Attitude Dynamics Model Research Articles

Compound Attitude Control Strategy for Reusable Launch Vehicle Based on Improved Particle Swarm Optimization Algorithm

This study introduces an advanced dual-mode compound attitude control framework for reusable launch vehicles (RLVs), underpinned by an enhanced particle swarm optimization (PSO) algorithm. This innovative strategy is tailored to meet the stringent demands for precision and robust anti-interference capabilities across the entire flight envelope of RLVs. The research commences with the formulation of a comprehensive attitude dynamics model and diverse heterogeneous actuator representations, meticulously crafted to reflect the distinct phases of RLV flight. Building upon this foundation, a synergistic control paradigm is engineered, integrating PID and fuzzy PID controllers and dynamically adjusting the inertia weights and learning factors of the PSO algorithm to achieve the balance between global and local optimization performance, complemented by a refined fitness evaluation function. The crux of the study is the application of an upgraded PSO algorithm to fine-tune the controllers’ weighting coefficients, culminating in an optimized dual-mode compound attitude control system. A series of comparative simulation analyses are thoroughly executed to appraise the system’s responsiveness, stability, precision, and resilience to interference. The simulation outcomes demonstrate an average reduction of 42.21% in step response overshoot, an 18.52% decrease in settling time, a 53.18% decline in steady-state error, a 56.80% drop in the maximum deviation value, a 55.82% improvement in recovery speed, and a 75.61% enhancement in tracking precision for the proposed controller. The findings clearly verify the superior performance of the proposed control system, affirming its contribution to the advancement of RLV attitude control. The proposed controller holds promising potential for real application in attitude control systems and is poised to augment the reliability and mission success rate of RLVs under intricate flight scenarios.

Multiple model fault diagnosis and fault tolerant control for the launch vehicle’s attitude control system

Abstract For the launch vehicle attitude control problem, traditional methods can seldom accurately identify the fault types, making the control method lack of pertinence, which largely affects the effect of attitude control. This paper proposes an active fault tolerant control strategy, which mainly includes fault diagnosis and fault tolerant control. In the fault diagnosis part, a small deviation attitude dynamics model of the launch vehicle is established, Kalman filters with different structures are designed to detect and isolate faults through residual changes, and the fault quantity of the actuator is further estimated. In the fault tolerant control part, the following control scheme is adopted according to the above diagnostic information: when the sensor fault is detected, the sensor measurement data is reconstructed; when the actuator fault is identified, the control allocation matrix is reconstructed. Simulation results show that the proposed method can effectively diagnose sensor fault and actuator faults, and significantly improve attitude tracking accuracy and control adjustment time.

Finite-time state-constrained adaptive fault-tolerant control for heavy launch vehicles with input quantization

This paper proposes the finite-time state-constrained adaptive fault-tolerant control method for a class of heavy launch vehicles subject to quantized input signals and actuator faults. Firstly, the attitude dynamic model of the heavy launch vehicles suffering from the actuator faults and disturbances is formulated. Secondly, to deal with the completely unknown nonlinear functions, radial basis function neural networks (RBFNNs) are introduced for approximation and compensation. Meanwhile, the barrier Lyapunov function (BLF) is introduced to ensure that all the states in the closed-loop system are bounded and the constraints of the system states are satisfied. As a result, the finite-time state-constrained adaptive fault-tolerant control structure is constructed for the heavy launch vehicles and the semi-globally practical finite-time stability (SGPFS) of the closed-loop control system is proved. Finally, numerical simulation results show the effectiveness and the satisfactory performance of the proposed control algorithm.

Deep Deterministic Policy Gradient (DDPG) Agent-Based Sliding Mode Control for Quadrotor Attitudes

A novel reinforcement deep learning deterministic policy gradient agent-based sliding mode control (DDPG-SMC) approach is proposed to suppress the chattering phenomenon in attitude control for quadrotors, in the presence of external disturbances. First, the attitude dynamics model of the quadrotor under study is derived, and the attitude control problem is described using formulas. Second, a sliding mode controller, including its sliding mode surface and reaching law, is chosen for the nonlinear dynamic system. The stability of the designed SMC system is validated through the Lyapunov stability theorem. Third, a reinforcement learning (RL) agent based on deep deterministic policy gradient (DDPG) is trained to adaptively adjust the switching control gain. During the training process, the input signals for the agent are the actual and desired attitude angles, while the output action is the time-varying control gain. Finally, the trained agent mentioned above is utilized in the SMC as a parameter regulator to facilitate the adaptive adjustment of the switching control gain associated with the reaching law. The simulation results validate the robustness and effectiveness of the proposed DDPG-SMC method.

Robust Approximate Optimal Trajectory Tracking Control for Quadrotors

This paper uses the adaptive dynamic programming (ADP) method to achieve optimal trajectory tracking control for quadrotors. Relying on an established mathematical model of a quadrotor, the approximate optimal trajectory tracking control, which consists of the steady-state control input and the approximate optimal feedback control input, is designed for a nominal system. Considering the compound disturbances in position and attitude dynamic models, disturbance observers are introduced. The estimated values are used to design robust compensation inputs to suppress the effect of the compound disturbances for good trajectory tracking performance. Theoretically, the Lyapunov theorem demonstrates the stability of a closed-loop system. The robustness and effectiveness of the proposed controller are confirmed by the simulation results.

Convergence guaranteed attitude control of underactuated spacecraft using two control torques

In this paper, the convergence guaranteed attitude stabilization of underactuated spacecraft using two control torques is investigated. By introducing the (w,z) parameters to describe the attitude motion of the underactuated spacecraft, a unified integrated attitude kinematic and dynamic model is originally derived, based on which the controllers can be directly designed for the two actuated axes. Then, three types of controllers are designed to stabilize the attitude and angular velocity along the two actuated axes to zero in fixed time. After that, it is strictly evaluated that the attitude and angular velocity along the underactuated axis can eventually stabilize to the constant values. In this way, the convergence property of the designed controllers can be guaranteed. The utilized controllers are the fixed-time proportional-differential (PD)-like controller, the fixed-time nonsingular terminal sliding mode (NTSM) controller, and the fixed-time integral sliding mode (ISM) controller, respectively. Among them, the fixed-time ISM controller is best since it is strongly robust against disturbances and has no singularity problem naturally, which overcomes the drawbacks of the fixed-time PD-like controller and the fixed-time NTSM controller simultaneously. Lastly, simulated studies are executed to examine the derived results.

Self-triggered formation control for multi-spacecraft attitude coordination with communication delays

This article addresses the event-triggered formation control problem for multi-spacecraft systems subject to time-varying delays. Firstly, a formation attitude dynamics model considering communication delays is proposed, and two auxiliary trigger instants are designed to transform the event-based control problem subject to delays into the conventional event-triggered control problem. Next, a nonlinear observer based on the triggering information of neighbors is developed to estimate the lumped nonlinear term. To avoid continuous communication, a dynamic event-based formation control strategy is proposed based on the nonlinear observer. To avoid continuous computation of the trigger mechanism, a self-triggered function is developed based on the current trigger information. Moreover, the system is Zeno-free under the proposed event-based control algorithms. Finally, simulation results show that compared with the dynamic triggering function, the self-triggered function avoids continuous computation and improves the control accuracy by nearly one order of magnitude while increasing communication frequency by 67.8 %.

Dissecting moral judgements: Using moral foundation theory to advance the contingency continuum

Incorporating Moral Foundation Theory, this study introduces an enhanced Contingency Continuum to advance the Contingency Theory of Strategic Conflict Management by dissecting the origins of conflict formation. The enhanced Contingency Continuum treats conflict as a function of moral judgment based on which people judge right and wrong. This study explores how an event’s moral implication could be deconstructed into the enhanced Contingency Continuum and contribute to the formation of a conflict through a case study of Harvey Weinstein’s scandal. Our analysis and findings of the case were then validity-tested in an extensive verification interview with a practitioner/educator who has been in the PR field for more than 40 years. Three attributions of how the enhanced Contingency Continuum could advance the Contingency Theory are identified and summarized as a three-step-cyclic model, Moral Attitude Dynamic Model (MADM) to fully exploit the potential of the enhanced Contingency Continuum on managing not only moral conflicts but also conflicts that lack resolution such as long-standing social controversial issues.

Adaptive Terminal Sliding Mode Fault-Tolerant Control of Spacecraft Based on the Left Attitude Error Function of SO(3)

For the problem of spacecraft attitude actuator failure, an adaptive terminal sliding mode fault-tolerant controller (ATSMFTC) based on the differential manifold SO(3) modelling is designed in this paper. First, SO(3) is used to provide a global and unique description of the spacecraft attitude dynamic model. This modelling method not only avoids the problems of singularity and unwinding that exist in traditional modelling methods but also the SO(3) modelling has a simple formulation of the dynamic equations. Then a left attitude error descriptor function is constructed on SO(3) to design an ATSMFTC. This controller is capable of fast and accurate tracking of the time-varying desired attitude. At the same time, it can react quickly to maintain system stability in case of spacecraft attitude actuator failure. The controller designed based on the left attitude error description system of SO(3) has the features of small computational effort and simple design process. Finally, the numerical simulation of the attitude tracking error verifies the feasibility and high efficiency of the controller designed in this paper.

Variable-structure PD controller for satellite attitude: Stability analysis and design for optimal performance

A novel variable structure controller is investigated for satellite attitude control. This novel controller does not lead to a sliding mode, which avoids the chattering problem, making it suitable for practical implementation. Detailed formulation of the controller is presented along with analytical stability analysis for a second order system. The system having this nonlinear controller is homogeneous, which leads to a similar response at large and small deviations from the equilibrium. A procedure for tuning homogeneous controllers for all initial conditions is proposed. A detailed model of the satellite attitude dynamics, actuator dynamics, and delays in the system is utilized to optimize controller gains numerically. A comparative analysis shows the superiority of the proposed controller over a conventional PID controller in terms of better transients and lower energy consumption.

Attitude Tracking Adaptive Control of a Geocentric Polar Displaced Solar Sail

To deal with the attitude tracking control problem of a struck or pierced geocentric polar displaced solar sail (GPDSS), an attitude adaptive control strategy is proposed in this paper under the complex conditions of unknown inertial parameters, external disturbance and input saturation. First, on the basis of a flexible solar sail spacecraft attitude dynamics model with damping terms and vibration initial values, an integrated disturbance term, including inertial parameter uncertainties and external disturbance, is constructed. Second, a radial basis function neural network is applied to design a disturbance estimator with an adaptive law to estimate the integrated disturbance in real time. Then, a sliding-mode controller with fixed-time convergence in the reach phase and finite-time stability in the sliding phase is designed, and stability analysis is conducted by using the Lyapunov theory. Finally, comparative simulations with a linear sliding-mode controller and numerical simulations under various workings are performed. The results show that the designed adaptive control strategy can effectively achieve the attitude tracking control of the GPDSS.

Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions

AbstractIn this article, the optimal attitude consensus control problem of distributed spacecraft formation through local information exchange is solved in the presence of parameter uncertainty and disturbance. The attitude dynamics model of rigid spacecraft formation is established based on unit quaternion under an undirected graph. Then, the optimal attitude consensus control scheme based on control Lyapunov functions is adopted for rigid spacecraft formation. The approach to construct an appropriate Lyapunov function for multiple spacecraft is developed. Then the lumped disturbance is estimated by an extended state observer (ESO) and using the sliding mode control approach improves the robustness of the controller. The proposed optimal controller can not only ensure the global consensus convergence of the system but also make the preset performance index function achieve the minimum value. In addition, the mathematical proof is given for the stability analysis of the system by the Lyapunov stability theory. Finally, some simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller.

Sliding-Mode-Based Attitude Tracking Control of Spacecraft Under Reaction Wheel Uncertainties

The attitude tracking operations of an on-orbit spacecraft with degraded performance exhibited by potential actuator uncertainties (including failures and misalignments) can be extraordinarily challenging. Thus, the control law development for the attitude tracking task of spacecraft subject to actuator (namely reaction wheel) uncertainties is addressed in this paper. More specially, the attitude dynamics model of the spacecraft is firstly established under actuator failures and misalignment (without a small angle approximation operation). Then, a new non-singular sliding manifold with fixed time convergence and anti-unwinding properties is proposed, and an adaptive sliding mode control (SMC) strategy is introduced to handle actuator uncertainties, model uncertainties and external disturbances simultaneously. Among this, an explicit misalignment angles range that could be treated herein is offered. Lyapunov-based stability analyses are employed to verify that the reaching phase of the sliding manifold is completed in finite time, and the attitude tracking errors are ensured to converge to a small region of the closest equilibrium point in fixed time once the sliding manifold enters the reaching phase. Finally, the beneficial features of the designed controller are manifested via detailed numerical simulation tests.

Fault-tolerant attitude tracking control for carrier-based aircraft using RBFNN-based adaptive second-order sliding mode control

This paper proposes a fault-tolerant attitude tracking control for carrier-based aircraft with external disturbances and actuator faults, which is based on backstepping control, second-order sliding mode control (SOSMC) and the radial basis function neural network (RBFNN) adaptation algorithm. First, the generic attitude dynamic model of carrier-based aircraft is presented. Based on backstepping method, the attitude control system is divided into two simple and low-order subsystems. Then, the basic SOSMC using the type of proportional integral (PI) sliding mode variable are designed respectively for two subsystems, which can guarantee the system stable with no chattering in the finite time. To compensate for disturbances and faults more accurately, we design RBFNN-based adaptive second-order sliding mode control (RASOSMC) where RBFNN algorithm is utilized to approximate the lumped perturbation, which attenuates the impact of disturbances and faults more effectively and improves attitude tracking performance. Furthermore, the adaptive online algorithms for the RBFNN weights are proposed based on Lyapunov theory. Finally, numerical simulation results are given to indicate the effectiveness and robustness of the SOSMC scheme and RASOSMC scheme.

Uncertain optimal attitude control for space power satellite based on interval Riccati equation with non-probabilistic time-dependent reliability

Considering the multi-source uncertainties and disturbances in the attitude dynamics of space power satellite (SPS), an interval dynamic model of SPS is proposed based on the non-probabilistic theory, which is controlled by a novel uncertainty-based linear–quadratic regulator (LQR) method with time-dependent reliability. Based on the interval analysis method, an interval time-varying attitude dynamic model of SPS for sun-pointing is established considering the uncertain inertia and initial states as unknown-but-bounded parameters. Feedforward and feedback controllers are designed to offset the disturbance and control attitude, respectively. An interval Riccati equation-based optimal control method is proposed to develop a novel uncertainty-based LQR method. Non-probabilistic time-dependent reliability is constituted based on the interval process and first passage theory to assess attitude states. An uncertain multi-objective optimization of attitude control with reliability constraints is proposed to realize the uncertain LQR method. Verified by a numerical example of SPS, the proposed method takes only 0.6‰∼0.8‰ time consumption of 10,000 Monte Carlo simulations while maintaining a certain accuracy.

Predefined-Time Control of a Spacecraft Attitude with Thrust Booms

A predefined-time attitude controller for electric spacecraft and its thrust booms is investigated by combining a second-order sliding mode control with predefined-time disturbance observer. First, an Eulerian–Lagrangian attitude dynamics model of the electric spacecraft with thrust booms is constructed; meanwhile, the coupling between the spacecraft platform and thrust boom is treated as the disturbance when designing the controller. Next, a predefined-time convergent second-order sliding surface and reaching law are designed to ensure the predefined-time fast convergence. The second-order sliding surface can avoid the chattering problem of controller and improve the anti-disturbance capability of the spacecraft. Furthermore, a novel predefined-time disturbance observer is developed to handle the disturbances, ensuring that the tracking error of the system converges to the equilibrium. At last, the simulation is performed to verify the feasibility and advantages of the proposed algorithm.

Spacecraft attitude estimation under attitude tracking maneuver during close-proximity operations

This paper presents a real-time relative three-axis attitude estimation using a camera and two gyros under momentum changes during close-proximity operations. The camera sensor provides quaternion measurements that relate the body frame of the deputy spacecraft with respect to the body frame of the chief spacecraft. The quaternion measurements are coupled with gyro measurements and attitude dynamics model in a multiplicative extended Kalman filter to determine relative attitude and gyro biases under momentum changes. The relative quaternion kinematics is augmented with spacecraft relative motion dynamics to represent the filter process dynamics. The quaternion measurements from a camera sensor and inertial measurement units (IMU) are utilized to the filter measurement model. The fault-tolerant attitude controller actuated by four reaction wheels, which has no unwinding problem is used for attitude tracking maneuvers during close-proximity operations in the presence of external disturbances, uncertain inertia parameter and actuator faults. This controller is combined with the extended Kalman filter to filter noisy measurements and to estimate gyro biases, which leads to a full-state feedback control system. Numerical simulations are performed to verify the effectiveness of the attitude estimation and control systems of the spacecraft with four reaction wheels during close-proximity operations of spacecraft in low-Earth orbit.

An Adaptive Control Methodology for Spacecraft Attitude Tracking Under Model and Environmental Uncertainties

This study investigates the attitude tracking problem for rigid spacecraft under model and environmental uncertainties. Two different control laws are separately developed and combined. First, based on a nominal attitude dynamic model assuming no uncertainty, the first controller is developed that exactly tracks a prespecified attitude reference trajectory with minimized control cost. The designer can generate this reference to prescribe desired performance specifications such as the maximum convergence time and overshoot. Next, an uncertain attitude dynamic system is considered, and the second controller is designed and added so that the controlled system can successfully track the predesigned reference trajectory with a user-specified tolerance even subject to uncertainty whose bounds are unknown. Compared to existing adaptive control schemes, the proposed approach possesses a very simple structure with a small number of control parameters and is not computationally intensive, making it more attractive for practical implementation. The proposed control laws generate smooth control signals and any information about the uncertainty bound is not needed in its design. Simulation results are provided to demonstrate the practical feasibility of the proposed approach, where reorientation/slew maneuvers of a large spacecraft are considered. The effects of limitations on the control torques are also investigated to show the effectiveness of the control methodology developed herein.

Adaptive predefined-time control for liquid-filled flexible spacecraft attitude stabilization during orbit maneuver

A predefined-time attitude stabilization for complex structure spacecraft with liquid sloshing and flexible vibration is investigated under input saturation during orbital maneuver. First, the attitude dynamics model of liquid-filled flexible spacecraft is constructed. Meanwhile, the influence of solar panel vibration and liquid sloshing is treated as a disturbance in the controller design. Next, an adaptive predefined-time control scheme is proposed by applying sliding mode control theory. A predefined-time convergent sliding surface and reaching law are designed to ensure the predefined-time fast convergence rate. Furthermore, a novel adaptive algorithm is developed to handle the disturbances from liquid sloshing and flexible vibration, ensuring that the system converges to a small neighborhood of the equilibrium. Additionally, a new auxiliary system is constructed to deal with the effects of input saturation. At last, one simulation case is performed to verify the feasibility and advantages of the proposed algorithm.

Adaptive neural fault-tolerant control for output-constrained attitude tracking of unmanned space vehicles

The challenging problem of attitude tracking control for unmanned space vehicles (USVs) subject to actuator faults and output constraints is addressed in this study. A novel adaptive neural fault-tolerant controller is proposed by integrating the neural networks (NNs) and barrier Lyapunov function (BLF) with the backstepping technique. Two NNs are adopted to approximate the uncertain nonlinear terms caused by unknown attitude dynamics and actuator faults, respectively. Moreover, the BLF is introduced to tackle the output constraints. It is strictly proved that all the closed-loop error signals are uniformly ultimately bounded under the proposed controller. Totally, the proposed adaptive neural fault-tolerant controller has the following two distinctive features. (1) The proposed controller is model-free and can still be applicable even when the USV attitude dynamic model is completely unknown in advance. (2) The proposed controller can guarantee the attitude tracking error always within the predefined output constraints even in the presence of actuator faults and thus ensuring safety. Finally, the excellent tracking performance of the proposed controller is verified through numerical simulations and comparisons.