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ROBOOP::mRobot

ROBOOP::mRobot Class Reference

#include <robot.h>

Inheritance diagram for ROBOOP::mRobot:

Inheritance graph
[legend]
List of all members.

Detailed Description

Modified DH notation robot class.

Definition at line 448 of file robot.h.

Public Member Functions

 mRobot (const int ndof=1)
 Constructor.
 mRobot (const Matrix &initrobot_motor)
 Constructor.
 mRobot (const Matrix &initrobot, const Matrix &initmotor)
 Constructor.
 mRobot (const mRobot &x)
 Copy constructor.
 mRobot (const string &filename, const string &robotName)
 Constructor.
 mRobot (const Config &robData, const string &robotName)
 ~mRobot ()
 Destructor.
mRobot & operator= (const mRobot &x)
 Overload = operator.
virtual void robotType_inv_kin ()
 Identify inverse kinematics familly.
virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj=0)
 Overload inv_kin function.
virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj, bool &converge)
 Numerical inverse kinematics. See inv_kin(const Matrix & Tobj, const int mj, const int endlink, bool & converge).
virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj, const int endlink, bool &converge)
 Inverse kinematics solutions.
virtual ReturnMatrix inv_kin_rhino (const Matrix &Tobj, bool &converge)
 Analytic Rhino inverse kinematics.
virtual ReturnMatrix inv_kin_puma (const Matrix &Tobj, bool &converge)
 Analytic Puma inverse kinematics.
virtual void kine_pd (Matrix &Rot, ColumnVector &pos, ColumnVector &pos_dot, const int ref) const
 Direct kinematics with velocity.
virtual ReturnMatrix jacobian (const int ref=0) const
 Jacobian of mobile links expressed at frame ref.
virtual ReturnMatrix jacobian (const int endlink, const int ref) const
 Jacobian of mobile joints up to endlink expressed at frame ref.
virtual ReturnMatrix jacobian_dot (const int ref=0) const
 Jacobian derivative of mobile joints expressed at frame ref.
virtual void dTdqi (Matrix &dRot, ColumnVector &dpos, const int i)
 Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).
virtual ReturnMatrix dTdqi (const int i)
 Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).
virtual void dTdqi (Matrix &dRot, ColumnVector &dpos, const int i, const int endlink)
 Partial derivative of the robot position (homogeneous transf.).
virtual ReturnMatrix dTdqi (const int i, const int endlink)
 Partial derivative of the robot position (homogeneous transf.).
virtual ReturnMatrix torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp)
 Joint torque, without contact force, based on Recursive Newton-Euler formulation.
virtual ReturnMatrix torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &Fext_, const ColumnVector &Next_)
 Joint torque based on Recursive Newton-Euler formulation.
virtual ReturnMatrix torque_novelocity (const ColumnVector &qpp)
 Joint torque. when joint velocity is 0, based on Recursive Newton-Euler formulation.
virtual void delta_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, const ColumnVector &dqp, const ColumnVector &dqpp, ColumnVector &torque, ColumnVector &dtorque)
 Delta torque dynamics.
virtual void dq_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, ColumnVector &torque, ColumnVector &dtorque)
 Delta torque due to delta joint position.
virtual void dqp_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &dqp, ColumnVector &torque, ColumnVector &dtorque)
 Delta torque due to delta joint velocity.
virtual ReturnMatrix G ()
 Joint torque due to gravity based on Recursive Newton-Euler formulation.
virtual ReturnMatrix C (const ColumnVector &qp)
 Joint torque due to centrifugal and Corriolis based on Recursive Newton-Euler formulation.

Constructor & Destructor Documentation

ROBOOP::mRobot::mRobot ( const int  ndof = 1  )  [explicit]

Constructor.

Definition at line 1436 of file robot.cpp.

ROBOOP::mRobot::mRobot ( const Matrix &  initrobot_motor  )  [explicit]

Constructor.

Definition at line 1445 of file robot.cpp.

ROBOOP::mRobot::mRobot ( const Matrix &  initrobot,
const Matrix &  initmotor 
) [explicit]

Constructor.

Definition at line 1454 of file robot.cpp.

ROBOOP::mRobot::mRobot ( const mRobot &  x  ) 

Copy constructor.

Definition at line 1484 of file robot.cpp.

ROBOOP::mRobot::mRobot ( const string &  filename,
const string &  robotName 
) [explicit]

Constructor.

Definition at line 1464 of file robot.cpp.

ROBOOP::mRobot::mRobot ( const Config &  robData,
const string &  robotName 
) [explicit]

Definition at line 1474 of file robot.cpp.

ROBOOP::mRobot::~mRobot (  )  [inline]

Destructor.

Definition at line 456 of file robot.h.

Member Function Documentation

ReturnMatrix ROBOOP::mRobot::C ( const ColumnVector &  qp  )  [virtual]

Joint torque due to centrifugal and Corriolis based on Recursive Newton-Euler formulation.

Implements ROBOOP::Robot_basic.

Definition at line 631 of file dynamics.cpp.

void ROBOOP::mRobot::delta_torque ( const ColumnVector &  q,
const ColumnVector &  qp,
const ColumnVector &  qpp,
const ColumnVector &  dq,
const ColumnVector &  dqp,
const ColumnVector &  dqpp,
ColumnVector &  ltorque,
ColumnVector &  dtorque 
) [virtual]

Delta torque dynamics.

This function computes

\[ \delta \tau = D(q) \delta \ddot{q} + S_1(q,\dot{q}) \delta \dot{q} + S_2(q,\dot{q},\ddot{q}) \delta q \]

Murray and Neuman Cite_: Murray86 have developed an efficient recursive linearized Newton-Euler formulation. In order to apply the RNE as presented in let us define the following variables

\[ p_{di} = \frac{\partial p_i}{\partial d_i} = \left [ \begin{array}{ccc} 0 & \sin \alpha_i & \cos \alpha_i \end{array} \right ]^T \]

\[ Q = \left [ \begin{array}{ccc} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right ] \]

Forward Iterations for $i=1, 2, \ldots, n$. Initialize: $\delta \omega_0 = \delta \dot{\omega}_0 = \delta \dot{v}_0 = 0$.

\[ \delta \omega_i = R_i^T \delta \omega_{i-1} + \sigma_i (z_0 \delta \dot{\theta}_i - QR_i^T \omega_i \delta \theta_i) \]

\[ \delta \dot{\omega}_i = R_i^T \delta \dot{w}_{i-1} + \sigma_i [R_i^T \delta \omega_{i-1} \times z_0 \dot{\theta}_i + R_i^T \omega_{i-1} \times z_0 \delta \dot{\theta}_i + z_0 \ddot{\theta}_i - (QR_i^T \dot{\omega}_{i-1} + QR_i^T \omega_{i-1} \times \omega{z}_0 \dot{\theta}_i) \delta \theta_i ] \]

\[ \delta \dot{v}_i = R_i^T\Big(\delta \dot{\omega}_{i-1} \times p_i + \delta \omega_{i-1} \times(\omega_{i-1} \times p_i) + \omega_{i-1} \times( \delta \omega_{i-1} \times p_i) + \delta \dot{v}_i\Big) + (1-\sigma_i)\Big(2\delta \omega_i \times z_0\dot{d}_i + 2\omega_i \times z_0 \delta \dot{d}_i + z_0 \delta \ddot{d}_i\Big) - \sigma_i QR_i^T \Big(\dot{\omega}_{i-1} \times p_i + \omega_{i-1} \times(w_{i-1}\times p_i) + \dot{v}_i\Big) \delta \theta_i + (1-\sigma_i) R_i^T \Big(\dot{\omega}_{i-1} \times p_{di} + \omega_{i-1} \times(\omega_{i-1}\times p_{di})\Big) \delta d_i \]

Backward Iterations for $i=n, n-1, \ldots, 1$. Initialize: $\delta f_{n+1} = \delta n_{n+1} = 0$.

\[ \delta \dot{v}_{ci} = \delta \dot{v}_i + \delta \dot{\omega}_i\times r_i + \delta \omega_i \times(\omega_i \times r_i) + \omega_i \times ( \delta \omega_i \times r_i) \]

\[ \delta F_i = m_i \delta \dot{v}_{ci} \]

\[ \delta N_i = I_{ci} \delta \dot{\omega}_i + \delta \omega_i \times (I_{ci}\omega_i) + \omega_i \times (I_{ci} \delta \omega_i) \]

\[ \delta f_i = R_{i+1} \delta f_{i+1} + \delta F_i + \sigma_{i+1} R_{i+1} Qf_{i+1} \delta \theta_{i+1} \]

\[ \delta n_i = \delta N_i + R_{i+1} \delta n_{i+1} + r_i\times \delta F_i + p_{i+1} \times R_{i+1} \delta f_{i+1} + \sigma_{i+1} \Big( R_{i+1} Qn_{i+1} + p_{i+1} \times R_{i+1} Qf_{i+1} \Big) \delta \theta_{i+1} + (1-\sigma_{i+1} ) p_{di+1} p_{di+1} \times R_{i+1} f_{i+1} \delta d_{i+1} \]

\[ \delta \tau_i = \sigma \delta n_i^T z_0 + (1 - \sigma_i) \delta f_i^T z_0 \]

Implements ROBOOP::Robot_basic.

Definition at line 289 of file delta_t.cpp.

void ROBOOP::mRobot::dq_torque ( const ColumnVector &  q,
const ColumnVector &  qp,
const ColumnVector &  qpp,
const ColumnVector &  dq,
ColumnVector &  ltorque,
ColumnVector &  dtorque 
) [virtual]

Delta torque due to delta joint position.

This function computes $S_2(q, \dot{q}, \ddot{q})\delta q$. See mRobot::delta_torque for equations.

Implements ROBOOP::Robot_basic.

Definition at line 205 of file comp_dq.cpp.

void ROBOOP::mRobot::dqp_torque ( const ColumnVector &  q,
const ColumnVector &  qp,
const ColumnVector &  dqp,
ColumnVector &  ltorque,
ColumnVector &  dtorque 
) [virtual]

Delta torque due to delta joint velocity.

This function computes $S_1(q, \dot{q}, \ddot{q})\delta \dot{q}$. See mRobot::delta_torque for equations.

Implements ROBOOP::Robot_basic.

Definition at line 188 of file comp_dqp.cpp.

ReturnMatrix ROBOOP::mRobot::dTdqi ( const int  i,
const int  endlink 
) [virtual]

Partial derivative of the robot position (homogeneous transf.).

See mRobot::dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink) for equations.

Implements ROBOOP::Robot_basic.

Definition at line 867 of file kinemat.cpp.

void ROBOOP::mRobot::dTdqi ( Matrix &  dRot,
ColumnVector &  dpos,
const int  i,
const int  endlink 
) [virtual]

Partial derivative of the robot position (homogeneous transf.).

This function computes the partial derivatives:

\[ \frac{\partial{}^0 T_n}{\partial q_i} = {}^0 T_{i} Q_i \; {}^{i} T_n \]

with

\[ Q_i = \left [ \begin{array}{cccc} 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right ] \]

for a revolute joint and

\[ Q_i = \left [ \begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{array} \right ] \]

for a prismatic joint.

$dRot$ and $dp$ are modified on output.

Implements ROBOOP::Robot_basic.

Definition at line 785 of file kinemat.cpp.

virtual ReturnMatrix ROBOOP::mRobot::dTdqi ( const int  i  )  [inline, virtual]

Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).

Reimplemented from ROBOOP::Robot_basic.

Definition at line 470 of file robot.h.

virtual void ROBOOP::mRobot::dTdqi ( Matrix &  dRot,
ColumnVector &  dpos,
const int  i 
) [inline, virtual]

Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).

Reimplemented from ROBOOP::Robot_basic.

Definition at line 469 of file robot.h.

Referenced by dTdqi().

ReturnMatrix ROBOOP::mRobot::G (  )  [virtual]

Joint torque due to gravity based on Recursive Newton-Euler formulation.

Implements ROBOOP::Robot_basic.

Definition at line 594 of file dynamics.cpp.

ReturnMatrix ROBOOP::mRobot::inv_kin ( const Matrix &  Tobj,
const int  mj,
const int  endlink,
bool &  converge 
) [virtual]

Inverse kinematics solutions.

The solution is based on the analytic inverse kinematics if robot type (familly) is Rhino or Puma, otherwise used the numerical algoritm defined in Robot_basic class.

Reimplemented from ROBOOP::Robot_basic.

Definition at line 1107 of file invkine.cpp.

virtual ReturnMatrix ROBOOP::mRobot::inv_kin ( const Matrix &  Tobj,
const int  mj,
bool &  converge 
) [inline, virtual]

Numerical inverse kinematics. See inv_kin(const Matrix & Tobj, const int mj, const int endlink, bool & converge).

Reimplemented from ROBOOP::Robot_basic.

Definition at line 460 of file robot.h.

ReturnMatrix ROBOOP::mRobot::inv_kin ( const Matrix &  Tobj,
const int  mj = 0 
) [virtual]

Overload inv_kin function.

Reimplemented from ROBOOP::Robot_basic.

Definition at line 1099 of file invkine.cpp.

Referenced by inv_kin().

ReturnMatrix ROBOOP::mRobot::inv_kin_puma ( const Matrix &  Tobj,
bool &  converge 
) [virtual]

Analytic Puma inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements ROBOOP::Robot_basic.

Definition at line 1236 of file invkine.cpp.

Referenced by inv_kin().

ReturnMatrix ROBOOP::mRobot::inv_kin_rhino ( const Matrix &  Tobj,
bool &  converge 
) [virtual]

Analytic Rhino inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements ROBOOP::Robot_basic.

Definition at line 1129 of file invkine.cpp.

Referenced by inv_kin().

ReturnMatrix ROBOOP::mRobot::jacobian ( const int  endlink,
const int  ref 
) const [virtual]

Jacobian of mobile joints up to endlink expressed at frame ref.

See Robot::jacobian for equations.

Implements ROBOOP::Robot_basic.

Definition at line 885 of file kinemat.cpp.

virtual ReturnMatrix ROBOOP::mRobot::jacobian ( const int  ref = 0  )  const [inline, virtual]

Jacobian of mobile links expressed at frame ref.

Reimplemented from ROBOOP::Robot_basic.

Definition at line 466 of file robot.h.

ReturnMatrix ROBOOP::mRobot::jacobian_dot ( const int  ref = 0  )  const [virtual]

Jacobian derivative of mobile joints expressed at frame ref.

See Robot::jacobian_dot for equations.

Implements ROBOOP::Robot_basic.

Definition at line 938 of file kinemat.cpp.

void ROBOOP::mRobot::kine_pd ( Matrix &  Rot,
ColumnVector &  pos,
ColumnVector &  pos_dot,
const int  j 
) const [virtual]

Direct kinematics with velocity.

Parameters:
Rot,: Frame j rotation matrix w.r.t to the base frame.
pos,: Frame j position vector wr.r.t to the base frame.
pos_dot,: Frame j velocity vector w.r.t to the base frame.
j,: Frame j. Print an error on the console if j is out of range.

Implements ROBOOP::Robot_basic.

Definition at line 755 of file kinemat.cpp.

mRobot & ROBOOP::mRobot::operator= ( const mRobot &  x  ) 

Overload = operator.

Definition at line 1489 of file robot.cpp.

void ROBOOP::mRobot::robotType_inv_kin (  )  [virtual]

Identify inverse kinematics familly.

Identify the inverse kinematics analytic solution based on the similarity of the robot DH parameters and the DH parameters of know robots (ex: Puma, Rhino, ...). The inverse kinematics will be based on a numerical alogorithm if there is no match .

Implements ROBOOP::Robot_basic.

Definition at line 1496 of file robot.cpp.

Referenced by mRobot().

ReturnMatrix ROBOOP::mRobot::torque ( const ColumnVector &  q,
const ColumnVector &  qp,
const ColumnVector &  qpp,
const ColumnVector &  Fext_,
const ColumnVector &  Next_ 
) [virtual]

Joint torque based on Recursive Newton-Euler formulation.

In order to apply the RNE, let us define the following variables (referenced in the $i^{th}$ coordinate frame if applicable):

$\sigma_i$ is the joint type; $\sigma_i = 1$ for a revolute joint and $\sigma_i = 0$ for a prismatic joint.

$ z_0 = \left [ \begin{array}{ccc} 0 & 0 & 1 \end{array} \right ]^T$

$p_i = \left [ \begin{array}{ccc} a_{i-1} & -d_i sin \alpha_{i-1} & d_i cos \alpha_{i-1} \end{array} \right ]^T$ is the position of the $i^{th}$ with respect to the $i-1^{th}$ frame.

Forward Iterations for $i=1, 2, \ldots, n$. Initialize: $\omega_0 = \dot{\omega}_0 = 0$ and $\dot{v}_0 = - g$.

\[ \omega_i = R_i^T\omega_{i-1} + \sigma_i z_0\dot{\theta_i} \]

\[ \dot{\omega}_i = R_i^T\dot{\omega}_{i-1} + \sigma_i R_i^T\omega_{i-1}\times z_0 \dot{\theta}_i + \sigma_iz_0\ddot{\theta}_i \]

\[ \dot{v}_i = R_i^T(\dot{\omega}_{i-1}\times p_i + \omega_{i-1}\times(\omega_{i-1}\times p_i) + \dot{v}_{i-1}) + (1 - \sigma_i)(2\omega_i\times z_0 dot{d}_i + z_0\ddot{d}_i) \]

Backward Iterations for $i=n, n-1, \ldots, 1$. Initialize: $f_{n+1} = n_{n+1} = 0$.

\[ \dot{v}_{ci} = \dot{\omega}_i\times r_i + \omega_i\times(\omega_i\times r_i) + v_i \]

\[ F_i = m_i \dot{v}_{ci} \]

\[ N_i = I_{ci}\ddot{\omega}_i\ + \omega_i \times I_{ci}\omega_i \]

\[ f_i = R_{i+1}f_{i+1} + F_i \]

\[ n_i = N_i + R_{i+1} n_{i+1} + r_i \times F_i + p_{i+1}\times R_{i+1}f_{i+1} \]

\[ \tau_i = \sigma_i n_i^T z_0 + (1 - \sigma_i) f_i^T z_0 \]

Implements ROBOOP::Robot_basic.

Definition at line 417 of file dynamics.cpp.

ReturnMatrix ROBOOP::mRobot::torque ( const ColumnVector &  q,
const ColumnVector &  qp,
const ColumnVector &  qpp 
) [virtual]

Joint torque, without contact force, based on Recursive Newton-Euler formulation.

Implements ROBOOP::Robot_basic.

Definition at line 407 of file dynamics.cpp.

ReturnMatrix ROBOOP::mRobot::torque_novelocity ( const ColumnVector &  qpp  )  [virtual]

Joint torque. when joint velocity is 0, based on Recursive Newton-Euler formulation.

Implements ROBOOP::Robot_basic.

Definition at line 550 of file dynamics.cpp.

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

ROBOOP v1.21a
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