-s1(s4c5c6+c4s6) \\ r_{21} = -s1(c23(-c4c5c6+s4s6)+s23s5c6)+c1(s4c5c6+c4s6) \\ r_{31} = s23(s4s6-c4c5c6)-c23s5c6 \\ \\ r_{12} = -c1(c23(c4c5s6+s4c6)-s23s5s6)+s1(s4c5s6-c4c6)\\ r_{22} = -s1(c23(c4c5s6+s4c6)-s23s5s6)-c1(s4c5s6-c4c6)\\ r_{32} = s23(c4c5s6+s4c6)+c23s5s6\\ \\ r_{13} = c1(c23c4s5+s23c5)-s1s4s5\\ r_{23} = s1(c23c4s5+s23c5)+c1s4s5\\ r_{33} = -s23c4s5+c23c5\\ \\ t_x = c1(-c23a3+s23d4+a1+a2c2)\\ t_y = s1(-c23a3+s23d4+a1+a2c2)\\ t_z = s23a3+c23d4-a2s2+d1\\ \end{array} \]

Definition at line 828 of file vpViper.cpp.

References a1, a2, a3, d1, and d4.

Referenced by get_eJe(), and get_fJe().

void vpViper::get_wMe ( vpHomogeneousMatrix wMe) const

Return the transformation between the wrist frame and the end-effector. The wrist frame is located on the intersection of the 3 last rotations.

Parameters
wMeThe homogeneous matrix corresponding to the transformation between the wrist frame and the end-effector frame (wMe).

Definition at line 893 of file vpViper.cpp.

References d6, and vpHomogeneousMatrix::setIdentity().

Referenced by get_eJe(), get_fJe(), and getInverseKinematics().

double vpViper::getCoupl56 ( ) const

Return the coupling factor between join 5 and joint 6.

This factor should be only useful when motor positions are considered. Since the positions returned by the robot are joint positions which takes into account the coupling factor, it has not to be considered in the modelization of the robot.

Definition at line 1248 of file vpViper.cpp.

References c56.

vpHomogeneousMatrix vpViper::getForwardKinematics ( const vpColVector q) const

Compute the forward kinematics (direct geometric model) as an homogeneous matrix.

By forward kinematics we mean here the position and the orientation of the camera relative to the base frame given the six joint positions.

This method is the same than get_fMc(const vpColVector & q).

Parameters
q: A six dimension vector corresponding to the robot joint positions expressed in radians.
Returns
The homogeneous matrix $^f{\bf M}_c $ corresponding to the direct geometric model which expresses the transformation between the base frame and the camera frame.
See also
get_fMc(const vpColVector & q)
getInverseKinematics()

Definition at line 129 of file vpViper.cpp.

References get_fMc().

unsigned int vpViper::getInverseKinematics ( const vpHomogeneousMatrix fMc,
vpColVector q,
const bool &  verbose = false 
) const

Compute the inverse kinematics (inverse geometric model).

By inverse kinematics we mean here the six joint values given the position and the orientation of the camera frame relative to the base frame.

Parameters
fMc: Homogeneous matrix $^f{\bf M}_c $ describing the transformation from base frame to the camera frame.
q: In input, a six dimension vector corresponding to the current joint positions expressed in radians. In output, the solution of the inverse kinematics, ie. the joint positions corresponding to $^f{\bf M}_c $.
verbose: Add extra printings.
Returns
Add printings if no solution was found.
The number of solutions (1 to 8) of the inverse geometric model. O, if no solution can be found.

The code below shows how to compute the inverse geometric model:

vpColVector q1(6), q2(6);
vpViper robot;
// Get the current joint position of the robot
robot.getPosition(vpRobot::ARTICULAR_FRAME, q1);
// Compute the pose of the camera in the reference frame using the
// direct geometric model
fMc = robot.getForwardKinematics(q1);
// this is similar to fMc = robot.get_fMc(q1);
// or robot.get_fMc(q1, fMc);
// Compute the inverse geometric model
int nbsol; // number of solutions (0, 1 to 8) of the inverse geometric model
// get the nearest solution to the current joint position
nbsol = robot.getInverseKinematics(fMc, q1);
if (nbsol == 0)
std::cout << "No solution of the inverse geometric model " << std::endl;
else if (nbsol >= 1)
std::cout << "Nearest solution: " << q1 << std::endl;
See also
getForwardKinematics(), getInverseKinematicsWrist

Definition at line 577 of file vpViper.cpp.

References get_eMc(), get_wMe(), getInverseKinematicsWrist(), and vpHomogeneousMatrix::inverse().

Referenced by vpSimulatorViper850::initialiseCameraRelativeToObject(), vpSimulatorViper850::setPosition(), vpRobotViper650::setPosition(), and vpRobotViper850::setPosition().

unsigned int vpViper::getInverseKinematicsWrist ( const vpHomogeneousMatrix fMw,
vpColVector q,
const bool &  verbose = false 
) const

Compute the inverse kinematics (inverse geometric model).

By inverse kinematics we mean here the six joint values given the position and the orientation of the camera frame relative to the base frame.

Parameters
fMw: Homogeneous matrix $^f{\bf M}_w $ describing the transformation from base frame to the wrist frame.
q: In input, a six dimension vector corresponding to the current joint positions expressed in radians. In output, the solution of the inverse kinematics, ie. the joint positions corresponding to $^f{\bf M}_w $.
verbose: Add extra printings.
Returns
Add printings if no solution was found.
The number of solutions (1 to 8) of the inverse geometric model. O, if no solution can be found.

The code below shows how to compute the inverse geometric model:

vpColVector q1(6), q2(6);
vpViper robot;
// Get the current joint position of the robot
robot.getPosition(vpRobot::ARTICULAR_FRAME, q1);
// Compute the pose of the wrist in the reference frame using the
// direct geometric model
robot.get_fMw(q1, fMw);
// Compute the inverse geometric model
int nbsol; // number of solutions (0, 1 to 8) of the inverse geometric model
// get the nearest solution to the current joint position
nbsol = robot.getInverseKinematicsWrist(fMw, q1);
if (nbsol == 0)
std::cout << "No solution of the inverse geometric model " << std::endl;
else if (nbsol >= 1)
std::cout << "Nearest solution: " << q1 << std::endl;
See also
getForwardKinematics(), getInverseKinematics()

Definition at line 232 of file vpViper.cpp.

References a1, a2, a3, d1, d4, vpMatrix::getRows(), njoint, vpMath::rad(), vpColVector::resize(), and vpMath::sqr().

Referenced by getInverseKinematics().

vpColVector vpViper::getJointMax ( ) const

Get maximal joint values.

Returns
A 6-dimension vector that contains the maximal joint values for the 6 dof. All the values are expressed in radians.
Examples:
servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, and servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp.

Definition at line 1232 of file vpViper.cpp.

References joint_max.

vpColVector vpViper::getJointMin ( ) const

Get minimal joint values.

Returns
A 6-dimension vector that contains the minimal joint values for the 6 dof. All the values are expressed in radians.
Examples:
servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, and servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp.

Definition at line 1219 of file vpViper.cpp.

References joint_min.

Friends And Related Function Documentation

VISP_EXPORT std::ostream& operator<< ( std::ostream &  os,
const vpViper viper 
)
friend

Print on the output stream os the robot parameters (joint min/max, coupling factor between axis 5 and 6, hand-to-eye constant homogeneous matrix $^e{\bf M}_c $.

Parameters
os: Output stream.
viper: Robot parameters.

Definition at line 1262 of file vpViper.cpp.

Member Data Documentation

double vpViper::c56
protected

Mechanical coupling between joint 5 and joint 6.

Definition at line 157 of file vpViper.h.

Referenced by getCoupl56(), vpViper(), vpViper650::vpViper650(), and vpViper850::vpViper850().

double vpViper::d1
protected
double vpViper::d6
protected