rt_tr2jac - compute a Jacobian to map differential motion between frames[view code]

Calling Sequence

J = rt_tr2jac(T)

Parameters

• T : 4-by-4 matrix. The homogeneous transform which relates the two frames.
• J : 6-by-6 matrix. The Jacobian matrix which maps differential motions between the two frames related by T.

Description

This function returns a Jacobian matrix to map differential motions or velocities between frames related by the homogeneous transform T.

If T is a homogeneous transformation from frame A to frame B, T_AB, then

     dx_B = J_BA * dx_A

where J_BA is given by rt_tr2jac(T_AB).

Examples

   // A differential motion can be represented by a 6-element vector with
   // elements [dx dy dz drx dry drz]. This example shows how rt_tr2jac()
   // can be used to map a differential motion between frames A and B.

   // Let A be the world frame and B be the frame represented by the
   // transform
   T_AB = rt_transl(100, 200, 300) * rt_roty(%pi/8) * rt_rotz(-%pi/4),

   // now, let dx_A be the differential motion expressed with respect to A
   dx_A = [0.1, 0.2, 0, -0.2, 0.1, 0.1].',

   // then the differential motion in B would be given by
   dx_B = rt_tr2jac(T_AB) * dx_A,
   
  

See Also

rt_tr2diff,  rt_diff2tr,  

Authors

original Matlab version by

Peter I. Corke CSIRO Manufacturing Science and Technology

Scilab implementation by

Matteo Morelli Interdepartmental Research Center "E. Piaggio", University of Pisa

Bibliography

Corke, P.I. "A Robotics Toolbox for MATLAB", IEEE Robotics and Automation Magazine, Volume 3(1), March 1996, pp. 24-32

R. P. Paul, Robot Manipulators: Mathematics, Programming and Control. Cambridge, Massachusetts: MIT Press, 1981.