Quaternion Feedback Controller Research Articles

Integrated attitude—orbit control of solar sail with single-axis gimbal mechanism

AbstractA new attitude control method for solar sails is proposed using a single-axis gimbal mechanism and three-axis reaction wheels. The gimbal angle is varied to change the geometrical relationship between the force due to solar radiation pressure (SRP) and the center of mass of the spacecraft, such that the disturbance torque is minimized during attitude maintenance for orbit control. Attitude maneuver and maintenance are performed by the reaction wheels based on the quaternion feedback control method. Even if angular momentum accumulates on the reaction wheels due to modelling error, it can also be unloaded by using the gimbal to produce suitable torque due to SRP. In this study, we analyzed the attitude motion under the reaction wheel control by linearizing the equations of motion around the equilibrium point. Further, we newly derived the propellent-free unloading method based on the analytical formulation. Finally, we constructed the integrated attitude{orbit control method, and its validity was verified in integrated attitude{orbit control simulations.

Robust Hybrid Global Dual Quaternion Pose Control of Spacecraft-Mounted Robotic Systems

We propose a nonlinear hybrid dual quaternion feedback control law for multibody spacecraft-mounted robotic systems (SMRSs) pose control. Indeed, screw theory expressed via a unit dual quaternion representation and its associated algebra can be used to compactly formulate both the forward (position and velocity) kinematics and pose control of -degree-of-freedom robot manipulators. Recent works have also established the necessary theory for expressing the rigid multibody dynamics of an SMRS in dual quaternion algebra. Given the established framework for expressing both kinematics and dynamics of general -body SMRSs via dual quaternions, this paper proposes a dual quaternion control law that achieves simultaneous global asymptotically stable pose tracking for the end effector and the spacecraft base of an SMRS. The proposed hybrid control law is robust to chattering caused by noisy feedback and avoids the unwinding phenomenon innate to continuous-based (dual) quaternion controllers. Additionally, an actuator allocation technique is proposed in the neighborhood of system singularities to ensure bounded control inputs, with minimum deviation from the specified spacecraft base and end-effector trajectories during controller execution.

Real-Time Fuel Optimization and Guidance for Spacecraft Rendezvous and Docking

Autonomous rendezvous and docking (RVD) fuel optimization with field-of-view and obstacle avoidance constraints is a nonlinear and nonconvex optimization problem, making it computationally intensive for onboard computation on CubeSats. This paper proposes an RVD fuel optimization and guidance technique suitable for onboard computation on CubeSats, considering the shape, size and computational limitations of CubeSats. The computation time is reduced by dividing the guidance problem into separate orbit and attitude guidance problems, formulating the orbit guidance problem as a convex optimization problem by considering the CubeSat shape, and then solving the orbit guidance problem with a convex optimization solver and the attitude guidance problem analytically by exploiting the attitude geometry. The performance of the proposed guidance method is demonstrated through simulations, and the results are compared with those of conventional methods that perform orbit guidance optimization with attitude quaternion feedback control. The proposed method shows better performance, in terms of fuel efficiency, than conventional methods.

Optimal control on the attitude rotation of a flexible satellite model base on tetrahedral configured reaction wheels

The increase in demand for performance for satellite capabilities has pushed the design of the system to be more power consuming. Currently, most of the satellite design are equipped with large solar panel in order to produce sufficient power. Thus, this translates to a higher flexibility in the satellite which makes the satellite prone to vibratory motion. The primary cause of vibratory motion in satellite is the attitude rotation. Reaction wheel is a widely used attitude rotation actuator for a satellite Commonly, the reaction wheels are configured in the tetrahedral form. This causes uneven maximum torque at any direction. Hence, an iterative optimal control method is applied using GPOPS toolbox to achieve minimum time of rotation with low level of induced vibratory motion. The optimized control is compared with the Eigen-axis Quaternion Feedback control to observe the performance of the optimal control. Depending on the direction of attitude manoeuvre, the optimal control has shown an improvement between 3.49% to 25.11% in manoeuvre time. Overall, the optimal control outperformed the traditional the Eigen-axis Quaternion Feedback control.

Effects of Attitude Parameterization Methods on Attitude Controller Performance

This paper intends to compare the effect of the attitude parameterization method on the performance of the attitude controller designed with the direct feedback of corresponding attitude states. To achieve this, the proportional-derivative controllers using the finite rotation angles and the modified Rodrigues parameters are designed with the same structure and equivalent performance of the direct quaternion-feedback control. It has been demonstrated through a series of comparative analyses that three different parameterization methods can be commonly used in designing their direct feedbacks for the spacecraft’s attitude control. Next, the effects of the nonlinear transform relations among three parameterizations are thoroughly investigated through the controller-response analyses for an eigen-axis rest-to-rest maneuver with varying the initial angular position. The controller designed with the finite rotation angles shows a consistent performance regardless of the initial angular position. Whereas, those using other two methods show large variations in their response characteristics. From the results, it can be concluded that the direct feedback controller designed with the finite rotation angles outperforms those using the modified Rodrigues parameters or the quaternion, especially when the spacecraft experiences an aggressive maneuver or has a wide operating range of the attitude.

Optimal control of a tetrahedral configured reaction wheels for Quaternion rotation based on rigid satellite model

Reaction wheel is the most popular actuator for the attitude manoeuvring of a satellite system due to its compact size, reliability and able to produce precise torque. However, for redundancy purposes, the reaction wheels are assembled in a tetrahedral configuration that is able to generate torque in any direction even when one of the reaction wheel fails. The tetrahedral configured reaction wheel causes the maximum torque generation to be uneven in any direction. Hence, the quaternion rotation is completed at different rate in different direction. In order to optimize the rotation rate, an optimal control using iterative method via GPOPS toolbox. It is then compared with the traditional Eigen-axis Quaternion Feedback control. The improvement shown by the optimal control to be between 3.49% to 25.11% improvement in manoeuvre time depending on the direction of manoeuvre. The optimal control is able to outperform the traditional control method.

Control of a tethered Quadrotor using a quaternion feedback

In Japan, superannuation of infrastructures poses a problem and the application of unmanned aerial vehicles (UAVs) such as a Quadrotor etc. is being actively studied as one of ways of inspection. Such a Quadrotor needs any position control independent of GPS, when being used for the inspection of tunnels and of interior of building. In previous research, Ouchi et al. proposed a method for controlling the position of a Quadrotor using a tether. In addition, they derived the dynamical model of the Quadrotor considering the influence of a tether, and conducted some experiments on the attitude control. The objective of this study is to realize angle and angular velocity control in the tethered Quadrotor by applying quaternion feedback control proposed by Fresk et al. In the quaternion feedback controller, the angular velocity obtained from the gyro sensor is directly available in the controller design, so that there is a possibility that more stable attitude control can be performed. After giving the overview of the tethered Quadrotor and describing Quaternion feedback control, this paper gives some experiments to verify that it is more stable with an actual machine, compared to the conventional method.

Quaternion-based Finite-time Sliding Mode Controller Design for Attitude Tracking of a Rigid Spacecraft during High-thrust Orbital Maneuver in the Presence of Disturbance Torques

In this paper, a quaternion-based finite-time sliding mode attitude controller is designed for a spacecraft performing high-thrust orbital maneuvers, with cold gas thrusters as its actuators. The proposed controller results are compared with those of a quaternion feedback controller developed for the linearized spacecraft dynamics, in terms of settling time, steady-state error, number of thruster firings and their fuel usage. It is then proved that the sliding mode control has enough robustness against disturbances as well as a high accuracy in attitude tracking and also a low number of thruster firings. A 6 degree of freedom (DOF) total simulation, including spacecraft dynamics, guidance, navigation and control systems is also designed and the sliding mode controller performance in a sample transfer from an ecliptic orbit to a circular one is investigated. In order to solve the chattering problem caused mainly because of the discontinuity of sliding mode control algorithm and multiple switching on sliding surfaces, the sign function in the control input is replaced with a hyperbolic tangent function. Being aware of the advantages of sliding mode control method, using this algorithm in orbital transfers seems to be innovative and efficient.

Attitude Stabilization of Spacecraft in Very Low Earth Orbit by Center-Of-Mass Shifting

At very low orbital altitudes (≲450 km) the aerodynamic forces can become major attitude disturbances. Certain missions that would benefit from a very low operational altitude require stable attitudes. The use of internal shifting masses, actively shifting the location of the spacecraft center-of-mass, thus modulating, in direction and magnitude, the aerodynamic torques, is here proposed as a method to reject these aerodynamic disturbances. A reduced one degree-of-freedom model is first used to evaluate the disturbance rejection capabilities of the method with respect to multiple system parameters (shifting mass, shifting range, vehicle size, and altitude). This analysis shows that small shifting masses and limited shifting ranges suffice if the nominal center-of-mass is relatively close to the estimated center-of-pressure. These results are confirmed when the analysis is extended to a full three rotational degrees-of-freedom model. The use of a quaternion feedback controller to detumble a spacecraft operating at very low altitudes is also explored. The analysis and numerical simulations are conducted using a nonlinear dynamic model that includes the full effects of the shifting masses, a realistic atmospheric model, and uncertain spacecraft aerodynamic properties. Finally, a practical implementation on a 3U CubeSat using commercial-off-the-shelf components is briefly presented, demonstrating the implementation feasibility of the proposed method.

Attitude tracking with an adaptive sliding mode response to reaction wheel failure

This paper proposes an attitude tracking control for a rigid spacecraft that adapts to two types of faults that commonly occur in reaction wheels: a gain fault and a deviation fault. In its normal operating mode the tracking controller replicates that of a continuous quaternion feedback controller. When a fault occurs in the system the attitude of the spacecraft will deviate from the reference trajectory and will consequently trigger a sliding mode response of the control which introduces robustness. For the proposed control law, we construct a suitable Lyapunov function to prove the closed-loop system is asymptotically stable in the presence of such faults. However, the proposed control is not practically suitable over long periods as the gain on the sliding mode component will always increase unless the sliding surface is exactly zero (in practise this is never the case because of sensor noise). To address this problem a simple adaptive parameter is defined such that it converges to an appropriate upper-limit. Simulations of the attitude dynamics of a spacecraft are undertaken which compares the tracking performance in the presence of a fault with and without the adaptive sliding mode component.

Planning natural repointing manoeuvres for nano-spacecraft

In the work presented here the natural dynamics of a rigid body are exploited to plan attitude manoeuvres for a small spacecraft. By using the analytical solutions of the angular velocities and making use of Lax pair integration, the time evolution of the attitude of the spacecraft in a convenient quaternion form is derived. This enables repointing manoeuvres to be generated by optimising the free parameters of the analytical expressions, the initial angular velocities of the spacecraft, to match prescribed boundary conditions on the final attitude of the spacecraft. This produces reference motions that can be tracked using a simple proportional-derivative (PD) controller. The natural motions are compared in simulation with a conventional quaternion feedback controller and found to require lower accumulated torque. A simple obstacle avoidance algorithm, exploiting the analytic form of natural motions, is also described and implemented in simulation. The computational efficiency of the motion planning method is discussed.

Attitude and Vibration Control of Flexible Spacecraft Using Singular Perturbation Approach

This paper addresses a composite two-time-scale control system for simultaneous three-axis attitude maneuvering and elastic mode stabilization of flexible spacecraft. By choosing an appropriate time coordinates transformation system, the spacecraft dynamics can be divided into double time-scale subsystems using singular perturbation theory (SPT). Attitude and vibration control laws are successively designed by considering a time bandwidths separation between the oscillatory flexible parts motion describing a fast subsystem and rigid body attitude dynamics as a slow subsystem. A nonlinear quaternion feedback control, based on modified sliding mode (MSM), is chosen for attitude control design and a strain rate feedback (SRF) scheme is developed for suppression of vibrational modes. In the attitude control law, the modification to sliding manifold for slow subsystem ensures that the spacecraft follows the shortest possible path to the sliding manifold and highly reduces the switching action. Stability proof of the overall closed-loop system is given via Lyapunov analysis. The proposed design approach is demonstrated to combine excellent performance in the compensation of residual flexible vibrations for the fully nonlinear system under consideration, as well as computational simplicity.

Chaos control in attitude dynamics of a gyrostat satellite based on linearised Poincare' map estimation by support vector machine

Chaos control of an apparent-type gyrostat satellite (GS) is investigated in this work. The GS under study consists of a main platform along with the three reaction wheels. The mathematical model of the GS is first derived using the quaternion-based kinematic and Euler-based kinetic equations of motion under the gravity gradient perturbation. Chaotic dynamics of the open-loop system without a feedback is then analyzed by the use of the numerical simulation in the phase portrait trajectories, Poincare' section, and time series responses. The existence of chaos is also demonstrated using the Lyapunov exponent criterion. In order to suppress chaos in the GS, a quaternion feedback controller is designed by the modification of Ott–Grebogi–Yorke (OGY) algorithm based on the linearisation of Poincare' map. In the controller strategy, the Poincare' map is estimated by the least square-support vector machine technique. Then, the discrete-time proportional-integral-derivative (PID) controller is applied on the linearised Poincare' map. The discrete-time PID-OGY control system rejects the chaotic behaviours in the attitude orientation of GS with the generation of a small control input leading to a decrease in the control effort and energy consumption.

Discretized Constrained Attitude Pathfinding and Control for Satellites

A general purpose guidance, navigation, and control algorithm is developed for satellites with three degree-of-freedom rotation maneuverability. The algorithm is capable of meeting multiple pointing constraints autonomously by using a combination of constrained attitude pathfinding and control elements. The unit sphere is discretized into a graph using an icosahedron-based pixelization subroutine. An admissible path between attitude keep-out zones is found with the A* pathfinding algorithm. The trajectory is followed using a rate and torque constrained quaternion feedback controller. The algorithm is capable of running in real time on a low-power flight computer. An embedded version of the algorithm has secured flight opportunities on two student-built three-unit CubeSats. Both sets of mission requirements are satisfied with the same three-unit CubeSat attitude control system, demonstrating the algorithm’s versatility as a general purpose controller. The autonomy provided by the constrained control algorithm enables more complex satellite missions to be performed and decreases the cost of spacecraft subsystems by shifting requirements away from the hardware and onto the control algorithm.

Attitude maneuver control of a two-wheeled spacecraft with bounded wheel speeds

The attitude control problem of a spacecraft using two reaction wheels is revisited. Controllability analysis shows that the reduced dynamics of a two-wheeled spacecraft are locally controllable at any equilibrium if the total angular momentum of the system is zero, and all the possible equilibrium attitudes form the whole attitude configuration manifold. Under zero-momentum restriction, a singular quaternion feedback controller is first derived based on the generalized dynamic inverse method to stabilize the attitude kinematics. By introducing a novel saturated function, this controller is developed into a switching control logic to account for the singularities as well as yielding bounded inputs. Then a full-state feedback with bounded wheel speeds is synthesized to globally reorientate the spacecraft to any desired orientation. Numerical simulation results demonstrate the effectiveness of the proposed control algorithm.

Relative attitude dynamics and control for a satellite inspection mission

The problem of conducting an inspection mission from a chaser satellite orbiting a target spaceraft is considered. It is assumed that both satellites follow nearly circular orbits. The relative orbital motion is described by the Hill–Clohessy–Wiltshire equation. In the case of an elliptic relative orbit, it is shown that an inspection mission is feasible when the chaser is inertially pointing, provided that the camera mounted on the chaser satellite has sufficiently large field of view. The same possibility is shown when the optical axis of the chaser's camera points in, or opposite to, the tangential direction of the local vertical local horizontal frame. For an arbitrary relative orbit and arbitrary initial conditions, the concept of relative Euler angles is defined for this inspection mission. The expression of the desired relative angular velocity vector is derived as a function of Cartesian coordinates of the relative orbit. A quaternion feedback controller is then designed and shown to perform relative attitude control with admissible internal torques. Three different types of relative orbits are considered, namely the elliptic, Pogo and drifting relative orbits. Measurements of the relative orbital motion are assumed to be available from optical navigation.

Adaptive attitude control of spacecraft using neural networks

An adaptive control technique can be applicable to reorient spacecraft with uncertain properties such as mass, inertial and various misalignments. A nonlinear quaternion feedback controller is chosen as a baseline attitude controller. A linearly added adaptive input supported by neural networks to the baseline controller can estimate and eliminate the uncertain spacecraft property adaptively. The normalized input neural networks (NINNs) are examined for reliable computation of the adaptive input. The newly defined learning rules of the neural networks are established appropriately for a spacecraft. To prove the stability of the closed-loop dynamics with the control law, Lyapunov stability theory is considered. As a result, the proposed approach results in the uniform ultimate boundedness in tracking error and robustness of the chattering and the singularity problems.

Attitude Tracking Maneuver Using Adaptive Sliding Mode Control.

Attitude synchronization is a key technology to facilitate the capturing process of tumbling satellites. Tumbling motion of the satellites is a nonlinear system and the inertia ratio of the satellite is a dominant parameter of the motion. Estimation of the inertia ratio of the tumbling satellites is thus important function for a chaser satellite to synchronize its attitude motion with the tumbling satellite motion. The present study is devoted to investigate an adaptive sliding mode control (ASMC) algorithm applied to attitude tracking maneuvers. The adaptive law added to the sliding mode control (SMC) algorithm is employed to estimate the inertia ratio of the tumbling satellite. Attitude tracking performances of the ASMC method is studied numerically to compare with those of a quaternion feedback control method and a simple SMC method. It is shown that the precise synchronization can be executed by the ASMC method even if there exist some errors between the real value of the inertia ratio of the tumbling satellite and the estimated one at the beginning of tracking maneuvers.

平滑規範モデル適応スライディングモード制御によるターゲット衛星への姿勢追従

Attitude synchronization is a key technology in the capture of tumbling satellites. The inertia ratio of the satellite is a dominant parameter of the motion. Estimation of the inertia ratio of tumbling satellites is thus an important function for a chaser satellite in order to synchronize its attitude motion with the tumbling satellite motion. This paper proposes a new control scheme named “Smooth Reference Model Adaptive Sliding-Mode Control”(SRMASMC) algorithm for attitude tracking maneuvers. The adaptive law installed on the sliding mode control (SMC) algorithm is employed to estimate the inertia ratio of the tumbling satellite. A smooth reference model is introduced to reduce the control torques at the beginning of the tracking maneuver by the SMC method. The attitude tracking performance of the SRMASMC method is evaluated numerically in comparison to a quaternion feedback control method and a SMC method.

Attitude acquisition system for communication spacecraft

A new method for the attitude acquisition of a momentum-biased communication spacecraft that is spin stabilized in the transfer orbit is presented. The initial spin axis attitude is parameterized as a quaternion vector using the transfer orbit horizon and sun sensors. The acquisition control system employs direct rate and quaternion feedback to autonomously despin the spacecraft and align the momentum wheel axis along the orbit normal. The quaternion feedback control gains are selected to perform the maneuver along the Euler axis. The control torques are realized by thruster pulse width modulation. A simple thruster pulse width scaling is included to keep the maneuver axis along the Euler axis. A typical attitude acquisition including momentum wheel spin up to the nominal bias level is completed in 1800 s. The momentum wheel axis is brought within 1 deg of the orbit normal. T Tci co Nomenclature = /th axis rate damping gain = inertia matrix = /th axis quarternion feedback gain = externally applied torque vector = torque commanded along the /th axis = angular velocity vector = body rate threshold