Quaternion-based satellite attitude control—A direct parametric approach

Abstract

In this paper, the dynamical model in a matrix second-order nonlinear form with respect to the quaternion coordinates is firstly established for the attitude system of a satellite, which is complete in the sense that no approxima tion is taken. Then, with the help of a recently proposed general parametric design approach for general fully-actuated second-order nonlinear systems, a direct parametric approach for satellite attitude control via proportional plus derivative quaternion feedback is proposed, which gives a complete parametrization of the pair of feedback gains. The approach pos sesses two important features. Firstly, with the proposed controller parametrization, the satellite attitude system, though highly nonlinear, can be turned into a constant linear system with desire eigenstructure. Secondly, in such a design there are still degrees of freedom which may be further utilized to improve the system performance. An example is considered to demonstrate the use of the proposed approach.

Quaternion Filtering Based on Quaternion Involutions and its Application in Signal Processing

“…The real-valued cost function based on MSE is given by ( 1) and (2). For the error signal model (33),…”

“…Quaternions provide a compact model of mutual information between data channels, and have been used in fields such as traditional navigation [1], [2], Kalman filtering [3]- [5], neural networks [6], [7], spectral estimation [8], [9], communication [10], system control [11], motion tracking [5], [12], biomedical engineering [13], and adaptive filtering [7], [14]- [29]. The quaternion domain is a non-commutative extension of the complex domain.…”

“…The cost function is real-valued and nonanalytic, and the variables are quaternionvalued. The real-valued cost function based on MSE for the quaternion linear filter in the discrete time domain i is given by J MSE (w) = |e(i)| 2 = e(i)e * (i) = e * (i)e(i).…”

A Nonlinear Second-order Spacecraft Attitude Tracking Control Model for Control System Stabilization

“…As a significant part of spacecraft navigation control, spacecraft attitude control has been a hot problem for several years. Many different methods are applied on the problem of spacecraft attitude control as in [1][2][3][4][5][6] and [9][10][11]. For instance, Bang designed a new sliding model control method which can deal with flexible spacecraft attitude maneuver problem in [5].…”

“…Singh utilized adaptive output feedback control method to track the flexible spacecraft attitude in [6]. Additionally, Guan raised a direct parametric approach to stabilize the nonlinear second-order spacecraft attitude model, and the controller can turn the original model into a stable linear constant system certain degrees of freedom in [1].…”