Attitude control strategies overcoming the topological obstruction on SO(3)

Abstract

This paper presents global tracking strategies for the attitude dynamics of a rigid body. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological restriction has been dealt with either by constructing smooth attitude control systems that exclude a set of measure zero in the region of attraction, or by introducing hybrid control systems to obtain global asymptotic stability. This paper proposes alternative attitude control systems that are continuous in time to achieve exponential stability, where the region of attraction covers the entire special orthogonal group. The main contribution of this paper is providing a new framework to overcome the topological restriction in attitude controls without relying on discontinuities through the controlled maneuvers. The efficacy of the proposed methods is illustrated by numerical simulations and experiments.

On controller design for systems on manifolds in Euclidean space

“…The following proposition essentially derives the control law in Equation 13 in the work of Lee et al, which was derived using geometric control theory therein, but is easily derived here with the linearized dynamics (25).…”

Robust attitude tracking with exponential convergence

“…Equations (58) and (59) lead to conclusions as follows: (i) Disturbance rejection can be enhanced by increasing ; (ii) a larger value can be assigned for to improve the robustness against the uncertain inertia parameters; and (iii) the rise of l and that of can both lessen the tracking error resulted from the external disturbances and the uncertain inertia parameters. Remark 4 Here the proposed controller is compared with the exponentially convergent attitude tracking controllers in [19, 29] and FT convergent ones in [23–26]. All these papers did not not consider the uncertainties of the inertia parameters.…”

“…Gui et al [23] just considered attitude stabilisation which is a special case of attitude tracking. Attitude tracking was considered in [19, 24–26, 29]. Only Guo et al [24] considered bounded disturbances.…”

“…Only Guo et al [24] considered bounded disturbances. The authors of [19, 25, 29] just considered constant disturbances, while [23, 26, 29] considered no disturbance. Furthermore, those in [23–25] are invalid for some initial states.…”

“…In contrast, the proposed controller can accommodate bounded disturbances and uncertain inertia matrix, therefore has stronger robustness than the above mentioned attitude controller. Like [19, 26, 29], the proposed controller is valid for any initial states. Furthermore, by including a variable gain, the proposed controller can have moderate gain in the start stage, whilst much higher gain in steady state, thus it is more likely to obtain higher control precision than the aforementioned attitude controllers when uncertainties exist for a given control amplitude.…”