Swing-twist decomposition in Clifford algebra

Understand

The swing-twist decomposition is a standard routine in motion planning for humanoid limbs.

• In this paper the decomposition formulas are derived and discussed in terms of Clifford algebra.
• With the decomposition one can express an arbitrary spinor as a product of a twist-free spinor and a swing-free spinor (or vice-versa) in 3-dimensional Euclidean space.
• It is shown that in the derived decomposition formula the twist factor is a generalized projection of a spinor onto a vector in Clifford algebra.