Eng Kee Poh

Decentralized Robust Adaptive Control for Attitude Synchronization Under Directed Communication Topology

T HE need to maintain accurate relative orientation between spacecraft is critical in many satellite formation missions. For instance, in interferometry application, the relative orientation between spacecraft in a formation is required to be maintained precisely during formation maneuvers. In interspacecraft laser communication operation, the participating spacecraft are also required to maintain accurate relative attitude throughout the communication process. This control problem, commonly referred to as attitude synchronization in the literature, has attracted much research attention. Various solutions have been proposed and these can be broadly classified according to the advocated techniques: leader– follower [1–4], virtual structure [5,6], behavior-based [7–11], and graph-theoretical approach [12–15]. In particular, the graph-theoretical approach has been actively studied for cooperative control of multi-agent system using limited local interaction [16,17] and was adopted for attitude synchronization problem in [12–15]. In the above-cited decentralized attitude synchronization results, except [14,15], it is assumed that the interspacecraft communication links are undirected (i.e. bidirectional). However, in practice, the interspacecraft communication topology may be restricted to be directed, such as in unidirectional satellite laser communication system. The control problem of attitude synchronization under directed communication topology is more challenging as compared with the case with undirected communication topology. This issue was studied in [14] but the proposed control law requires derivative of the angular velocity, which may introduce additional noise into the system. Furthermore, the attitude-tracking performance analysis in [14] is applicable only to the casewhere the directed graph can be simplified to a graph with only one node. This constraint on communication topology is relaxed in [15], which uses modified Rodriguez parameters and Euler– Lagrange system to describe the satellite attitude dynamics. However,modifiedRodriguez parameters contain singularity and are thus not suitable for the development of globally stabilizing control algorithms. This Note proposes a decentralized adaptive sliding-mode control lawwhich regulates attitude and angular velocity errors of individual spacecraft with respect to reference commands and minimizes relative attitude and angular velocity errors between spacecraft. Thus, the proposed control law ensures that each spacecraft attains desired time-varying attitude and angular velocity while maintaining attitude synchronization with other spacecraft in the formation even in the presence of model uncertainties and external disturbances. Moreover, the design is applicable to general communication topology and is not restricted to ring topology or undirected communication topology. In the following section, unit quaternion representation will be introduced into the satellite attitude control problem and algebraic graph theory will be applied to describe general directed communication topology.

Integral-Type Sliding Mode Fault-Tolerant Control for Attitude Stabilization of Spacecraft

Two fault-tolerant control (FTC) schemes for spacecraft attitude stabilization with external disturbances are proposed in this brief. The approach is based on integral-type sliding mode control strategy to compensate for actuator faults without controller reconfiguration. First, a basic integral-type sliding mode FTC scheme is designed so that sliding manifold can be maintained from the very beginning. Once the system enters the sliding mode, the dynamics of the closed-loop system with actuator fault is identical to that of the nominal healthy system. Second, the integral-type sliding mode fault-tolerant controller is incorporated with adaptive technique to accommodate actuator faults so that the required boundary information can be relaxed. The effectiveness of the proposed schemes against actuator faults is demonstrated in simulation.

Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation: Legendre Pseudospectral Approach

In this paper, we focus on the design of a fuel-optimal maneuver strategy to reconfigure satellite formation using a low-thrust propulsion system. We cast it as an optimization problem with a desired final satellite formation configuration subject to collision avoidance constraints on the paths of the chief and all deputy satellites. The satellite terminal orbit states corresponding to this desired formation configuration are ensured by imposing an energy-matching condition and final geometry configuration constraints in the problem formulation. In addition, we adopt our recently developed relative satellite kinematics model to accurately describe relative satellite orbit geometry in the presence of J 2 effects. The resulting nonlinear optimal control problem is converted into a nonlinear programming problem by the application of the Legendre pseudospectral method and is then solved by using a sparse nonlinear optimization software named TOMLAB/SNOPT. Simulation results demonstrate the efficiency of our proposed method in designing fuel-optimal maneuvers for a wide class of satellite formation problems.

Fault-Tolerant Robust Automatic Landing Control Design

A new approach is presented for developing reliable automatic landing controllers that can tolerate actuator stuck faults. The approach is based on the solvability of linear matrix inequalities and polytopic fault models. The H 2 control technique is used to guarantee tracking performance with respect to a given glide slope trajectory. A high-fidelity fighter aircraft model is studied to illustrate the proposed approach. The six-degree-of-freedom nonlinear aircraft model with independent left and right control surfaces is established using the appropriate aerodynamic data from wind-tunnel test and computational fluid dynamics. A single fixed reliable automatic landing controller is designed for the whole landing process. It achieves optimized tracking performance in normal operation and maintains an acceptable level of tracking performance in the case of single contingency actuator stuck fault among the left and right ailerons and horizontal stabilators. Nonlinear simulation under various faults, measurement noises, and wind disturbances such as deterministic wind, wind turbulence, and wind shear are included in this study. Simulation results show that such a reliable controller design approach can achieve zero steady-state tracking error, good tracking response, robustness against wind disturbances, and reliability against actuator stuck faults.

Attitude Tracking Control of Rigid Spacecraft With Actuator Misalignment and Fault

A control scheme is developed to address the attitude tracking problem of a rigid spacecraft. A sufficient condition to accommodate actuator misalignment is presented. The controller asymptotically stabilizes the closed-loop attitude tracking system. The desired attitude trajectories can be tracked in finite time, even in the presence of uncertain inertia tensor, external disturbances, actuator fault, and actuator misalignment. The attitude tracking performance of the controller is evaluated through an illustrative example.

Non-linear output feedback tracking control for AUVs in shallow wave disturbance condition

This article presents a non-linear output feedback tracking controller deisgn for autonomous underwater vehicles (AUVs) operating in shallow water area. In a shallow water environment, significant disturbances due to shallow water waves affect the motion of marine vehicles greatly. Since it is not energy efficient to counteract the oscillatory disturbances due to waves, it is critical to obtain the wave information or wave induced disturbance information and design an energy efficient controller to reduce the action of actuators to counteract wave disturbances to avoid wear and tear on actuators. In this article, a non-linear observer is first designed to estimate the low frequency (LF) motion of AUVs and to filter out wave-frequency (WF) motion of AUVs due to shallow water wave by using position and attitude measurements. Based on the designed observer, a non-linear output feedback controller is subsequently derived by using the observer backstepping technique. By using this approach, the AUV achieves global exponential tracking without excessive energy consumption to counteract the wave disturbance and also avoids excessive wear and tear on thrusters. Global exponential stability (GES) of overall observer-controller system is proved through Lyapunov stability theory. A set of simulations is carried out by using the KAMBARA (Silpa-Anan 2001) AUV model to demonstrate the performance of the proposed observer and output feedback controller.

Inertia-free fault-tolerant spacecraft attitude tracking using control allocation

The problem of fault-tolerant attitude tracking control for an over-actuated spacecraft in the presence of actuator faults/failures and external disturbances is addressed in this paper. Assuming that information on the inertia and bounds on the disturbances are unknown, a novel fault-tolerant control (FTC) law incorporating on-line control allocation (CA) is developed to handle actuator faults/failures. To improve the robustness of the adaptive law and stop the adaptive gain from increasing, the time-varying dead-zone modification technique is employed in parameter adaptations. It is shown that uniform ultimate boundedness of the tracking errors can be ensured. To illustrate the efficiency of the CA-based FTC strategy, numerical simulations are carried out for a rigid spacecraft under actuator faults and failures.

Attitude Control of Spacecraft with Actuator Uncertainty

A LTHOUGH safe-mode transition is a technique widely applied to handle component faults of spacecraft, it is not an option during critical phases. To increase onboard autonomy in fault management fault-tolerant-control (FTC) design without ground intervention has attracted increasing attention [1,2]. Feedback linearization control was developed for automated attitude recovery of spacecraft [3]. An FTC attitude control was presented in [4] to accommodate reaction-wheel faults. In particular, sliding mode control (SMC) is becoming an effective approach to tackle with uncertainty and external disturbance. SMC is successfully applied to design FTC for spacecraft. In [5] an SMC-based lawwas synthesized to stabilize attitudewith actuator outage fault. In [6] an adaptive SMC scheme was proposed to tolerate thruster failures. Accommodating partial loss of actuator effectiveness without angular-velocity measurements was discussed in [7]. In [8] rapid reorientation was studied in the absence of control along either roll or yaw axes. The preceding FTC schemes assume that actuators are free of misalignments. However, finite manufacturing tolerance or warping of structure may introduce actuator alignment errors. This issue may cause performance degradation of the attitude-control system. To address this problem an adaptive-control law was developed to handle small gimbals’ alignment error of variable speed-control moment gyros [9]. In [10] a model reference adaptive controller was tested with alignment errors up to 15 deg. An extended Kalman filter was used for on-orbit alignment calibration [11]. Unknown inertia parameters and actuator uncertainty were investigated in [12]. In [13] an adaptive-control law was presented to compensate for thrustmagnitude error and misalignment. This study investigates attitude stabilization with external disturbance, unknown inertia parameters, and actuator uncertainties including fault and misalignment. An adaptive control is proposed to render the closed-loop system input-to-state stable and is organized as follows: Sec. II presents a mathematical model of a rigid spacecraft, Sec. III presents main results, and simulation results are given in Sec. IV followed by the conclusions in Sec. V.

Satellite formation keeping via real-time optimal control and iterative learning control

In this paper, we focus on the design of fuel-optimal satellite formation keeping strategy using a low thrust propulsion system. The proposed controller includes feedback control and feedforward control. For feedback control, a real-time fuel-optimal control approach is proposed. The fuel-optimal control problem is then converted into a quadratic programming problem by application of a Legendre pseudospectral method. In the optimization problem, we adopt our recently developed linear time-varying relative dynamics to accurately describe relative motion in the presence of earth oblateness effect and eccentricity effect. The control acceleration constraints are included in the optimization problem to avoid control saturation for low-thrust propulsion system. In addition, in order to meet the requirement of high-precision formation keeping for some satellite formation flying missions, a feedforward control: iterative learning control (ILC) is used for the existing close-loop feedback control system. ILC aims to improve formation keeping accuracy by eliminating the effects of periodic perturbations such as gravitational perturbation, atmospheric drag. Simulation results demonstrate the efficiency of our proposed method.

Time-optimal reorientation for rigid satellite with reaction wheels

This article introduces a time-optimal reorientation manoeuvre controller with saturation constraints on both reaction wheels’ torques and angular momentum. The proposed control scheme consists of two parts. The first part is an open-loop time-minimum reorientation trajectory generated by the Legendre pseudospectral method. Actuator dynamics, saturations on control torques and angular momentums of reaction wheels are taken into account in generating the open-loop optimal trajectory. The second part is a closed-loop tracking control law to track the optimised reference trajectory based on attitude error dynamics with reaction wheel dynamics. Numerical simulations show that reaction wheel dynamics play an important role in attitude manoeuvres. The proposed controller performs better for rest-to-rest reorientation manoeuvre than other existing methods.