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trexp

matrix exponential for so(3) and se(3)

For so(3)

R = trexp(omega) is the matrix exponential (3x3) of the so(3) element omega that yields a rotation matrix (3x3).

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 (1x3) where w = s * theta. Rotation by ||w|| about the vector w.

For se(3)

T = trexp(sigma) is the matrix exponential (4x4) of the se(3) element sigma that yields a homogeneous transformation matrix (4x4).

T = trexp(tw) as above, but the se(3) value is expressed as a twist vector tw (1x6).

T = trexp(sigma, theta) as above, but se(3) motion of sigma*theta, the rotation part of sigma (4x4) must be unit norm.

T = trexp(tw, theta) as above, but se(3) motion of tw*theta, the rotation part of tw (1x6) must be unit norm.

Notes

References

See also

angvec2r, trlog, trexp2, skew, skewa, Twist


 

© 1990-2014 Peter Corke.