STEREOGRAPHIC ORIENTATION PARAMETERS FOR ATTITUDE DYNAMICS - A GENERALIZATION OF THE RODRIGUES PARAMETERS

A new family of orientation parameters derived from the Euler paramete rs is presented. They are found by a general stereographic projection of the Euler parameter constraint surface, a four-dimensional unit sph ere, onto a three-dimensional hyperplane. The resulting set of three s tereographic parameters have a low degree polynomial nonlinearity in t he corresponding kinematic equations and direction cosine matrix param eterization. The stereographic parameters are not unique, but have a c orresponding set of ''shadow'' parameters. These shadow parameters are distinct, yet represent the same physical orientation. Using the orig inal stereographic parameters combined with judicious switching to the ir shadow set, it is possible to describe any rotation without encount ering a singularity. The symmetric stereographic parameters are nonsin gular for up to a principal rotation of +/-360 degrees. The asymmetric stereographic parameters are well suited for describing the kinematic s of spinning bodies, since they only go singular when oriented at a s pecific angle about a specific axis. A globally regular and stable con trol law using symmetric stereographic parameters is presented which c an bring a spinning body to rest in any desired orientation without ba cktracking the motion.