rt_trinterp - interpolate homogeneous transforms[view code]

Calling Sequence

T = rt_trinterp(T0, T1, r)

Parameters

• T0 : 4-by-4 matrix. Homogeneous transform representing a first configuration in the operational space.
• T1 : 4-by-4 matrix. Homogeneous transform representing a second configuration in the operational space.
• r : scalar. It represents a "step" between the two configurations described by T0 and T1. It can vary between 0 and 1 inclusively.
• T : 4-by-4 matrix. The interpolated homogeneous transform.

Description

This function interpolates between the two homogeneous transforms T0 and T1 as r varies between 0 and 1 inclusively. This is generally used for computing straight line or 'Cartesian' motion. Rotational interpolation is achieved using quaternion spherical linear interpolation (slerp).

Examples

   // Consider the following example of interpolation of homogeneous
   // transforms
   T1 = rt_rotx(0.2),
   T2 = rt_transl(1, 4, 5) * rt_roty(0.3),

   // r = 0
   Ta = rt_trinterp(T1, T2, 0),         // should be T1

   // r = 1
   Tb = rt_trinterp(T1, T2, 1),         // should be T2

   // r = 0.5
   Tc = rt_trinterp(T1, T2, 0.5),       // 'half way' in between

  

See Also

rt_ctraj,  rt_qinterp,  

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.