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