Global Asymptotic Stabilization of a Spinning Top With Torque Actuators Using Stereographic Projection

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57817/1/CJWan1997.pd

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero-momentum mode. Three-axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories.Two approaches are proposed and compared to achieve three-axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full-state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three-axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Inertia-Free Spacecraft Attitude Tracking with Disturbance Rejection and Almost Global Stabilization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76737/1/AIAA-41565-705.pd

分娩第1期におけるアロママッサージの効果 ： 初産婦6名経産婦4名に実施して

The article of record as published may be located at http://dx.doi.org/10.2514/6.2008-7012AIAA Guidance, Navigation and Control Conference and Exhibit ; Paper no. AIAA-2008-7012, Honolulu, Hawaii, 2008Minimum-time solutions are developed for the rest-to-rest reorientation of an asymmetric rigid-body. The optimality of the open-loop solutions are demonstrated by application of Pontryagin's Minimum Principle. Bellman's theory is used to further demonstrate optimality while extending open-loop theory to real-time application. The open-loop time optimal control is, next, used to construct the closed-loop Caratheodory- control solution for a similar maneuver. Closed-loop results presented for the system with and without parameter uncertainties verify the successful implementation of the method in practical applications

Distributed Adaptive Attitude Synchronization of Multiple Spacecraft

This paper addresses the distributed attitude synchronization problem of multiple spacecraft with unknown inertia matrices. Two distributed adaptive controllers are proposed for the cases with and without a virtual leader to which a time-varying reference attitude is assigned. The first controller achieves attitude synchronization for a group of spacecraft with a leaderless communication topology having a directed spanning tree. The second controller guarantees that all spacecraft track the reference attitude if the virtual leader has a directed path to all other spacecraft. Simulation examples are presented to illustrate the effectiveness of the results.Comment: 13 pages, 11 figures. To appear in SCIENCE CHINA Technological Science