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 91 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.
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.

Member Function Documentation

short 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 100 of file controller.cpp.

References Mp, and WRONG_SIZE.

Referenced by Impedance().

short 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 117 of file controller.cpp.

References Mp, and WRONG_SIZE.

short 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 133 of file controller.cpp.

References Dp, and WRONG_SIZE.

Referenced by Impedance().

short 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 150 of file controller.cpp.

References Dp, and WRONG_SIZE.

short 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 166 of file controller.cpp.

References Kp, and WRONG_SIZE.

Referenced by Impedance().

short 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 183 of file controller.cpp.

References Kp, and WRONG_SIZE.

short 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 199 of file controller.cpp.

References Mo, and WRONG_SIZE.

Referenced by Impedance().

short 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 216 of file controller.cpp.

References Mo, and WRONG_SIZE.

short 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 232 of file controller.cpp.

References Do, and WRONG_SIZE.

Referenced by Impedance().

short 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 249 of file controller.cpp.

References Do, and WRONG_SIZE.

short 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 265 of file controller.cpp.

References Ko, and WRONG_SIZE.

Referenced by Impedance().

short 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 282 of file controller.cpp.

References Ko, and WRONG_SIZE.

short 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 298 of file controller.cpp.

References BASE_FRAME, Do, Quaternion::dot(), Quaternion::dot_prod(), Dp, Quaternion::E(), Quaternion::i(), Integ_quat(), Integ_Trap(), Ko, Ko_prime, Kp, Mo, Mp, pc, pcd, pcdp, pcp, pcp_prev, pcpp, pcpp_prev, qc, qcd, qcp, qcp_prev, quat, Quaternion::v(), wc, wcd, wcp, wcp_prev, and WRONG_SIZE.

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