Adaptive and Supertwisting Adaptive Spacecraft Orbit Control Around Asteroids

This paper addresses the development of control systems for the orbit control of spacecraft around irregularly shaped rotating asteroids with uncertain parameters. The objective is to steer the spacecraft along prescribed orbits. First, a nonlinear adaptive law for orbit control was designed. This was followed by the design of a supertwisting adaptive (STWA) control system. In the closed-loop system, which includes the adaptive law or the STWA law, all the signals remain bounded, and the trajectory tracking error asymptotically converges to zero for any initial condition. Finally, under the assumption of boundedness of the derivative of the uncertain functions of the model in a region of the state space, a supertwisting control (STW) law for finite-time convergence of the trajectory was obtained. Based on the Lyapunov theory, stability properties of the closed-loop systems were analyzed. Simulation results for 433 Eros and Ida asteroids were presented for illustration. The results showed that control of spacecraft along closed orbits or to a fixed point is accomplished using each of these controllers, despite uncertainties in the parameters of the asteroid models

Constrained Motion Analysis and Control of Spacecraft Asteroid Hovering with Formulation Extension in Geometric Mechanics Framework

This thesis studies the constrained motion for a spacecraft hovering over an asteroid, where the Udwadia-Kalaba (UK) formulation is applied for nominal control, and an adaptive controller is developed to account for unknowns in the dynamics. Then, the formulation is extended in the geometric mechanics framework to account for rigid body spacecraft asteroid hovering. Constraints are developed and applied for fully constrained and under-constrained asteroid hovering. The fully constrained solutions provided by the UK fundamental equation are compared to an optimal linear quadratic regulator. An adaptive controller is designed using the UK fundamental equation as a basis in the form of a model reference adaptive controller. The controller is proven to have asymptotic tracking of the reference system designed by the desired constraints on the spacecraft. The convergence of the tracking error dynamics is studied using the Lyapunov’s direct method. It is shown that the controller, with accurate estimation of the unknown parameters, results in the minimum required control response due to its basis on the UK equation. The parameters are successfully estimated using a finite-time estimation method. Furthermore, the extension of the UK formulation into the geometric mechanics framework is developed to account for rigid-body spacecraft, where the formulation also allows orientation constraints to be applied on the spacecraft. Constraints with a basis on the Lie algebra of special Euclidean group SE(3) are developed to fully constrain a spacecraft’s position and orientation for hovering over an asteroid. The geometric mechanics UK formulation successfully gives the required angular and translational accelerations to maintain the desired configuration (pose) of the rigid-body spacecraft. The developments above are discussed for a spacecraft hovering over the asteroid Bennu and the closed-loop response of the system, control inputs, and control efforts are provided and discussed

Control of Hovering Spacecraft Near Small Bodies: Application to Asteroid 25143 Itokawa

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76879/1/AIAA-3890-246.pd

Adaptive-Optimal Control of Spacecraft near Asteroids

Spacecraft dynamics and control in the vicinity of an asteroid is a challenging and exciting problem. Currently, trajectory tracking near asteroid requires extensive knowledge about the asteroid and constant human intervention to successfully plan and execute proximity operation. This work aims to reduce human dependency of these missions from a guidance and controls perspective. In this work, adaptive control and model predictive control are implemented to generating and tracking obstacle avoidance trajectories in asteroid’s vicinity. Specifically, direct adaptive control derived from simple adaptive control is designed with e modification to track user-generated trajectories in the presence of unknown system and sensor noise. This adaptive control methodology assumes no information on the system dynamics, and it is shown to track trajectories successfully in the vicinity of the asteroid. Then a nonlinear model predictive control methodology is implemented to generate obstacle avoidance trajectories with minimal system information namely mass and angular velocity of the asteroid. Ultimately, the adaptive control system is modified to include feed-forward control input from the nonlinear model predictive control. It is shown through simulations that the new control methodology names direct adaptive model predictive control (DAMPC), is able to generate sub-optimal trajectories. A comparative study is done with Asteroid Bennu, Kleopatra and Eros to show the benefits of DAMPC over adaptive control and MPC. A study on effect of noisy measurements and model is also conducted on adaptive control and direct adaptive model predictive control

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

Survey of highly non-Keplerian orbits with low-thrust propulsion

Celestial mechanics has traditionally been concerned with orbital motion under the action of a conservative gravitational potential. In particular, the inverse square gravitational force due to the potential of a uniform, spherical mass leads to a family of conic section orbits, as determined by Isaac Newton, who showed that Kepler‟s laws were derivable from his theory of gravitation. While orbital motion under the action of a conservative gravitational potential leads to an array of problems with often complex and interesting solutions, the addition of non-conservative forces offers new avenues of investigation. In particular, non-conservative forces lead to a rich diversity of problems associated with the existence, stability and control of families of highly non-Keplerian orbits generated by a gravitational potential and a non-conservative force. Highly non-Keplerian orbits can potentially have a broad range of practical applications across a number of different disciplines. This review aims to summarize the combined wealth of literature concerned with the dynamics, stability and control of highly non-Keplerian orbits for various low thrust propulsion devices, and to demonstrate some of these potential applications

Feedback stabilization of displaced periodic orbits : Application to binary asteroid

This paper investigates displaced periodic orbits at linear order in the circular restricted Earth-Moon system (CRTBP), where the third massless body utilizes a hybrid of solar sail and a solar electric propulsion (SEP). A feedback linearization control scheme is implemented to perform stabilization and trajectory tracking for the nonlinear system. Attention is now directed to binary asteroid systems as an application of the restricted problem. The idea of combining a solar sail with an SEP auxiliary system to obtain a hybrid sail system is important especially due to the challenges of performing complex trajectories

Asteroid Redirect Mission (ARM) using Solar Electric Propulsion (SEP) for Research, Mining, and Exploration Endeavors of Near-Earth Objects (NEOs)

The feasibility of relocating a small (~500,000 kg) Near-Earth Asteroid (NEA) to High Earth Orbit via Solar Electric Propulsion (SEP) is evaluated with the orbital simulation software General Mission Analysis Tool (GMAT). Using prior research as a basis for the mission parameters, a retrieval mission to NEA 2008 HU4 is simulated in two parts: approach from Earth and return of the Asteroid Redirect Vehicle (ARV) with the asteroid in tow. Success of such a mission would pave the way for future missions to larger NEAs and other deep space endeavors. It is shown that for a hypothetical launch time of 24 May 2016, the ARV could arrive within 25 km of 2008 HU4 on 28 Jun 2017 with a Delta V of 0.406 km/s, begin return maneuver on 08 Dec 2017 and reach Earth altitude of 450,000 km by 23 Apr 2026 with a Delta V of 44.639 m/s