Constructing Kinematic Confidence Regions with Double Quaternions
摘要
A spatial displacement as an element of SE(3) can be approximated by a 4D rotation, which is an element of SO(4). In this way, the problem of constructing confidence regions of uncertain spatial displacements may be studied as that of constructing confidence ellipsoids in SO(4). In this light, a double-quaternion formulation of kinematic confidence regions is presented that approximately preserve the geometry of SE(3). Examples are provided to demonstrate the efficacy of this approach in comparison with the dual-quaternion formulation.