Attitude Error Dynamics Research Articles

Saturated Attitude Control of Multi-Spacecraft Systems on SO(3) Subject to Mixed Attitude Constraints With Arbitrary Initial Attitude

In this paper, for multi-spacecraft systems (MSSs) with a directed complete communication topology and a time-varying virtual leader, an adaptive saturated attitude controller is proposed to achieve attitude consensus and attitude tracking under arbitrary initial attitude, mixed attitude constraints, input saturation and external disturbances. Firstly, considering the time-varying desired attitude provided by the virtual leader in a directed complete topology, an MSS attitude error function and an MSS attitude error dynamics based on SO(3) are developed. Next, an effective mixed potential function for the MSS on SO(3) is proposed for the static attitude-forbidden zones, the relative dynamic attitude-forbidden zones and the attitude-mandatory zones. In particular, different from the existing potential functions, the proposed mixed potential function is suitable for arbitrary initial attitude of the spacecraft in MSS, relaxing the restriction on the initial attitude associated with each static and dynamic attitude constraint zones. Then, an adaptive saturated attitude controller is designed to realize attitude consensus and tracking for the MSSs on SO(3) under arbitrary initial attitude, mixed attitude constraints, saturation constraints and external disturbances. Finally, simulation results of an MSS with a time-varying virtual leader are demonstrated to illustrate the efficiency of the proposed attitude controller.

Suboptimal attitude tracking control law and eigenvalue analysis for a near-space hypersonic vehicle based on Koopman operator and stable manifold method

This paper proposes a novel strategy to design a suboptimal attitude tracking control law for a near-space hypersonic vehicle (NSHV) based on the Koopman operator and stable manifold theory. The nonlinear vector field of the NSHV attitude model is locally Lipschitz continuous and can be approximated by a high-dimensional linear system over a compact set. Linear and nonlinear parts of the attitude dynamics are determined based on this system. Subsequently, the stable manifold theory is applied to determine the unconstrained approximated optimal control law that is used to further consider the control input constraints of the NSHV attitude model. The suboptimality of the control law is analyzed, and the local exponential stability of the closed-loop system with input constraints is proven. Furthermore, the eigenvalues for the closed-loop nonlinear attitude error dynamics are analyzed. After the control input saturation, the nonlinear closed-loop error dynamics of the NSHV can be approximated by a high-dimensional linear system with a minimal dimension. The eigenvalues of this linear system indicate the stability and time response characteristics of the attitude error dynamics of the NSHV. The numerical simulation results demonstrate the effectiveness and suboptimality of the proposed attitude tracking control law and workflow of the eigenvalue analysis.

Suboptimal control law for a near-space hypersonic vehicle based on Koopman operator and algebraic Riccati equation

This paper presents a novel suboptimal attitude tracking controller based on the algebraic Riccati equation for a near-space hypersonic vehicle (NSHV). Since the NSHV’s attitude dynamics is complexly nonlinear, it is hard to directly construct an appropriate algebraic Riccati equation. We design the construction based on the Chebyshev series and the Koopman operator theory, which includes three steps. First, the Chebyshev series are considered to transform the error dynamics of the NSHV’s attitude into a polynomial system. Second, the Koopman operator is used to obtain a series of high-dimensional linear dynamics to approximate each of the polynomial system’s vector fields. In this step, our contribution is to determine a well-posed linear dynamics with the minimal dimension to approximate the original nonlinear vector field, which helps to design the control law and analyze the control performance. Third, based on the high-dimensional dynamics, the NSHV’s attitude error dynamics is separated into the linear part and the nonlinear part, such that the algebraic Riccati equation can be constructed according to the linear part. Then, the suboptimal error feedback control law is derived from the algebraic Riccati equation. The closed-loop control system is proved to be locally exponentially stable. Finally, the numerical simulation demonstrates the effectiveness of the suboptimal control law.

Distributed Formation Centroid Tracking Control of Clustered Rotorcraft

We design a distributed control algorithm for clustered rotorcraft to cooperatively realize the formation centroid tracking objective in this paper. In particular, the rotorcraft cluster are capable of constructing a prescribed configuration while making the configuration centroid track a reference trajectory. However, constrained by decentralization, each rotorcraft has no idea where the configuration centroid is. Besides, the reference trajectory information is just available to parts of rotorcraft. To begin with, resorting to the cascaded system stability theory, the original formation centroid tracking problem of clustered rotorcraft is translated into designing a bounded transition force and an applied torque for the respective stabilization of the nominal position error dynamics and attitude error dynamics of each individual. Then, by introducing two feasible distributed observers to accurately estimate the configuration centroid and reference acceleration, respectively, a transition force with saturation attribute is designed such that the nominal position error dynamics is stabilized. With such a saturated transition force, a choice criterion of control parameters that is independent of system states is built for the non-singular demand attitude extraction. Next, an applied torque is designed such that the attitude error dynamics is stabilized. A detailed stability analysis using generalized Lyapunov theory is carried out. Simulation results verify the effectiveness of the designed distributed control algorithm.

Estimation on IMU yaw misalignment by fusing information of automotive onboard sensors

In the development of automotive electronics, nearly every automobile is equipped with an inertial measurement unit (IMU). However, the yaw misalignment of the IMU is inevitable when mounted to a vehicle's body. It is difficult to measure directly, so its estimation is required to acquire accurate data from the IMU. This study proposes a method for the IMU and automotive onboard sensors to estimate the yaw misalignment autonomously. In order to estimate the IMU yaw misalignment, first, the attitude and velocity integration method in the vehicle level frame is presented. In addition, the attitude error dynamics consisting of yaw misalignment, pitch, and roll, and velocity error dynamics consisting of longitudinal and lateral velocities, are derived. Then, on the basis of the error dynamics and observation equations, the degree of the observability of the yaw misalignment is analyzed through the piece-wise constant system (PWCS) and singular value decomposition (SVD) theory. Next, a Kalman filter is implemented to estimate the yaw misalignment and the velocity error. Finally, an experimental test in straight line acceleration and deceleration maneuvers is conducted to verify the yaw misalignment estimation method. When the longitudinal or lateral acceleration varies, the yaw misalignment is observable and can be estimated without aids from external information. After compensating for the yaw misalignment, the accuracy of the state estimation result, such as lateral velocity, can be improved significantly when the IMU is integrated with other sensors.

Incremental Twisting Fault Tolerant Control for Hypersonic Vehicles With Partial Model Knowledge

A passive fault tolerant control scheme is proposed for the full reentry trajectory tracking of a hypersonic vehicle in the presence of modeling uncertainties, external disturbances, and actuator faults. To achieve this goal, the attitude error dynamics with relative degree two is formulated first by ignoring the nonlinearities induced by the translational motions. Then, a multivariable twisting controller is developed as a benchmark to ensure the precise tracking task. Theoretical analysis with the Lyapunov method proves that the attitude tracking error and its first-order derivative can simultaneously converge to the origin exponentially. To depend less on the model knowledge and reduce the system uncertainties, an incremental twisting fault tolerant controller is derived based on the incremental nonlinear dynamic inversion control and the predesigned twisting controller. In this article, it is shown that not only the benefits of both incremental control and twisting control are inherited, but also their side effects are reduced. Notably, the proposed controller is user friendly in that only fixed gains and partial model knowledge are required. Numerical simulations in various cases and comparison studies are conducted to verify the effectiveness of the proposed method.

Controller Synthesis and Performance Optimization for Aerobatic Quadrotor Flight

We present a method for synthesizing high-performance controllers for the autonomous execution of aerobatic quadrotor maneuvers that are defined by rapid variations of the flyer's angular velocity, such as multi-flips or the Pugachev's cobra. In the proposed approach, we employ Lyapunov theory to find the sets of control parameters that make the unique fixed point of the closed-loop angular-velocity error dynamics exponentially stable during an aerobatic maneuver, provided that the angular-velocity reference satisfies a set of conditions. Then, we show that the resulting closed-loop attitude error dynamics remain bounded. The proposed controller synthesis method allows for the minimization of a parameterized performance figure of merit (PFM), which is employed to measure the angular-velocity control error accumulated during a maneuver. The approach adopted here is to show that a primal optimization problem can be reformulated as a series of quasiconvex sub-problems; then, we introduce a technique to find a solution and prove that this optimum is global. By design, the resulting controllers have a simple linear time-invariant (LTI) structure that depends on a small number of coefficients, which makes the experimental implementation of the control schemes extremely efficient and the associated real-time computational cost very low. The effectiveness of the introduced methods for controller design and performance optimization is compellingly demonstrated through theoretical analysis, simulations, and experiments in which high-speed multi-flip aerobatic maneuvers are executed.

Autonomous Underwater Vehicles Attitude control using Neuro-Adaptive Generalized Dynamic Inversion

A novel two loops control architecture is presented for motion control of Autonomous Underwater Vehicle (AUVs). The outer (slow) positional loop incorporates classical Proportional-Derivative control to generate reference pitch and yaw tilting commands based on the positional errors. The reference attitude commands are fed to the inner (fast) attitude control loop, which utilizes Neuro-Adaptive Generalized Dynamic Inversion (NAGDI) control to generate the elevator and rudder deflections. The baseline Generalized Dynamic Inversion (GDI) control composed of particular and auxiliary parts. The particular part is designed by dynamically scaled generalized inversion of the attitude error dynamics, and the auxiliary part is constructed via a Lyapunov control function to provide global asymptotic stability to the angular body rate dynamics. A discontinuous control based on the concept of Sliding Mode Control (SMC) theory is augmented with baseline GDI. The modulation gain of discontinuous term is made adaptive to avoid chattering. Furthermore, online estimation of the unknown nonlinear attitude dynamics is achieved through radial basis function neural networks to obtain the resultant NAGDI control law. The proposed control law guarantees semi-global practically stable attitude tracking. Computer simulations are conducted on a six degrees of freedom simulator of the Monterey Bay Aquarium Research Institute AUV under nominal and perturbed marine environments.

Tilt-Prioritized Quadrocopter Attitude Control

This paper presents an attitude tracking control law and control allocation strategy for quadrocopters which prioritizes the vehicle’s ability to achieve a desired translational acceleration. The quadrocopter’s attitude error is split into a reduced attitude error, which describes the misalignment of the thrust direction, and a yaw error, which describes the orientation error about the thrust direction. A model-based proportional–derivative control law is derived, where the proportional action is in terms of the reduced attitude and yaw errors, and the derivative action is in terms of the quadrocopter’s angular velocity error. Almost global asymptotic convergence of the reduced attitude error is established, and the convergence of the yaw error is proven. It is further shown that the attitude control law decouples the reduced attitude error dynamics from the yaw error dynamics. A control allocation strategy is derived which exploits the decoupling in order to prioritize the correction of the reduced attitude over the yaw error. The proposed control strategy is computationally lightweight and therefore well-suited to run on board quadrocopters at high rates. Experimental results demonstrate improved error recovery and position tracking performance.

Active attitude fault-tolerant tracking control of flexible spacecraft via the Chebyshev neural network

This paper describes a novel finite-time attitude tracking control approach for flexible spacecraft. This is achieved by integrating sliding-mode control and the active real-time fault-tolerant reconfiguration method. In this approach, the attitude error dynamics and the kinematics of the flexible spacecraft are first established. Then, a nonsingular terminal sliding-mode surface is designed, based on finite-time control theory. Applying the Chebyshev neural network, the uncertain dynamics induced by external disturbances and uncertain inertia parameters are approximated and estimated. The nominal control law and the compensation control law to obtain the active reconfiguration fault-tolerant controller are finally developed in normal and fault conditions, respectively. The closed-loop tracking system is proved to be uniformly ultimately bounded stable after a finite time. Numerical simulations are presented for a flexible spacecraft to illustrate the efficiency of the proposed controller.

Adaptive fault tolerant control for trajectory tracking of a quadrotor helicopter

In this paper, an adaptive fault tolerant controller based on [Formula: see text] control is developed and applied to the trajectory tracking for a quadrotor helicopter. Both multiplicative and additive actuator faults are considered. The proposed design is based on nonlinear feed-forward compensations and a typical nonlinear quadrotor model with uncertain inertial parameters and external disturbances. The [Formula: see text] adaptive control design is slightly modified to adapt with the position and the attitude error dynamics. The proposed adaptive controller yields uniformly verifiable bounds on the transient and the steady-state tracking error for any designated bounded reference trajectory. In the presence of fast adaptation, the adaptive controller compensates for actuator fault and disturbances in a particular frequency range. Finally, simulation results are included to validate the effectiveness of the proposed design.

Robust attitude tracking for rigid spacecraft with prescribed transient performance

ABSTRACTThis paper investigates the prescribed performance attitude tracking control problem of a rigid spacecraft with uncertain dynamics and bounded disturbances. By suitable selection of the configuration error function, the trajectory tracking problem on SO(3) is transformed into a point stabilisation problem of an error dynamic system in the associated Lie algebra. The predefined transient performance indexes, which include the maximum steady-state error and overshoot, and the minimum convergence rate of the attitude error vector, are characterised as the inequality constraints. For the tracking controller design, the error transformation technique is utilised to transform the attitude error dynamics with inequality constraints to an equivalent ‘unconstrained’ error one. Then, a coordinate-free robust tracking controller is designed for the ‘unconstrained’ error dynamics to solve the prescribed performance attitude tracking control problem. A rigorous mathematical stability proof is given. Finally, numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed controller.

Finite‐time attitude control of multiple rigid spacecraft using terminal sliding mode

SummaryThis paper investigates the control problem of finite‐time attitude synchronization and tracking for a group of rigid spacecraft in the presence of environmental disturbances. A new fast terminal sliding manifold is developed for multiple spacecraft formation flying under the undirected graph topology. On the basis of the finite‐time control and adaptive control strategies, two novel decentralized finite‐time control laws are proposed to force the spacecraft attitude error dynamics to converge to small regions in finite time, and adaptive control is applied to reject the disturbance. The finite‐time convergence and stability of the closed‐loop system can be guaranteed by Lyapunov theory. Simulation examples are provided to illustrate the feasibility of the control algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Decentralised finite-time attitude synchronisation and tracking control for rigid spacecraft

The problem of finite-time attitude synchronisation and tracking for a group of rigid spacecraft nonlinear dynamics is investigated in this paper. First of all, in the presence of environmental disturbance, a novel decentralised control law is proposed to ensure that the spacecraft attitude error dynamics can converge to the sliding surface in finite time; then the final practical finite-time stability of the attitude error dynamics can be guaranteed in small regions. Furthermore, a modified finite-time control law is proposed to address the control chattering. The control law can guarantee a group of spacecraft to attain desired time-varying attitude and angular velocity while maintaining attitude synchronisation with other spacecraft in the formation. Simulation examples are provided to illustrate the feasibility of the control algorithm presented in this paper.

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.

PID+ BACKSTEPPING CONTROL OF RELATIVE SPACECRAFT ATTITUDE

In this paper we present a PID+ backstepping controller, as a solution to the problem of coordinated attitude control in spacecraft formations. The control scheme is based on quaternions and modified Rodrigues parameters as attitude representation of the relative attitude error. Utilizing the invertibility of the modified Rodrigues parameter kinematic differential equation, a globally exponentially stable control law for the relative attitude error dynamics is obtained through the use of integrator augmentation and backstepping. Finally, simulation results are presented to show controller performance.