Attitude Tracking Research Articles

Geometric Adaptive Robust Hierarchical Control for Quadrotors With Aerodynamic Damping and Complete Inertia Compensation

In this article, the geometric adaptive robust hierarchical control strategy is proposed for underactuated quadrotor, in which the negative effects of nonlinearities, uncertainties, and coupling are thoroughly considered and effectively attenuated. For handling nonlinearities, geometric control is adopted, i.e., the attitude error is directly defined on tangent space of rotation group, thus better attitude tracking performance can be achieved. To deal with uncertainties, a comprehensive dynamic model is established with compound damping terms representing the main aerodynamic effects and all inertia parameters including mass, inertia tensor, and center of gravity. Then, integrated direct/indirect adaptive robust control is developed with adaptive compensation of aerodynamic damping and complete inertia, which is beneficial to improve tracking performance. As for the coupling, hierarchical control architecture is utilized to relax the strong coupling between attitude and translational subsystems. Moreover, the stability of the overall closed-loop hierarchical system, together with transient performance and final tracking accuracy, has been rigorously analyzed without time-scale separation assumption. Finally, comparative experiments demonstrate the better performance of the proposed method in terms of tracking accuracy and robustness.

Adaptive Deformation Control of a Flexible Variable-Length Rotary Crane Arm With Asymmetric Input-Output Constraints.

This article constructs two adaptive control laws to achieve deformation reduction and attitude tracking for a rotary variable-length crane arm with system parameter uncertainties and asymmetric input-output constraints. Two auxiliary systems are given to deal with the input constraints, an asymmetric-logarithm-barrier Lyapunov function is established for achieving the asymmetric output constrains, and five adaptive laws are constructed to handle system parameter uncertainties. Besides, the control design is based on a partial differential equation model, and the S-curve acceleration and deceleration method is used for regulating the arm extension speed. Both the system stability and uniform ultimate boundedness of the controlled crane arm are analyzed. Simulation results validate the effectiveness of our established control laws.

Attitude tracking control for quadrotor based on time-varying gain extended state observer

Considering the problems of unknown external disturbances and parametric uncertainties in attitude tracking of a quadrotor, a backstepping sliding mode control method based on the time-varying gain extended state observer is proposed in this article. First, the mathematical model of the attitude system of the quadrotor is introduced. Second, a time-varying gain extended state observer is proposed to observe the unmeasurable states, total disturbance, and reduce the “peaking value” phenomenon, which often occurs in traditional linear extended state observers. It is proved that the observation errors are bounded. Third, a novel controller synthesized by backstepping sliding mode control method and the time-varying gain extended state observer is proposed for the attitude system of the quadrotor. Moreover, the designed controller can ensure that all signals of the closed-loop system are bounded. Finally, the effectiveness and superiority of the proposed control method are verified by simulation.

Adaptive fixed-time quantized fault-tolerant attitude control for hypersonic reentry vehicle

This paper focuses on the adaptive fixed-time quantized fault-tolerant attitude tracking problem for hypersonic reentry vehicle (HRV). Due to the strong nonlinearity, tight coupling, uncertain characteristics and potential actuator faults, the attitude control of HRV poses a considerable challenge. By resorting to feedback linearization technique, the inherently nonlinear attitude model of HRV is decoupled into a linear control-oriented model, where the actuator malfunction, quantization nonlinearities and multiple disturbances are incorporated into the lumped disturbance. Then a fixed-time neural network disturbance observer is designed to estimate the lumped disturbance, with the practical fixed-time stability of the observation error ensured independent of initial conditions. Subsequently, by using a hyperbolic-tangent-like function, a novel paradigm is proposed for achieving adaptive fixed-time convergence and based on the paradigm, an adaptive fixed-time nonsingular sliding mode controller is proposed. The main features of the controller include: 1) The controller gain is adjusted adaptively following the current magnitude of the output variable to obtain high transient performance. 2) The tracking error can converge to zero within a fixed time even in the case of actuator faults and signal quantization. 3) A hysteretic quantizer is implemented in the attitude control loop such that the on-board communication load can be significantly reduced. Moreover, the proposed fault-tolerant control scheme design is non-recursive, rendering the controller structure simple. Ultimately, the effectiveness of the proposed method is demonstrated by numerical simulations.

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.

Fixed-time robust trajectory tracking control for quadrotor UAV with disturbances

Trajectory tracking control of nonlinear system with disturbances has been extensively investigated. A novel fixed-time robust trajectory tracking control scheme for quadrotor unmanned aerial vehicle (UAV) with disturbances is proposed in this paper. First, the quadrotor system is split into position and attitude loops. With the purpose of restraining coupling disturbances on position loop forced by imperfect attitude tracking, a novel fixed-time unknown input observer (UIO) is devised to accurately estimate the disturbances, with the unique feature that does not need the upper bound of disturbances or the derivatives. Second, taking unmeasurable velocity and unknown external disturbances into account for attitude loop, a fixed-time extended state observer (ESO) is proposed to precisely observe them within a fixed time. Third, considering control accuracy and convergence rate, robust fixed-time controllers are, respectively, designed for position and attitude loops, and the convergence time of overall system is independent of system initial states. Then, a comprehensive stability proof for the two-loop system is presented with a combination of bi-limit homogeneity and Lyapunov technique. Finally, simulations and comparisons are performed to demonstrate the effectiveness of the designed control scheme.

Finite-Time Attitude Tracking Control for Hypersonic Flight Vehicles with Actuator Saturation

This paper investigates finite-time attitude tracking control strategies for hypersonic flight vehicles (HFVs) with parameter uncertainties, external disturbances, and actuator saturations by applying sliding model control, adaptive mechanism, and nonlinear disturbance observer techniques. A nonlinear dynamic model of HFV attitude system in reentry flight phase is established. Then, a basic attitude control method of the HFV system is designed based on a terminal sliding mode control (TSMC) scheme to accommodate the system-lumped disturbance torques and guarantee the finite-time stability. To relax the prior knowledge of bounded lumped disturbance of the TSMC-based HFV attitude system, an adaptive TSMC (ATSMC) scheme is proposed. In order to relax the limit of compound uncertainties and attenuate chattering phenomenon of the TSMC-based HFV attitude system, a nonlinear disturbance observer-based TSMC (DO-TSMC) scheme is presented, which enhances the disturbance attenuation and robust tracking performance. Finally, simulation results of a generic X-33 nonlinear model exhibit the effectiveness of the proposed TSMC, ATSMC, and DO-TSMC schemes.

Composite adaptive attitude control for combined spacecraft with inertia uncertainties

This paper examines the attitude control problem of the combined spacecraft subject to inertia uncertainties. A composite adaptive finite-time control scheme with guaranteed parameter convergence is proposed to address this challenging problem, in the absence of persistent excitation. As a stepping stone, the attitude dynamics of the combined spacecraft is first established with explicit consideration of the center-of-mass variation and thruster reconfiguration. Then, a composite adaptive finite-time controller is developed based on a constructive time-varying sliding manifold, and in particular, the concurrent learning technique is used in conjunction with the dynamic regressor extension and mixing procedure to achieve parameter convergence under finite excitation that is strictly weaker than the persistent excitation. Lyapunov stability analysis shows that the derived adaptive controller can simultaneously guarantee finite-time convergence of the attitude tracking and parameter estimation errors; moreover, its robustness against inertia variations and external disturbances is also analyzed. Finally, a set of numerical simulations under ideal and practical scenarios are performed to validate the effectiveness and outperformance of the proposed method.

Steering Law for Control Moment Gyroscopes with Online Torque Capacity Maximization

While single-gimbal control moment gyroscopes (CMGs) remain the actuators of choice for agile spacecraft, using over-redundant or overdesigned CMG arrays will cease to be a viable approach as agility requirements increase. The torque envelope of a CMG array under gimbal rate constraints is a zonotope, whose geometrical characteristics can be used to systematically increase the torque capacity around an arbitrarily given axis. For a four-CMG roof array, which consists of two coplanar CMG pairs, the torque capacity is a function of the allocation of angular momentum between the pairs. Based on the latter, a gimbal angle steering law is developed that maximizes the CMG array’s torque capacity around a preferred axis defined by the current slew maneuver. A main feature of the proposed steering law is that this maximization does not require offline computations for any given preferred axis. In addition, an angular-momentum-based attitude tracking control law is formulated. As verified in numerical simulations, the developed steering and attitude control algorithms are able to follow a typical agile reference profile with adequate time domain performance while satisfying actuator constraints.

Output-feedback asymptotic tracking control for rigid-body attitude via adaptive neural backstepping

In this note, a novel neural adaptive output-feedback control (NAOC) with asymptotic tracking performance for rigid-body attitude is investigated subject to inertia uncertainty, unavailability of the angular velocity and unknown external disturbance. First, by virtue of the combination of the first-order filter and the coordinate transformation, the original output feedback system with immeasurable angular velocity and unknown dynamics is converted into the full-state strict feedback system with mismatched disturbance. Second, aided by infinitely integrable inequality with saturation function, an innovative neural network (NN) based adaptive control scheme is proposed via backstepping technique. By adopting the model transformation and proposed algorithm, the asymptotic tracking performance of the transformed system and the attitude tracking system without angular velocity can be achieved simultaneously. Finally, comparative numerical simulations illustrate the efficacy of the developed algorithm.

Fully distributed event‐triggered asymptotic attitude coordination of multiple spacecraft systems with disturbances

AbstractThis article studies the leader‐following attitude coordination problem of a group of rigid spacecraft subject to communication constraint, disturbances and uncertain control coefficient matrices. A fully distributed adaptive anti‐disturbance attitude coordinated control scheme with event‐triggering mechanism is developed. First, the event‐triggered adaptive distributed observer is designed for each follower to estimate the leader's information without continuous communication requirement. Based on the estimated information, the adaptive anti‐disturbance attitude tracking controller is designed such that asymptotic coordinated tracking can be achieved under additive disturbances and actuators' partial loss of efficiency. The proposed control scheme ensures that all the closed‐loop signals are bounded and the positive lower bound of inter‐event times exists in each subsystem. Simulation results illustrate the effectiveness and flexibility of the proposed control scheme.

Velocity-free fixed-time output feedback attitude tracking control of rigid spacecraft

This paper studies the problem of velocity-free fixed-time attitude tracking control for spacecraft. A new fixed-time sliding mode control method is proposed for the spacecraft attitude tracking control system. And, a novel fixed-time convergent sliding surface is designed based on the fixed-time control theory. In order to estimate the unmeasurable spacecraft information, the fixed-time observer was used to estimate the attitude information of the spacecraft. Combined with the above method, the fixed-time tracking controller is developed to guarantee the attitude tracking error of spacecraft converges to a small region within a fixed time. The fixed-time stability of the closed-loop system is proved based on the Lyapunov theory, and numerical simulations are presented to illustrate the effectiveness and superiority of the controllers.

Adaptive Dynamic Surface Control for Attitude Tracking of Spacecraft under Measurement Biases

Adaptive Dynamic Surface Control for Attitude Tracking of Spacecraft under Measurement Biases

Barrier Lyapunov function based fixed-time control for automatic carrier landing with disturbances

This paper studies the automatic carrier landing controller design problem with output constraint and fixed-time convergence requirements. The proposed flight controller is separated into guidance, attitude control, and approach power compensation system. In each submodule, universal barrier Lyapunov function and fixed-time control scheme are applied in the controller design. In addition, adaptive estimation method is incorporated to improve the robustness to the external disturbances. The proposed controller ensures the position tracking error, attitude tracking error, and angle of attack tracking error not violate the predesigned boundaries, while the tracking errors will converge to a small set around zero in fixed-time. The output constraint and fixed-time convergence properties of the proposed controller improve the landing security to a narrow flight deck in a limited operation time. The simulation results verify the proposed controller in automatic carrier landing mission.

Hybrid Approach Control of Micro-Positioning Stage with a Piezoelectric Actuator

For a class of system with nonlinear hysteresis, this paper presents an adaptive hybrid controller based on the hybrid backstepping-sliding mode, and describes the controller analytically by the LuGre model. Both backstepping and the sliding mode techniques are based on the Lyapunov theory. Drawing on this common point, the authors developed a new controller combining the two control techniques with a recursive design. The design aims to achieve two effects: assuring the stability of the closed loop system, and improving the continuous performance of the tracking position trajectory. The performance of the proposed hybrid controller was verified by implementing the identified Piezo model. The results show that our controller can track the system output desirably with the reference trajectory.

Extended sliding mode observer‐based high‐accuracy motion control for uncertain electro‐hydraulic systems

AbstractIn this paper, a novel robust backstepping control strategy is introduced to achieve high‐accuracy tracking performance for electro‐hydraulic servo systems (EHSSs) without velocity information in the presence of uncertainties and disturbances. Firstly, system dynamics of the studied EHSS considering parameter deviations, modeling errors, and unknown external loads which are grouped into lumped mismatched and matched disturbances in the mechanical system and pressure dynamics, respectively, are developed. On the basis of the sliding mode theory, two extended sliding mode observers (ESMOs) are originally established to simultaneously estimate the immeasurable angular velocity of the actuator, and lumped mismatched and matched uncertainties. As a consequence, an observer‐based controller is designed using the conventional backstepping technique to ensure a highly accurate tracking position control. In addition, the stability of the observer and overall closed‐loop control system is conclusively proven through the Lyapunov theory. Finally, several numerical simulations for an EHSS with a hydraulic rotary actuator are conducted to demonstrate the advantage of the recommended method compared to the existing well‐known extended state observer‐based control approaches.

Fuzzy adaptive fixed-time fault-tolerant attitude tracking control for tailless flying wing aircrafts

This work investigates the fault-tolerant attitude tracking control problem for the tailless flying wing aircraft in the presence of an external disturbance, uncertain parameters, and time-varying actuator failures. First, the external disturbance, uncertainty, and time-varying actuator failures are skillfully transformed into a lumped uncertainty, followed by an approximator constructed by employing an interval type-2 fuzzy logic system (IT2-FLS). On this basis, a fixed-time IT2 fuzzy fault-tolerant control scheme is proposed, which can guarantee that all the signals of the closed-loop system have fixed-time convergence. The desired control torque is allocated to each control surface through a recurrent neural network (RNN) based control allocation algorithm by considering the magnitude and rate constraints of the actuators. Finally, the two representative simulations have been conducted to validate the effectiveness and superiority of the proposed control scheme and control allocation algorithm.

Practical predefined-time attitude coordination control for multiple rigid spacecraft

This paper investigates the practical predefined-time attitude cooperation control problem for a group of rigid spacecraft under an undirected communication graph. First, since the leader is accessible to only a subset of the group members, a distributed practical predefined-time state observer is proposed to estimate the leader’s states by using a time-varying scaling function. Second, a distributed practical predefined-time attitude coordination controller is designed to guarantee that the attitude tracking errors of all follower spacecraft converge to the neighborhood of the origin within a preset time. Finally, the effectiveness of the proposed control law is demonstrated by illustrative numerical examples.

Adaptive sliding mode fault-tolerant control for satellite attitude tracking system

In this paper, an adaptive modified sliding mode control approach is developed for attitude tracking of a nano-satellite with three magnetorquers and one reaction wheel. A sliding variable is chosen based on finite-time convergence of the nano-satellite attitude tracking error and avoiding the singularity of the control signal. The control gain of the proposed method is developed adaptively to reduce the tracking error and improve the closed-loop control performance. The sliding variable and adaptive parameter are also employed in the reaching phase of the control law to decrease the chattering phenomenon. In addition, the finite-time convergence of attitude variables in the presence of actuator faults, inertia uncertainty, and external disturbances is proved using the extended Lyapunov theorem. The simulations are conducted to evaluate the performance of the proposed method according to different evaluation criteria. Monte Carlo simulations are also used to survey the reliability of the system in the presence of the mentioned condition.

Predefined-Time Nonsingular Attitude Control for Vertical-Takeoff Horizontal-Landing Reusable Launch Vehicle

This paper presents a novel predefined-time nonsingular tracking control system for a vertical-takeoff horizontal-landing (VTHL) reusable launch vehicle (RLV) in the face of parameter uncertainties, model couplings and external disturbances. Firstly, this paper proposes a novel predefined-time prescribed performance function (PTPPF) with desired steady-state and transient performance. The convergence time of PTPPF from the transient state to the steady state can be flexibly adjusted by changing one parameter. Moreover, the decreasing rate of PTPPF in the transient phase can also be adjusted by changing one parameter on the premise of not changing the convergence time of PPF to reach steady state. A novel predefined-time terminal sliding mode surface (SMS) is designed to avoid the singularity, and the attitude tracking errors on SMS are predefined-time stable. By utilizing PTPPF and error transformation, this paper designs a novel nonsingular sliding mode controller to guarantee the attitudes of RLV with desired tracking performance. Without using piecewise functions, the phenomenon of singularity can be avoided. The Lyapunov method is used to verify the stability of the controller. Lastly, a numerical simulation is presented to validate the efficiency of the proposed controller.