An almost global estimator on SO(3) with measurement on S²

Abstract

Abstract-This paper presents an almost globally convergent state estimator for the orientation of a rotating rigid body. The estimator requires knowledge of the angular velocity of the body at each time instant and the measurement consists of a single unit vector on the body, which we take without loss of generality to be the first column of the rotation matrix. The stability proof involves a relatively simple Lyapunov and invariance-like analysis. A mild non-degeneracy constraint on the control input guarantees the fulfillment of the invariance criterion. We apply the result to needle-tip orientation estimation for tip-steerable needles.

Gaussian approximation of non-linear measurement models on Lie groups

“…In attitude estimation the group of rotations, SO (3), is of interest [12], [13], [29] and works on filtering in this context include [14], [16], [23], [24], [25], [26], [28]. And even outside of the context of attitude estimation, the group SO(3) arises in other applications [15]. In mobile robot localization [30], the groups of rigid-body motions of the plane and of 3D space, SE(2) and SE (3), are of interest [8], [7], [18], [21].…”

Factor Graph Modeling of Rigid‐body Dynamics for Localization, Mapping, and Parameter Estimation of a Spinning Object in Space

“…It is well understood that the covariance matrix of a quaternion is rank‐deficient due to its normalization constraint. While there is active research in a number of estimation systems that do not use Gaussian random variables (Markley, ; Psiaki, ; Shuster, , ; Swensen & Cowan, ), a typical approach for dealing with this is to use three‐vector error parametrization and reset the quaternion [see Crassidis & Junkins (), Lefferts, Markley, & Shuster (), Markley (), and Tweddle ()]. This is what will be used here since it fits well with the iSAM system for Gaussian random variables and has a history of good performance.…”

Unscented kalman filtering on euclidean and riemannian manifolds

“…Indeed, every element of S 3 -the sphere of radius 1 centered at the origin of the Euclidean space R 4 ; it is isomorphic to the set of all unit quaternions-can be associated with an element of SO (3)-the special group of orthogonal matrices; actions (with the usual matrix product) of these matrices on three-dimensional vectors are rotations) [33]. Unit quaternions can be found modeling rotations and attitudes of elements in aerospace applications involving satellites [61], inertial navigation systems [62], unmanned aircraft vehicles [63]; and also in other areas, such as vision [64], robotics [65], and others.…”