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Purpose: This paper aims to investigate the relative translational control for multiple spacecraft formation flying. This paper proposes an engineering-friendly, structurally simple, fast and model-free control algorithm. Design/methodology/approach: This paper proposes a tanh-type self-learning control (SLC) approach with variable learning intensity (VLI) to guarantee global convergence of the tracking error. This control algorithm utilizes the controller's previous control information in addition to the current system state information and avoids complicating the control structure. Findings: The proposed approach is model-free and can obtain the control law without accurate modeling of the spacecraft formation dynamics. The tanh function can tune the magnitude of the learning intensity to reduce the control saturation behavior when the tracking error is large. Practical implications: This algorithm is model-free, robust to perturbations such as disturbances and system uncertainties, and has a simple structure that is very conducive to engineering applications. Originality/value: This paper verified the control performance of the proposed algorithm for spacecraft formation in the presence of disturbances by simulation and achieved high steady-state accuracy and response speed over comparisons. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose a high-precision attitude solution to solve the attitude drift problem caused by the dispersion of low-cost micro-electro-mechanical system devices in strap-down inertial navigation attitude solution of micro-quadrotor. Design/methodology/approach: In this study, a three-stage attitude estimation scheme that combines data preprocessing, gyro drifts prediction and enhanced unscented Kalman filtering (UKF) is proposed. By introducing a preprocessing model, the quaternion orientation is calculated as the composition of two algebraic quaternions, and the decoupling feature of the two quaternions makes the roll and pitch components independent of magnetic interference. A novel real-time based on differential value (DV) estimation algorithm is proposed for gyro drift. This novel solution prevents the impact of quartic characteristics and uses the iterative method to meet the requirement of real-time applications. A novel attitude determination algorithm, the pre-process DV-UKF algorithm, is proposed in combination with UKF based on the above solution and its characteristics. Findings: Compared to UKF, both simulation and experimental results demonstrate that the pre-process DV-UKF algorithm has higher reliability in attitude determination. The dynamic errors in the three directions of the attitude are below 2.0°, the static errors are all less than 0.2° and the absolute attitude errors tailored by average are about 47.98% compared to the UKF. Originality/value: This paper fulfils an identified need to achieve high-precision attitude estimation when using low-cost inertial devices in micro-quadrotor. The accuracy of the pre-process DV-UKF algorithm is superior to other products in the market. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the attitude control problem with mutating orbital rate and actuator fading. Design/methodology/approach: To avoid malicious physical attacks and hide itself, the spacecraft may irregularly switch its orbit altitude within a specific range, which will bring about variations in orbital rate, thereby causing mutations in the attitude dynamics model. The actuator faults will also cause changes in system dynamics. Both factors affect the control performance. First, this paper determines the potential switching orbits. Then under different conditions, design controllers that can accommodate actuator faults according to the statistical law of actuator fading. Findings: This paper, to the best of the authors' knowledge, for the first time, introduces the Markovian jump framework to model the possible unexpected mutating of orbital rate and actuator fading of spacecraft and then designs a novel control policy to solve the attitude control problem. Practical implications: This paper also provides the algorithm design processes in detail. A comparative numerical simulation is given to verify the effectiveness of the proposed algorithm. Originality/value: This is an early solution for spacecraft attitude control with dynamics model mutations. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems. Design/methodology/approach: The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems. Findings: The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis. Practical implications: An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results. Originality/value: The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to address the spacecraft attitude regulation problem in the presence of extrinsic disturbances and actuator faults. Design/methodology/approach: Based on adaptive backstepping design technique, a new concise adaptive dual-mode control scheme is proposed, which can either use the fault information detected by fault diagnosis mechanisms or switch to the fault-unknown mode when the fault diagnosis information is non-existent for control signal generation. These two modes share an adaptive mechanism that reduces the complexity of the algorithm. Findings: The new fault-tolerant attitude control algorithm can accommodate both modes with and without fault diagnosis mechanisms. Originality/value: The proposed algorithm in this paper can be applied to both cases when the attitude control system is equipped with or without fault diagnosis capability. This also enhances the robustness of attitude control algorithm. This study performs numerical simulations and verifies that the algorithm could effectively adapt to both modes. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the attitude regulation for spacecraft in the presence of time-varying inertia uncertainty and exogenous disturbances. Design/methodology/approach: The high gain approaches are typically used in existing researches for theoretical advantages, bringing better performance but sensitive to parameter selection, making the controller conservative. A reset-control policy is presented to achieve the spacecraft attitude control with easy control parameter tuning. Findings: The reset-control policy guarantees satisfying control performance despite using performance tuning function and saturation function besides reducing the conservativeness of the controller, thus reducing the effort in tuning control parameters. Originality/value: Notably, the adaptive function owns a reset mechanism, which is reset to a preset condition when the controlled variable crosses zero. The mathematical analysis also shows the system trajectory can converge to a set centered at the origin. [ABSTRACT FROM AUTHOR]

Purpose: Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion. Design/methodology/approach: This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model. Findings: While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination. Practical implications: The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models. Originality/value: The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the general actuator modeling in spacecraft attitude control systems. Design/methodology/approach: The proposed module in this paper provides various non-ideal factors such as the second-order dynamic time response, time-delay, bias torques, dead-zones and saturation. The actuator module can make the simulation as close to the practical situation as possible. Findings: This paper presents a practical integrated module for the simulation of attitude control algorithms. Based on theoretical modeling, we give simulation modules and numerical examples. The proposed model can be directly used in spacecraft control simulation. Instead of considering only a few of them, it makes the simulation more convincing. Though it may not be perfect, it is better than totally ignoring the actuator dynamics. Originality/value: The authors provide an integrated actuator model for spacecraft attitude control simulation, considering as many nonlinear factors as possible once time. [ABSTRACT FROM AUTHOR]

Purpose: Recent spacecraft attitude control systems tend to use wireless communication for cost-saving and distributed mission purposes while encountering limited communication resources and data exposure issues. This paper aims to study the attitude control problem with low communication frequency under the sampled-data. Design/methodology/approach: The authors propose constructive control system structures based on quantization and event-triggered methods for intra-spacecraft and multi-spacecraft systems, and they also provide potential solutions to shield the control system's data security. The proposed control architectures can effectively save communication resources for both intra-spacecraft and multi-spacecraft systems. Findings: The proposed control architectures no longer require sensors with trigger-ing mechanism and can achieve distributed control schemes. This paper also provides proposals of employing the public key encryption to secure the data in control-loop, which is transmitted by the event-triggered control mechanism. Practical implications: Spacecraft attempts to use wireless communication, yet the attitude control system does not follow up promptly to accommodate these variations. Compared with existing approaches, the proposed control structures can save communication resources of control-loop in multi-sections effectively, and systematically, by rationally configuring the location of quantization and event-triggered mechanisms. Originality/value: This paper presents several new control schemes and a necessary condition for the employment of encryption algorithms for control systems based on event-based communication. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate the attitude cooperation control of multi-spacecraft with in-continuous communication. Design/methodology/approach: A decentralized state-irrelevant event-triggered control policy is proposed to reduce control updating frequency and further achieve in-continuous communication by introducing a self-triggered mechanism. Findings: Each spacecraft transmits data independently, without the requirement for the whole system to communicate simultaneously. The local predictions and self-triggered mechanism avoid continuous monitoring of the triggering condition. Research limitations/implications: This investigation is suitable for small Euler angle conditions. Practical implications: The control policy based on event-triggered communication can provide potential solutions for saving communication resources. Originality/value: This investigation uses event- and self-triggered policy to achieve in-communication for the multi-spacecraft system. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the feasibility of using the combination of Lorentz force and aerodynamic force as a propellantless control method for spacecraft formation. Design/methodology/approach: It is assumed that each spacecraft is equipped with several large flat plates, which can rotate to produce aerodynamic force. Lorentz force can be achieved by modulating spacecraft's electrostatic charge. An adaptive output feedback controller is designed based on a sliding mode observer to account for unknown uncertainties and the absence of relative velocity measurements. Aiming at distributing the control input, an optimal control allocation method is proposed to calculate the electrostatic charge of the Lorentz spacecraft and control commands for the atmospheric-based actuators. Findings: Numerical examples are provided to demonstrate the effectiveness of the proposed control strategy in the presence of J2 perturbations. Simulation results show that relative motion in a formation can be precisely controlled by the proposed propellantless control method under uncertainties and unavailability of velocity measurements. Research limitations/implications: The controllability of the system is not theoretically investigated in the current work. Practical implications: The proposed control method introduced in this paper can be applied for small satellites formation in low Earth orbit. Originality/value: The main contribution of the paper is the proposal of the propellantless control approach for satellite formation using the combination of Lorentz force and aerodynamic force, which can eliminate the requirement of the propulsion system. [ABSTRACT FROM AUTHOR]