ATTITUDE stabilization of a rigid body has been a subject that has attracted a considerable amount of interest in the control of rigid spacecraft and aircraft. Several control techniques that stabilize the arbitrary attitude motion of a spacecraft can be found in the literature. For example, Egeland and Godhavn [1] establish the passivity between the angular velocity vector and the Euler parameter vector, and they propose an adaptive control to complete the global asymptotic stabilization of a rigid spacecraft. Using the same idea, Lizarraide and Wen [2] develop velocity-free controllers. The results in [1,2] were later extended by Tsiotras [3]. Fjellstad and Fossen [4] show that linear proportional-derivative (PD) control law is able to asymptotically stabilize the attitude motion of a rigid body by using minimal three-dimensional parameterizations for the kinematics. The attitude stabilization of a rigid body, using the unit quaternion and the angular velocity in the feedback control law, has been investigated by many researchers, and a wide class of controllers has been proposed (see, for instance, [5–7]). Because of its inherent robustness with respect to external disturbances and uncertainties, various optimal control schemes have been proposed for solving the attitude stabilization problem for rigid spacecraft [8–10]. While these control schemes are simple, elegant, and intuitively appealing, there is an implicit assumption in the development of these schemes that the spacecraft actuators are able to provide any requested joint torque. This assumption can lead to difficulties in practice since the available torque amplitude is limited in actual spacecraft. Moreover, it is known that control system design approaches that do not incorporate input constraints directly into the design suffer from important performance limitations [11,12]. For example, if the controller commands more torque than the actuators can supply from the typical control methods, degraded or unpredictable motion and thermal or mechanical failure may result [13]. Recognizing these difficulties, several solutions that take into account actuator constraints have been proposed. Specifically, Tsiotras and Luo [14] developed a saturation control law for an underactuated rigid spacecraft. This control law is completed by using a nonstandard attitude representation, which allows the decomposition of general motion into two rotations. Boskovic et al. [15] formulated two robust sliding mode controllers for global asymptotic stabilization of spacecraft in the presence of control input saturation and uncertainties, based on the variable-structure control approach. Wallsgrove and Akella [16] developed a smooth attitude stabilizing control containing hyperbolic tangent functions. The controller can be viewed as a smooth analog of the variable-structure approach, with the degree of sharpness of the control permitted to vary with time according to a set of user-defined parameters. Belta [17] proposes a saturated controller for driving the system from initial to final regions of the state space locally. The saturated control law is constructed based on a control of multiaffine systems. Guerrero-Castellanos et al. [18] investigated the global stabilization of a rigid spacecraft with a bounded quaternion-based feedback. Recently, Ali et al. [19] presented a method to design a bounded control for spacecraft attitude maneuver with backstepping control. This Note complements and extends the results presented in [3] to the bounded input cases. In particular, two very simple saturated PD (SPD) controllers are proposed to ensure global asymptotic stabilization of rigid spacecraft subject to actuator saturation, in terms of the Euler parameter kinematic parameterizations. The contribution of this Note is twofold. Comparing with similar work presented in [3], the proposed controls are bounded; thus, they can remove the possibility of degraded or unpredictable motion and actuator failure due to excessive torque input levels. This is accomplished by selecting control gains a priori. The fact that the proposed controllers can be a priori bounded is a significant added advantage. The practical implications are that the actuators can be appropriately sized without an ad hoc saturation scheme to protect the actuator. In comparison with the available saturated controls for stabilization of spacecraft, the proposed saturated controllers do not refer to the model parameters in the control formulations and are very simple; thus, they are readily implemented. It is proven that spacecraft systems subject to actuator constraints can be globally asymptotically stabilized via the proposed SPD controls by using Lyapunov’s direct method and LaSalle’s invariance principle. Simulations are included to illustrate the effectiveness of the proposed approaches.
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Jun 6, 2021
Ji-Seok Han + 6
