Switching Principles to Circumvent Euler Angle Singularity

Abstract

In this paper, the singularity associated with a minimal attitude parameterization using Euler angles is circumvented by recently developed switching principles. These principles are based on describing the attitude as a function of time with two sets of Euler angle sequences that possess nonconjunctive singularities. This property exists when the singularity causing values of the relevant rotation variables associated with any two Euler angle sequences do not materialize simultaneously. For a given Euler angle set, either antisymmetric or symmetric, another Euler angle set exists such that the pair of representations possesses nonconjunctive singularities. Conditions determining when, and when not, a pair of representations possess this property are developed and analyzed. Nonconjunctive symmetric-antisymmertic and antisymmetric-antisymmetric pairs always exist. This property is exploited by a switching algorithm which facilitates motion description with a minimal parameterization not hindered by singularities. This description may possess computational savings and allow continued use of insightful variables when compared with nonminimal representations such as Euler parameters. The algorithm is numerically demonstrated and validated by a nonlinear six degree of freedom closed-loop spacecraft simulation test.