Journal ArticleDOI
New Control Laws for the Attitude Stabilization of Rigid Bodies
TLDR
In this paper, a new class of globally asymptotically stabilizing feedback control laws for the complete (i.e., dynamics and kinematics) attitude motion of a rotating rigid body is given in terms of two new parameterizations of the rotation group derived using stereographic projection.About:
This article is published in IFAC Proceedings Volumes.The article was published on 1994-09-01. It has received 103 citations till now. The article focuses on the topics: Lyapunov function & Lyapunov redesign.read more
Citations
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Journal ArticleDOI
Further passivity results for the attitude control problem
TL;DR: This paper establishes passivity for the system which describes the attitude motion of a rigid body in terms of minimal three-dimensional kinematic parameters and shows that linear asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties.
Journal ArticleDOI
Leader–follower cooperative attitude control of multiple rigid bodies
TL;DR: This paper extends the previous results on coordinated control of rotating rigid bodies to the case of teams with heterogenous agents, where only a certain subgroup of the agents are vested with the main control objective, that is, maintain constant relative orientation amongst themselves.
Journal ArticleDOI
Decentralized Coordinated Attitude Control Within a Formation of Spacecraft
TL;DR: A corollary of Barbalat’s Lemma is used to prove that the class of control laws globally asymptotically stabilizes the spacecraft formation.
Stereographic Orientation Parameters for Attitude Dynamics: A Generalization of the Rodrigues Parameters
Hanspeter Schaub,John L. Junkins +1 more
Abstract: A new family of orientation parameters derived from the Euler parameters is presented. They are found by a general stereographic projection of the Euler parameter constraint surface, a four-dimensional unit sphere, onto a three-dimensional hyperplane. The resulting set of three stereographic parameters have a low degree polynomial non-linearity in the corresponding kinematic equations and direction cosine matrix parameterization. The stereographic parameters are not unique, but have a corresponding set of “shadow” parameters. These “shadow” parameters are distinct, yet represent the same physical orientation. Using the original stereographic parameters combined with judicious switching to their shadow set, it is possible to describe any rotation without encountering a singularity. The symmetric stereographic parameters are nonsingular for up to a principal rotation of ±360°. The asymmetric stereographic parameters are well suited for describing the kinematics of spinning bodies, since they only go singular when oriented at a specific angle about a specific axis. A globally regular and stable control law using symmetric stereographic parameters is presented which can bring a spinning body to rest in any desired orientation without backtracking the motion.
Proceedings ArticleDOI
Leader-follower cooperative attitude control of multiple rigid bodies
TL;DR: This paper extends the previous results on coordinated control of rotating rigid bodies to the case of teams with heterogenous agents, where only a certain subgroup of the agents are vested with the main control objective, that is, maintain constant relative orientation amongst themselves.
References
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Book ChapterDOI
Functions of a Complex Variable
TL;DR: In this paper, a theory of complex-valued functions of a complexvalued argument is presented, which contains some remarkably powerful results which are applicable to a variety of problems, such as the Fourier series expansion.
Book
Functions of one complex variable
TL;DR: In this article, the authors defined the boundary values of Riemann maps and defined the corresponding boundary values for bounded analytic functions in the Bergman space of the Dirichlet problem.
Journal ArticleDOI
Quarternion feedback regulator for spacecraft eigenaxis rotations
Journal ArticleDOI
On the Parametrization of the Three-Dimensional Rotation Group
TL;DR: In this article, a group of rotations of Euclidean 3D space is used for integration of rigid body motion equations, and a parameterization of group of rotation groups is proposed.