Representing Attitude : Euler Angles , Unit Quaternions , and Rotation Vectors

By James Diebel. 2006

1,027 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5c0edc899359a69c3769da238491f93e7a2f6d6d

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Citations in the corpus

Contact-aided invariant extended Kalman filtering for robot state estimation (2019, methodology): “If we let q t vec( q x , q y , q z ) be a vector of Euler angles using the R z R y R x convention, then the orientation dynamics can be expressed as [33] d d t Let δ q t q t − ¯ q t ∈ R 3 be the error between the true and estimated Euler angles.”
Fast and Robust Iterative Closest Point (2020, background): “An alternative representation of rotation in R 3 without such singularities is the unit quaternions, which are identiﬁed with unit vectors in R 4 [52].”
Applied Tracking Control for Kite Power Systems (2014, background): “such that (v)S = STW · (v)W , see [20] for details.”
The three-dimensional normal-distributions transform : an efficient representation for registration, surface analysis, and loop detection (2009, background): “Please refer to Altmann [1] for an exhaustive reference on rotations or Diebel [27] for a more compact but thorough review.”
CHOMP: Covariant Hamiltonian optimization for motion planning (2013, background): “The exponential map encodes an (axis, angle) rotation as a single vector in the direction of the rotation axis whose magnitude is the rotation angle [18].”
Template-warping based speech driven head motion synthesis (2013, methodology): “The obtained relative head motions were converted into rotation vectors [13].”
Probabilistic Contact Estimation and Impact Detection for State Estimation of Quadruped Robots (2017, background): “In (3), we assume the effects of angular acceleration and centripetal force (see [18]) to be negligible.”