trexp
Matrix exponential for so(3) and se(3)
For so(3)
R = TREXP(OMEGA) is the matrix exponential (3×3) of the so(3) element OMEGA that yields a rotation matrix (3×3).
R = TREXP(OMEGA, THETA) as above, but so(3) motion of THETA*OMEGA.
R = TREXP(S, THETA) as above, but rotation of THETA about the unit vector S.
R = TREXP(W) as above, but the so(3) value is expressed as a vector W (1×3) where W = S * THETA. Rotation by ||W|| about the vector W.
For se(3)
T = TREXP(SIGMA) is the matrix exponential (4×4) of the se(3) element SIGMA that yields a homogeneous transformation matrix (4×4).
T = TREXP(SIGMA, THETA) as above, but se(3) motion of SIGMA*THETA, the rotation part of SIGMA (4×4) must be unit norm.
T = TREXP(TW) as above, but the se(3) value is expressed as a twist vector TW (1×6).
T = TREXP(TW, THETA) as above, but se(3) motion of TW*THETA, the rotation part of TW (1×6) must be unit norm.
Notes
- Efficient closed-form solution of the matrix exponential for arguments that are so(3) or se(3).
- If
THETAis given then the first argument must be a unit vector or a skew-symmetric matrix from a unit vector. - Angle vector argument order is different to ANGVEC2R.
References
- Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p42-43.
- Mechanics, planning and control, Park & Lynch, Cambridge, 2017.
See also
angvec2r, trlog, trexp2, skew, skewa, Twist