Quaternion-Based Robust Attitude Estimation Using an Adaptive Unscented Kalman Filter

This paper presents the Quaternion-based Robust Adaptive Unscented Kalman Filter (QRAUKF) for attitude estimation. The proposed methodology modifies and extends the standard UKF equations to consistently accommodate the non-Euclidean algebra of unit quaternions and to add robustness to fast and slow variations in the measurement uncertainty. To deal with slow time-varying perturbations in the sensors, an adaptive strategy based on covariance matching that tunes the measurement covariance matrix online is used. Additionally, an outlier detector algorithm is adopted to identify abrupt changes in the UKF innovation, thus rejecting fast perturbations. Adaptation and outlier detection make the proposed algorithm robust to fast and slow perturbations such as external magnetic field interference and linear accelerations. Comparative experimental results that use an industrial manipulator robot as ground truth suggest that our method overcomes a trusted commercial solution and other widely used open source algorithms found in the literature

Attitude and Phase Synchronization of Formation Flying Spacecraft: Lagrangian Approach

This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchroniza- tion to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. While the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of space-craft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework

Design of an Attitude Control System for Spin-Axis Control of a 3U CubeSat

This paper describes the design process of developing a spin-axis control system for a 3U CubeSat, a relatively small satellite. Design requires the CubeSat to de-spin after deployment and direct its antenna to track Earth nadir position. The one degree of freedom controller is developed for the TechEdSat, which is a CubeSat with a payload that allows for the assumption that rotation pitch and yaw rates are sufficiently close to zero. Satellite torqueing disturbances are modeled with reaction wheel noise for a more complete system analysis. Sensor noise is unmodeled. Frequency domain and time domain analyses are presented; the entire system bandwidth operates at 0.08 hertz with 43.2 decibels of gain and 67.7o of phase margin. During nominal operations, pointing accuracy with perfect state knowledge assumption maintains position with steady state error of 13.7 arc seconds and oscillates by 16.7 arc seconds at a rate of 0.7 mHertz. Artificial wheel noise is injected into the model causing the pointing accuracy to drop to ± 15 arc seconds. Environmental disturbances are modeled extensively; the magnetic field torque is the worst disturbance, at 4.2e-7 Newton-meters. A 0.2 Amp·m2 magnetorquer dumps the excess momentum every 7.75 hours and require 1.5 hours to complete. In the deployment simulation, a 1 rotation per minute spin is arrested with no angular offset in 60 seconds. Future plans include utilizing the model to build and fly a prototype reaction wheel on a future TechEdSat mission to verify modeled expectations

Spacecraft nonlinear attitude control with bounded control input

The research in this thesis deals with nonlinear control of spacecraft attitude stabilization and tracking manoeuvres and addresses the issue of control toque saturation on a priori basis. The cascaded structure of spacecraft attitude kinematics and dynamics makes the method of integrator backstepping preferred scheme for the spacecraft nonlinear attitude control. However, the conventional backstepping control design method may result in excessive control torque beyond the saturation bound of the actuators. While remaining within the framework of conventional backstepping control design, the present work proposes the formulation of analytical bounds for the control torque components as functions of the initial attitude and angular velocity errors and the gains involved in the control design procedure. The said analytical bounds have been shown to be useful for tuning the gains in a way that the guaranteed maximum torque upper bound lies within the capability of the actuator and, hence, addressing the issue of control input saturation. Conditions have also been developed as well as the generalization of the said analytical bounds which allow for the tuning of the control gains to guarantee prescribed stability with the additional aim that the control action avoids reaching saturation while anticipating the presence of bounded external disturbance torque and uncertainties in the spacecraft moments of inertia. Moreover, the work has also been extended blending it with the artificial potential function method for achieving autonomous capability of avoiding pointing constraints for the case of spacecraft large angle slew manoeuvres. The idea of undergoing such manoeuvres using control moment gyros to track commanded angular momentum rather than a torque command has also been studied. In this context, a gimbal position command generation algorithm has been proposed for a pyramid-type cluster of four single gimbal control moment gyros. The proposed algorithm not only avoids the saturation of the angular momentum input from the control moment gyro cluster but also exploits its maximum value deliverable by the cluster along the direction of the commanded angular momentum for the major part of the manoeuvre. In this way, it results in rapid spacecraft slew manoeuvres. The ideas proposed in the thesis have also been validated using numerical simulations and compared with results already existing in the literature

Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach

This paper presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on oscillator phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. Although the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework

A feedback linearization approach to spacecraft control using momentum exchange devices

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station

Discrete-time Stable Geometric Controller and Observer Designs for Unmanned Vehicles

In the first part of this dissertation, we consider tracking control of underactuated systems on the tangent bundle of the six-dimensional Lie group of rigid body motions, SE(3). We formulate both asymptotically and finite-time stable tracking control schemes for underactuated rigid bodies that have one translational and three rotational degrees of freedom actuated, in discrete time. Rigorous stability analyses of the tracking control schemes presented here guarantee the nonlinear stability of these schemes. The proposed schemes here are developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. A stable convergence of translational and rotational tracking errors to the desired trajectory is guaranteed for both asymptotically and finite-time stable schemes. In the second part, a nonlinear finite-time stable attitude estimation scheme for a rigid body that does not require knowledge of the dynamics is developed. The proposed scheme estimates the attitude and constant angular velocity bias vector from a minimum of two known linearly independent vectors for attitude, and biased angular velocity measurements made in the body-fixed frame. The constant bias in angular velocity measurements is also estimated. The estimation scheme is proven to be almost globally finite-time stable in the absence of measurement errors using a Lyapunov analysis. In addition, the behavior of this estimation scheme is compared with three state-of-the-art filters for attitude estimation, and the comparison results are presented

Kinematics and Robot Design I, KaRD2018

This volume collects the papers published on the Special Issue “Kinematics and Robot Design I, KaRD2018” (https://www.mdpi.com/journal/robotics/special_issues/KARD), which is the first issue of the KaRD Special Issue series, hosted by the open access journal “MDPI Robotics”. The KaRD series aims at creating an open environment where researchers can present their works and discuss all the topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”. KaRD2018 received 22 papers and, after the peer-review process, accepted only 14 papers. The accepted papers cover some theoretical and many design/applicative aspects

Attitude stabilization of a quadrotor aircraft

The quadrotor aircraft has seen a growing interest in the research community over the past few years, with a focus on modeling and control however. Early rotating wing aircraft pioneers designed similar four-rotor aircraft with varied success over a number of years. With the introduction of new lightweight sensors for measuring the attitude and angular velocity of a rigid body, model sized versions of traditional helicopters with autonomous capabilities have emerged, with the advantage of vertical take-off and landing (VTOL) over fixed wing aircraft. The quadrotor aircraft, with its symmetrical design, has a potential advantage with respect to the traditional helicopter in terms of maneuverability and mechanical simplicity. In fact, autonomous unmanned aerial vehicles (UAV’s) have gained popularity for their numerous potential applications where human interaction is difficult or hazardous. Attitude stabilization, which could be considered the most important component for flight control, is essential for autonomous or even pilotable aircraft such as the quadrotor, as their designs are inherently unstable. As the literature suggests, a number of control algorithms have been proposed for the attitude control of a rigid body. In this thesis, a control strategy for the attitude stabilization of the quadrotor aircraft as well as some simulation and experimental results are presented