trlog
Logarithm of SO(3) or SE(3) matrix
S = trlog(R) is the matrix logarithm (3×3) of R (3×3) which is a skew symmetric matrix corresponding to the vector theta*w where theta is the rotation angle and w (3×1) is a unit-vector indicating the rotation axis.
[theta,w] = trlog(R) as above but returns directly theta the rotation angle and w (3×1) the unit-vector indicating the rotation axis.
S = trlog(T) is the matrix logarithm (4×4) of T (4×4) which has a skew-symmetric upper-left 3×3 submatrix corresponding to the vector theta*w where theta is the rotation angle and w (3×1) is a unit-vector indicating the rotation axis, and a translation component.
[theta,twist] = trlog(T) as above but returns directly theta the rotation angle and a twist vector (6×1) comprising [v w].
Notes
- Efficient closed-form solution of the matrix logarithm for arguments that are SO(3) or SE(3).
- Special cases of rotation by odd multiples of pi are handled.
- Angle is always in the interval [0,pi].
- There is no Toolbox function for SO(2) or SE(2), use LOGM instead.
References
- Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p43.
- Mechanics, planning and control, Park & Lynch, Cambridge, 2016.