Integrated Optimal and Robust Control of Spacecraft in Proximity Operations

With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances

Dual-Quaternion-Based Fault-Tolerant Control for Spacecraft Tracking With Finite-Time Convergence

Results are presented for a study of dual-quaternion-based fault-tolerant control for spacecraft tracking. First, a six-degrees-of-freedom dynamic model under a dual-quaternion-based description is employed to describe the relative coupled motion of a target-pursuer spacecraft tracking system. Then, a novel fault-tolerant control method is proposed to enable the pursuer to track the attitude and the position of the target even though its actuators have multiple faults. Furthermore, based on a novel time-varying sliding manifold, finite-time stability of the closed-loop system is theoretically guaranteed, and the convergence time of the system can be given explicitly. Multiple-task capability of the proposed control law is further demonstrated in the presence of disturbances and parametric uncertainties. Finally, numerical simulations are presented to demonstrate the effectiveness and advantages of the proposed control method

Understandings of classical and incremental backstepping controllers with model uncertainties

This paper suggests closed-loop analysis results for both classical and incremental backstepping controllers considering model uncertainties. First, transfer functions with each control algorithm under the model uncertainties, are compared with the ones for the nominal case. The effects of the model uncertainties on the closed-loop systems are critically assessed via investigations on stability conditions and performance metrics. Second, closed-loop characteristics with classical and incremental backstepping controllers under the model uncertainties are directly compared using derived common metrics from their transfer functions. This comparative study clarifies how the effects of the model uncertainties to the closed-loop system become different depending on the applied control algorithm. It also enables understandings about the effects of additional measurements in the incremental algorithm. Third, case studies are conducted assuming that the uncertainty exists only in one aerodynamic derivative estimate while the other estimates have true values. This facilitates systematic interpretations on the impacts of the uncertainty on the specific aerodynamic derivative estimate to the closed-loop system

Learning-based 6-DOF control for autonomous proximity operations under motion constraints

This paper proposes a reinforcement learning (RL)-based six-degree-of-freedom (6-DOF) control scheme for the final phase proximity operations of spacecraft. The main novelty of the proposed method are from two aspects: 1) the closed-loop performance can be improved in real-time through the RL technique, achieving an online approximate optimal control subject to the full 6-DOF nonlinear dynamics of spacecraft; 2) Nontrivial motion constraints of proximity operations are considered and strictly obeyed during the whole control process. As a stepping stone, the dual-quaternion formalism is employed to characterize the 6-DOF dynamics model and motion constraints. Then, an RL-based control scheme is developed under the dual-quaternion algebraic framework to approximate the optimal control solution subject to a cost function and a Hamilton-Jacobi-Bellman equation. In addition, a specially designed barrier function is embedded in the reward function to avoid motion constraint violations. The Lyapunov-based stability analysis guarantees the ultimate boundedness of state errors and the weight of NN estimation errors. Besides, we also show that a PD-like controller under dual-quaternion formulation can be employed as the initial control policy to trigger the online learning process. The boundedness of it is proved by a special Lyapunov strictification method. Simulation results of prototypical spacecraft missions with proximity operations are provided to illustrate the effectiveness of the proposed method

Review of advanced guidance and control algorithms for space/aerospace vehicles

The design of advanced guidance and control (G&C) systems for space/aerospace vehicles has received a large amount of attention worldwide during the last few decades and will continue to be a main focus of the aerospace industry. Not surprisingly, due to the existence of various model uncertainties and environmental disturbances, robust and stochastic control-based methods have played a key role in G&C system design, and numerous effective algorithms have been successfully constructed to guide and steer the motion of space/aerospace vehicles. Apart from these stability theory-oriented techniques, in recent years, we have witnessed a growing trend of designing optimisation theory-based and artificial intelligence (AI)-based controllers for space/aerospace vehicles to meet the growing demand for better system performance. Related studies have shown that these newly developed strategies can bring many benefits from an application point of view, and they may be considered to drive the onboard decision-making system. In this paper, we provide a systematic survey of state-of-the-art algorithms that are capable of generating reliable guidance and control commands for space/aerospace vehicles. The paper first provides a brief overview of space/aerospace vehicle guidance and control problems. Following that, a broad collection of academic works concerning stability theory-based G&C methods is discussed. Some potential issues and challenges inherent in these methods are reviewed and discussed. Then, an overview is given of various recently developed optimisation theory-based methods that have the ability to produce optimal guidance and control commands, including dynamic programming-based methods, model predictive control-based methods, and other enhanced versions. The key aspects of applying these approaches, such as their main advantages and inherent challenges, are also discussed. Subsequently, a particular focus is given to recent attempts to explore the possible uses of AI techniques in connection with the optimal control of the vehicle systems. The highlights of the discussion illustrate how space/aerospace vehicle control problems may benefit from these AI models. Finally, some practical implementation considerations, together with a number of future research topics, are summarised

Nonlinear flight control with reduced model dependency

This thesis aims to innovate knowledge on nonlinear flight control algorithms with reduced model dependency by resolving the research gaps for practical applications. Two control schemes with different principles on reducing model dependency are considered in this thesis; incremental control scheme and adaptive control scheme. In incremental control scheme, state derivative and control surface deflection angle measurements are additionally utilized to substitute required model information except control effectiveness. In adaptive control scheme, uncertain model parameters are estimated online via adaptation law and these estimates are utilized in control input command calculation. Discussions in this thesis are based on incremental backstepping control (IBKS) and composite adaptive backstepping control (C-ABKS) which are obtained by applying those control schemes to backstepping control (BKS). Contributions of this thesis with each algorithm are detailed as follows. This thesis provides critical understandings on IBKS in a systematic way via theoretical analysis under various defects. As a starting point, closed-loop analyses under the model uncertainties are conducted with IBKS and BKS for theoretical interpretations on reduced model dependency in IBKS. Stability and performance of the closed-loop system with IBKS are shown to be not affected by the model uncertainties, while they significantly influence the closed-loop characteristics with BKS. One interesting observation is that the uncertainty on control effectiveness information, which is still required to implement IBKS, does not have any impact on the closed-loop system with IBKS if a control input is calculated, transmitted and reflected fast enough to an actual control surface. The next two analyses are conducted to identify how the defects on the additional measurements together with the model uncertainties affect stability and performance of the closed-loop system with IBKS. First, the closed-loop characteristics with IBKS is analyzed under biases on the additional measurements and the model uncertainties. The measurement biases result in a steady state error while not affecting the closed-loop system stability with IBKS. Unlike the analysis results only with the model uncertainties, the uncertainty in control effectiveness information has an impact on the steady-state error of the closed-loop system. Second, the closed-loop system with IBKS under delays on the additional measurements and the model uncertainties is examined with the analysis framework proposed in this thesis. New analysis framework with optimization concept is proposed to systematically and efficiently test the closed-loop system stability under measurement delays. The key finding is that the delays on the additional measurements should satisfy a specific relationship for the closed-loop stability with IBKS. Besides, it is identified that this stability condition is affected by the uncertainty on control effectiveness information. A new C-ABKS is designed by resolving research gaps of the composite adaptive control for a practical application as follows. First, parameter convergence under finite excitation (FE) is guaranteed with a new paradigm for the information matrix design which is suggested by developing a modulation-based approach. It is proven that the new information matrix is positive definite for all the time from the beginning under FE, while the accumulation-based approach in previous studies requires uncertain amount of time to populate the information matrix to be full rank. The closed-loop system with the C-ABKS utilizing the new information matrix is guaranteed to be globally exponentially stable for all the time under FE. Comparing to the accumulation-based approach, the new modulation-based approach provides advantages in adaptation speed and system robustness since the information matrix is designed to have all eigenvalues with moderate level of magnitudes. Second, the adaptation speed is improved without excessive increase of the adaptation gains in the new logarithmic regression-based composite adaptive control system. The parameter convergence speed is enhanced by slowing down the adaptation speed degeneration at the later stage where the estimation error is small; a concave and monotonically increasing characteristics of a logarithmic function is utilized for the regression term design in this research. The closed-loop system with the proposed logarithmic regression-based C-ABKS is shown to be asymptotically stable under FE by applying Lyapunov theory. Within the system boundary, the new logarithmic regression-based algorithm is proven to be always faster than the well-known linear regression-based algorithm under the same adaptation gain if its design parameters satisfy the suggested condition. In order to make the linear regression-based approach to become faster than the logarithmic regression-based approach with the design parameters satisfying this condition, the adaptation gain of the linear regression term should be increased and this can result in reduced robustness. Important findings for IBKS and C-ABKS are suggested and verified with simulations throughout the thesis. A comparative study is additionally conducted to show different properties of IBKS and C-ABKS under model uncertainties and measurement delays via numerical simulations.PhD in Aerospac

CONTROL STRATEGY OF MULTIROTOR PLATFORM UNDER NOMINAL AND FAULT CONDITIONS USING A DUAL-LOOP CONTROL SCHEME USED FOR EARTH-BASED SPACECRAFT CONTROL TESTING

Over the last decade, autonomous Unmanned Aerial Vehicles (UAVs) have seen increased usage in industrial, defense, research, and academic applications. Specific attention is given to multirotor platforms due to their high maneuverability, utility, and accessibility. As such, multirotors are often utilized in a variety of operating conditions such as populated areas, hazardous environments, inclement weather, etc. In this study, the effectiveness of multirotor platforms, specifically quadrotors, to behave as Earth-based satellite test platforms is discussed. Additionally, due to concerns over system operations under such circumstances, it becomes critical that multirotors are capable of operation despite experiencing undesired conditions and collisions which make the platform susceptible to on-board hardware faults. Without countermeasures to account for such faults, specifically actuator faults, a multirotors will experience catastrophic failure. In this thesis, a control strategy for a quadrotor under nominal and fault conditions is proposed. The process of defining the quadrotor dynamic model is discussed in detail. A dual-loop SMC/PID control scheme is proposed to control the attitude and position states of the nominal system. Actuator faults on-board the quadrotor are interpreted as motor performance losses, specifically loss in rotor speeds. To control a faulty system, an additive control scheme is implemented in conjunction with the nominal scheme. The quadrotor platform is developed via analysis of the various subcomponents. In addition, various physical parameters of the quadrotor are determined experimentally. Simulated and experimental testing showed promising results, and provide encouragement for further refinement in the future

On finite-time anti-saturated proximity control with a tumbling non-cooperative space target

For the challenging problem that a spacecraft approaching a tumbling target with non-cooperative maneuver, an anti-saturated proximity control method is proposed in this paper. First, a brand-new appointed-time convergent performance function is developed via exploring Bezier curve to quantitatively characterize the transient and steady-state behaviors of the pose tracking error system. The major advantage of the proposed function is that the actuator saturation phenomenon at the beginning can be effectively reduced. Then, an anti-saturated pose tracking controller is devised along with an adaptive saturation compensator. Wherein, the finite-time stability of both the pose and its velocity error signals are guaranteed simultaneously in the presence of actuator saturation. Finally, two groups of illustrative examples are organized and verify that the close-range proximity is effectively realized even with unknown target maneuver

Model Predictive Control Applications to Spacecraft Rendezvous and Small Bodies Exploration

The overarching goal of this thesis is the design of model predictive control algorithms for spacecraft proximity operations. These include, but it is not limited to, spacecraft rendezvous, hovering phases or orbiting in the vicinity of small bodies. The main motivation behind this research is the increasing demand of autonomy, understood as the spacecraft capability to compute its own control plan, in current and future space operations. This push for autonomy is fostered by the recent introduction of disruptive technologies changing the traditional concept of space exploration and exploitation. The development of miniaturized satellite platforms and the drastic cost reduction in orbital access have boosted space activity to record levels. In the near future, it is envisioned that numerous artificial objects will simultaneously operate across the Solar System. In that context, human operators will be overwhelmed in the task of tracking and commanding each spacecraft in real time. As a consequence, developing intelligent and robust autonomous systems has been identified by several space agencies as a cornerstone technology. Inspired by the previous facts, this work presents novel controllers to tackle several scenarios related to spacecraft proximity operations. Mastering proximity operations enables a wide variety of space missions such as active debris removal, astronauts transportation, flight-formation applications, space stations resupply and the in-situ exploration of small bodies. Future applications may also include satellite inspection and servicing. This thesis has focused on four scenarios: six-degrees of freedom spacecraft rendezvous; near-rectilinear halo orbits rendezvous; the hovering phase; orbit-attitude station-keeping in the vicinity of a small body. The first problem aims to demonstrate rendezvous capabilities for a lightweight satellite with few thrusters and a reaction wheels array. For near-rectilinear halo orbits rendezvous, the goal is to achieve higher levels of constraints satisfaction than with a stateof- the-art predictive controller. In the hovering phase, the objective is to augment the control accuracy and computational efficiency of a recent global stable controller. The small body exploration aims to demonstrate the positive impact of model-learning in the control accuracy. Although based on model predictive control, the specific approach for each scenario differs. In six-degrees of freedom rendezvous, the attitude flatness property and the transition matrix for Keplerian-based relative are used to obtain a non-linear program. Then, the control loop is closed by linearizing the system around the previous solution. For near-rectilinear halo orbits rendezvous, the constraints are assured to be satisfied in the probabilistic sense by a chance-constrained approach. The disturbances statistical properties are estimated on-line. For the hovering phase problem, an aperiodic event-based predictive controller is designed. It uses a set of trigger rules, defined using reachability concepts, deciding when to execute a single-impulse control. In the small body exploration scenario, a novel learning-based model predictive controller is developed. This works by integrating unscented Kalman filtering and model predictive control. By doing so, the initially unknown small body inhomogeneous gravity field is estimated over time which augments the model predictive control accuracy.El objeto de esta tesis es el dise˜no de algoritmos de control predictivo basado en modelo para operaciones de veh´ıculos espaciales en proximidad. Esto incluye, pero no se limita, a la maniobra de rendezvous, las fases de hovering u orbitar alrededor de cuerpos menores. Esta tesis est´a motivada por la creciente demanda en la autonom´ıa, entendida como la capacidad de un veh´ıculo para calcular su propio plan de control, de las actuales y futuras misiones espaciales. Este inter´es en incrementar la autonom´ıa est´a relacionado con las actuales tecnolog´ıas disruptivas que est´an cambiando el concepto tradicional de exploraci´on y explotaci´on espacial. Estas son el desarrollo de plataformas satelitales miniaturizadas y la dr´astica reducci´on de los costes de puesta en ´orbita. Dichas tecnolog´ıas han impulsado la actividad espacial a niveles de record. En un futuro cercano, se prev´e que un gran n´umero de objetos artificiales operen de manera simult´anea a lo largo del Sistema Solar. Bajo dicho escenario, los operadores terrestres se ver´an desbordados en la tarea de monitorizar y controlar cada sat´elite en tiempo real. Es por ello que el desarrollo de sistemas aut´onomos inteligentes y robustos es considerado una tecnolog´ıa fundamental por diversas agencias espaciales. Debido a lo anterior, este trabajo presenta nuevos resultados en el control de operaciones de veh´ıculos espaciales en proximidad. Dominar dichas operaciones permite llevar a cabo una gran variedad de misiones espaciales como la retirada de basura espacial, transferir astronautas, aplicaciones de vuelo en formaci´on, reabastecer estaciones espaciales y la exploraci ´on de cuerpos menores. Futuras aplicaciones podr´ıan incluir operaciones de inspecci´on y mantenimiento de sat´elites. Esta tesis se centra en cuatro escenarios: rendezvous de sat´elites con seis grados de libertad; rendezvous en ´orbitas halo cuasi-rectil´ıneas; la fase de hovering; el mantenimiento de ´orbita y actitud en las inmendiaciones de un cuerpo menor. El primer caso trata de proveer capacidades de rendezvous para un sat´elite ligero con pocos propulsores y un conjunto de ruedas de reacci´on. Para el rendezvous en ´orbitas halo cuasi-rectil´ıneas, se intenta aumentar el grado de cumplimiento de restricciones con respecto a un controlador predictivo actual. Para la fase de hovering, se mejora la precisi´on y eficiencia computacional de un controlador globalmente estable. En la exploraci´on de un cuerpo menor, se pretende demostrar el mayor grado de precisi´on que se obtiene al aprender el modelo. Siendo la base el control predictivo basado en modelo, el enfoque espec´ıfico difiere para cada escenario. En el rendezvous con seis grados de libertad, se obtiene un programa no-lineal con el uso de la propiedad flatness de la actitud y la matriz de transici´on del movimiento relativo Kepleriano. El bucle de control se cierra linealizando en torno a la soluci´on anterior. Para el rendezvous en ´orbitas halo cuasi-rectil´ıneas, el cumplimiento de restricciones se garantiza probabil´ısticamente mediante la t´ecnica chance-constrained. Las propiedades estad´ısticas de las perturbaciones son estimadas on-line. En la fase de hovering, se usa el control predictivo basado en eventos. Ello consiste en unas reglas de activaci´on, definidas con conceptos de accesibilidad, que deciden la ejecuci´on de un ´unico impulso de control. En la exploraci´on de cuerpos menores, se desarrolla un controlador predictivo basado en el aprendizaje del modelo. Funciona integrando un filtro de Kalman con control predictivo basado en modelo. Con ello, se consigue estimar las inomogeneidades del campo gravitario lo que repercute en una mayor precisi´on del controlador predictivo basado en modelo