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ROBOOP::Impedance Class Reference

#include <controller.h>

List of all members.


Detailed Description

Impedance controller class.

The implemantation of the impedance controller is made of two section: the first one is the generation of a compliance trajectory and the second one used a position controller to ensure the end effector follow the compliance trajectory (We recommended to used the resolve acceleration controller scheme, implemented in the class Resolved_acc).

This class generate a compliance path given by the translational and the rotational impedance.

\[ M_p\ddot{\tilde{p}} + D_p\dot{\tilde{p}} + K_p\tilde{p} = f \]

\[ M_o\dot{\tilde{\omega}} + D_o\tilde{\omega} + K_o'\tilde{v} = n \]

where $\tilde{x} = x_c - x_d$ and $ v$ is the vector par of the quaternion representing the orientation error between the compliant and desired frame. The orientation error can also be express by rotation matrix, $ \tilde{R} = R_d^TR_c$. The quaternion mathematics are implemented in the Quaternion class. The index $_c$ and $_d$ denote the compliance and the desired respectively.

The impedance parameters $M_p$, $D_p$, $K_p$, $M_o$, $D_o$ and $K_o$ are $3\times 3$ diagonal positive definite matrix

Definition at line 80 of file controller.h.


Public Member Functions

 Impedance ()
 Constructor.
 Impedance (const Robot_basic &robot, const DiagonalMatrix &Mp_, const DiagonalMatrix &Dp_, const DiagonalMatrix &Kp_, const DiagonalMatrix &Mo_, const DiagonalMatrix &Do_, const DiagonalMatrix &Ko_)
 Constructor.
 Impedance (const Impedance &x)
 Copy constructor.
Impedanceoperator= (const Impedance &x)
 Overload = operator.
short set_Mp (const DiagonalMatrix &Mp_)
 Assign the translational impedance inertia matrix $M_p$.
short set_Mp (const Real MP_i, const short i)
 Assign the translational impedance inertia term $M_p(i,i)$.
short set_Dp (const DiagonalMatrix &Dp_)
 Assign the translational impedance damping matrix $D_p$.
short set_Dp (const Real Dp_i, const short i)
 Assign the translational impedance damping term $D_p(i,i)$.
short set_Kp (const DiagonalMatrix &Kp_)
 Assign the translational impedance stifness matrix $K_p$.
short set_Kp (const Real Kp_i, const short i)
 Assign the translational impedance stifness term $K_p(i,i)$.
short set_Mo (const DiagonalMatrix &Mo_)
 Assign the rotational impedance inertia matrix $M_o$.
short set_Mo (const Real Mo_i, const short i)
 Assign the rotational impedance inertia term $M_o(i,i)$.
short set_Do (const DiagonalMatrix &Do_)
 Assign the rotational impedance damping matrix $D_o$.
short set_Do (const Real Do_i, const short i)
 Assign the rotational impedance damping term $D_o(i,i)$.
short set_Ko (const DiagonalMatrix &Ko_)
 Assign the rotational impedance stifness matrix $K_o$.
short set_Ko (const Real Ko_i, const short i)
 Assign the rotational impedance stifness term $K_o(i,i)$.
short control (const ColumnVector &pdpp, const ColumnVector &pdp, const ColumnVector &pd, const ColumnVector &wdp, const ColumnVector &wd, const Quaternion &qd, const ColumnVector &f, const ColumnVector &n, const Real dt)
 Generation of a compliance trajectory.

Public Attributes

Quaternion qc
 Compliant frame quaternion.
Quaternion qcp
 Compliant frame quaternion derivative.
Quaternion qcp_prev
 Previous value of qcp.
Quaternion qcd
 Orientation error (betweem compliant and desired frame) quaternion.
Quaternion quat
 Temporary quaternion.
ColumnVector pc
 Compliant position.
ColumnVector pcp
 Compliant velocity.
ColumnVector pcpp
 Compliant acceleration.
ColumnVector pcp_prev
 Previous value of pcp.
ColumnVector pcpp_prev
 Previous value of pcpp.
ColumnVector pcd
 Difference between pc and desired position.
ColumnVector pcdp
 Difference between pcp and desired velocity.
ColumnVector wc
 Compliant angular velocity.
ColumnVector wcp
 Compliant angular acceleration.
ColumnVector wcp_prev
 Previous value of wcp.
ColumnVector wcd
 Difference between wc and desired angular velocity.

Private Attributes

DiagonalMatrix Mp
 Translational impedance inertia matrix.
DiagonalMatrix Dp
 Translational impedance damping matrix.
DiagonalMatrix Kp
 Translational impedance stifness matrix.
DiagonalMatrix Mo
 Rotational impedance inertia matrix.
DiagonalMatrix Do
 Rotational impedance damping matrix.
DiagonalMatrix Ko
 Rotational impedance stifness matrix.
Matrix Ko_prime
 Modified rotational impedance stifness matrix.

Constructor & Destructor Documentation

ROBOOP::Impedance::Impedance (  ) 

Constructor.

Definition at line 40 of file controller.cpp.

ROBOOP::Impedance::Impedance ( const Robot_basic robot,
const DiagonalMatrix Mp_,
const DiagonalMatrix Dp_,
const DiagonalMatrix Kp_,
const DiagonalMatrix Mo_,
const DiagonalMatrix Do_,
const DiagonalMatrix Ko_ 
)

Constructor.

Definition at line 55 of file controller.cpp.

ROBOOP::Impedance::Impedance ( const Impedance x  ) 

Copy constructor.

Definition at line 86 of file controller.cpp.


Member Function Documentation

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

Overload = operator.

Definition at line 110 of file controller.cpp.

short ROBOOP::Impedance::set_Mp ( const DiagonalMatrix Mp_  ) 

Assign the translational impedance inertia matrix $M_p$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 136 of file controller.cpp.

Referenced by Impedance().

short ROBOOP::Impedance::set_Mp ( const Real  Mp_i,
const short  i 
)

Assign the translational impedance inertia term $M_p(i,i)$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 153 of file controller.cpp.

short ROBOOP::Impedance::set_Dp ( const DiagonalMatrix Dp_  ) 

Assign the translational impedance damping matrix $D_p$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 169 of file controller.cpp.

Referenced by Impedance().

short ROBOOP::Impedance::set_Dp ( const Real  Dp_i,
const short  i 
)

Assign the translational impedance damping term $D_p(i,i)$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 186 of file controller.cpp.

short ROBOOP::Impedance::set_Kp ( const DiagonalMatrix Kp_  ) 

Assign the translational impedance stifness matrix $K_p$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 202 of file controller.cpp.

Referenced by Impedance().

short ROBOOP::Impedance::set_Kp ( const Real  Kp_i,
const short  i 
)

Assign the translational impedance stifness term $K_p(i,i)$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 219 of file controller.cpp.

short ROBOOP::Impedance::set_Mo ( const DiagonalMatrix Mo_  ) 

Assign the rotational impedance inertia matrix $M_o$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 235 of file controller.cpp.

Referenced by Impedance().

short ROBOOP::Impedance::set_Mo ( const Real  Mo_i,
const short  i 
)

Assign the rotational impedance inertia term $M_o(i,i)$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 252 of file controller.cpp.

short ROBOOP::Impedance::set_Do ( const DiagonalMatrix Do_  ) 

Assign the rotational impedance damping matrix $D_o$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 268 of file controller.cpp.

Referenced by Impedance().

short ROBOOP::Impedance::set_Do ( const Real  Do_i,
const short  i 
)

Assign the rotational impedance damping term $D_o(i,i)$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 285 of file controller.cpp.

short ROBOOP::Impedance::set_Ko ( const DiagonalMatrix Ko_  ) 

Assign the rotational impedance stifness matrix $K_o$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 301 of file controller.cpp.

Referenced by Impedance().

short ROBOOP::Impedance::set_Ko ( const Real  Ko_i,
const short  i 
)

Assign the rotational impedance stifness term $K_o(i,i)$.

Returns:
short: 0 or WRONG_SIZE if the matrix is not $3\times 3$.

Definition at line 318 of file controller.cpp.

short ROBOOP::Impedance::control ( const ColumnVector pdpp,
const ColumnVector pdp,
const ColumnVector pd,
const ColumnVector wdp,
const ColumnVector wd,
const Quaternion qd,
const ColumnVector f,
const ColumnVector n,
const Real  dt 
)

Generation of a compliance trajectory.

Parameters:
pdpp,: desired end effector acceleration.
pdp,: desired end effector velocity.
pd,: desired end effector position.
wdp,: desired end effector angular acceleration.
wd,: desired end effector angular velocity.
qd,: desired quaternion.
f,: end effector contact force.
n,: end effector contact moment.
dt,: time frame.
Returns:
short: 0 or WRONG_SIZE if one of the vector input is not $3\times 1$.
The translational and rotational impedance equations are integrated, with input $f$ and $n$ to computed $\ddot{p}_c$ and $\dot{\omega}_c$, $\dot{p}_c$ and $\omega_c$, and then $p_c$ and $q_c$. The compliant quaternion $q_c$ is obtained with the quaternion propagation equations (see Quaternion class).

The quaternion -q represents exactly the same rotation as the quaternion q. The temporay quaternion, quat, is quatd plus a sign correction. It is customary to choose the sign G on q1 so that q0.Gq1 >=0 (the angle between q0 ang Gq1 is acute). This choice avoids extra spinning caused by the interpolated rotations.

Definition at line 334 of file controller.cpp.


Member Data Documentation

Compliant frame quaternion.

Definition at line 107 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Compliant frame quaternion derivative.

Definition at line 107 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Previous value of qcp.

Definition at line 107 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Orientation error (betweem compliant and desired frame) quaternion.

Definition at line 107 of file controller.h.

Referenced by control().

Temporary quaternion.

Definition at line 107 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Compliant position.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Compliant velocity.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Compliant acceleration.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Previous value of pcp.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Previous value of pcpp.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Difference between pc and desired position.

Definition at line 112 of file controller.h.

Referenced by control().

Difference between pcp and desired velocity.

Definition at line 112 of file controller.h.

Referenced by control().

Compliant angular velocity.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Compliant angular acceleration.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Previous value of wcp.

Definition at line 112 of file controller.h.

Referenced by control(), Impedance(), and operator=().

Difference between wc and desired angular velocity.

Definition at line 112 of file controller.h.

Referenced by control().

Translational impedance inertia matrix.

Definition at line 124 of file controller.h.

Referenced by control(), Impedance(), operator=(), and set_Mp().

Translational impedance damping matrix.

Definition at line 124 of file controller.h.

Referenced by control(), Impedance(), operator=(), and set_Dp().

Translational impedance stifness matrix.

Definition at line 124 of file controller.h.

Referenced by control(), Impedance(), operator=(), and set_Kp().

Rotational impedance inertia matrix.

Definition at line 124 of file controller.h.

Referenced by control(), Impedance(), operator=(), and set_Mo().

Rotational impedance damping matrix.

Definition at line 124 of file controller.h.

Referenced by control(), Impedance(), operator=(), and set_Do().

Rotational impedance stifness matrix.

Definition at line 124 of file controller.h.

Referenced by control(), Impedance(), operator=(), and set_Ko().

Modified rotational impedance stifness matrix.

Definition at line 130 of file controller.h.

Referenced by control(), Impedance(), and operator=().


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

ROBOOP v1.21a
Generated Thu Nov 22 00:51:35 2007 by Doxygen 1.5.4