Docking Manoeuvre Control for CubeSats

Rendezvous and Docking missions of small satellites are opening new scenarios to accomplish unprecedented in-obit operations. These missions impose to win the new technical challenges that enable the possibility to successfully perform complex and safety-critical manoeuvres. The disturbance forces and torques due to the hostile space environment, the uncertainties introduced by the onboard technologies and the safety constraints and reliability requirements lead to select advanced control systems. The paper proposes a control strategy based on Model Predictive Control for trajectory control and Sliding Mode Control for attitude control of the chaser in last meters before the docking. The control performances are verified in a dedicated simulation environment in which a non-linear six Degrees of Freedom and coupled dynamics, uncertainties on sensors and actuators responses are included. A set of 300 Monte Carlo Simulation with this Non-Linear system are carried out, demonstrating the capabilities of the proposed control system to achieve the final docking point with the required accuracy

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

Cooperative Platooning and Servicing for Spacecraft Formation Flying using Model Predictive Control

This work was partially funded by FCT project REPLACE (PTDC/EEIAUT/32107/2017) which includes Lisboa 2020 and PIDDAC funds, project CAPTURE (PTDC/EEIAUT/1732/2020).This paper addresses two complementary problems of spacecraft formation flying, namely spacecraft platooning and on-orbit spacecraft servicing, using Model Predictive Control (MPC). With the proposed solutions, these space formation scenarios can be regarded as a cooperative system composed of several spacecraft with a common goal, which may have clear advantages relative to other approaches. For each application scenario, a different optimization problem and MPC design is presented, including relevant constraints to deal with physical limitations, visibility problems, and also to guarantee a collision-free trajectory from other spacecraft or obstacles. The proposed methods are validated with realistic simulation results, showing that all vehicles demonstrate reliable performance following a given trajectory or goal in a formation, while satisfying all the considered constraints.publishersversionpublishe

Autonomous Rendezvous with a non-cooperative satellite: trajectory planning and control

Con la nascita di nuove problematiche e nuove esigenze in ambito spaziale, le più importanti riguardanti il tema della mitigazione dei detriti spaziali o dell’assistenza e del servizio dei satelliti in orbita, lo scenario di rendez-vous autonomo tra un satellite inseguitore e un satellite target non cooperativo sta diventando sempre più centrale, ambizioso e accattivante. Il grande scoglio da superare, tuttavia, consiste nell’individuazione di una strategia di approccio robusta e vincente: mentre l’esecuzione di una manovra di rendez-vous e docking o cattura con satellite cooperativo è già stata collaudata e possiede una consolidata eredità di volo, il rendez-vous autonomo con satellite non cooperativo ed in stato di tombolamento è uno scenario agli albori, con pochi studi al riguardo. Lo scopo di questa tesi consiste nell’identificazione di una strategia di approccio che consideri le principali problematiche legate al tema in questione, ovvero la non-cooperazione e le scarse informazioni sullo stato di moto del target da raggiungere. Queste due complicazioni portano alla necessità di eseguire un moto di ispezione del satellite target e alla considerazione di numerosi vincoli nella progettazione della traiettoria di ispezione e di approccio. Un controllore adatto a trattare questo problema complesso e multi-vincolato è il Model Predictive Controller, in forma lineare o non lineare, abbinato ad un filtro di Kalman. La capacità di questo controllore di previsione e pianificazione di una traiettoria d’approccio, a partire da stime di posizione relativa tra target e inseguitore, permette di portare a termine la manovra in modo sicuro e robusto.According to the rise of new problems and new demands in the space field, the most important concerning the mitigation of space debris or the spacecraft on-orbit servicing and assistance themes, the Autonomous Rendezvous scenario between a chase satellite and a non-cooperative target satellite is becoming increasingly significant, ambitious, and attractive. The main issue to overcome, however, consists in the identification of a robust and successful approach strategy: while the execution of a rendezvous and docking or capture maneuver with a cooperative satellite has already been tested and holds a solid flight heritage, the autonomous rendezvous with a non-cooperative satellite in a state of tumbling motion is a scenario in the early days, with few studies about it and a not yet mature technology. The aim of this thesis consists in the identification of an approach strategy that deals with the main challenges related to the considered problem, namely non-cooperativeness and exiguous information about the target to be reached. These two issues lead to the need of performing an inspection motion and considering several constraints in the trajectory design. A controller suitable to handle this complex and multi-constrained problem is the Model Predictive Controller, in a linear or non-linear form, paired with a Kalman filter. The ability of this controller to predict and plan an approaching trajectory, starting from estimates of the relative position between the target and the chaser, allows to complete the approaching maneuver safely and in a robust way

Analysis and modeling of satellite flexible bodies in Simscape Multibody

Questa Tesi Magistrale fornisce un’analisi per trovare un metodo numericamente efficiente per modellare i corpi flessibili di un satellite. L’analisi numerica è condotta su MATLAB - Simulink confrontando due rappresentazioni matematiche dei corpi flessibili: il metodo a “parametri forfettari” e il metodo della “trave flessibile”, utilizzati per modellare un pannello solare e un braccio robotico a 3 GdL. Questo studio ha lo scopo di contribuire ad un progetto condotto presso l’Università di Padova in collaborazione con l’Agenzia Spaziale Europea (ESA): esso si concentra sullo sviluppo di tecnologie di Guidance Navigation Control (GNC) per missioni di In-Orbit Servicing (IOS) e Active Debris Removal (ADR), condotte da un veicolo spaziale, dotato di un braccio robotico in grado di afferrare detriti spaziali e agganciare altri satelliti; in particolare, l’attività di ricerca oggetto del contratto è un simulatore della dinamica di scenari per Close Proximity Operations (CPOs), denominato Functional Engineering Simulator (FES). Il pannello solare e il braccio robotico, montati sul satellite, devono essere studiati perché le loro deformazioni possono occasionalmente diventare abbastanza severe da influenzare sia le proprie prestazioni che quelle degli altri sistemi. Se ciò dovesse accadere, le vibrazioni verrebbero notevolmente amplificate, accelerando il tasso di usura meccanica, aumentando il consumo di energia e interferendo con i compiti che necessitano un’alta precisione. Gli obiettivi di questa tesi Magistrale sono: (1) creare un Simulatore adatto per studiare la risposta dinamica del pannello solare soggetto a perturbazioni esterne e gli effetti degli elementi flessibili del braccio robotico durante il suo movimento, (2) confrontare i due metodi dei corpi flessibili in termini di accuratezza dei risultati e tempi di simulazione, (3) trovare il modello matematico che possa rappresentare adeguatamente la teoria dei corpi flessibili, in modo da poter essere utilizzato per modellare un vero simulatore. Il pannello solare è stato modellato secondo due diversi scenari, i quali rappresentano due esempi di architetture di missioni spaziali che prevederanno operazioni con bracci robotici nel prossimo futuro. Il suo comportamento è stato studiato analizzando la risposta degli impulsi causati dalle perturbazioni esterne che agiscono sulla superficie del pannello solare. Invece, il braccio robotico è stato modellato per seguire un percorso rettilineo da un punto iniziale a un punto finale e il comportamento dei suoi elementi flessibili è stato studiato ad ogni istante del suo movimento. Per modellare un elemento del veicolo spaziale, il metodo della trave flessibile utilizza un blocco già esistente di Simscape Multibody. Per questo motivo, esso è stato considerato come metodo di riferimento per verificare l’affidabilità di quello a parametri forfettari, per il quale i risultati hanno dimostrato essere uno metodo valido per descrivere il comportamento dei corpi flessibili di un veicolo spaziale, soprattutto grazie ai suoi rapidi tempi di simulazione, i quali lo rendono adatto per modellare in un vero simulatore.This Master Thesis provides an analysis to find a numerically efficient method to model a satellite flexible bodies in the MATLAB - Simulink environment. The numerical analysis is conducted by comparing two mathematical representations of flexible bodies: the Lumped-parameter method and the Flexible-beam method, which are implemented by the Simulation Tool to model and simulate the dynamics of a solar panel and a 3-DOF robotic arm. This study is on purpose to contribute to a project conducted at the University of Padua in collaboration with the European Space Agency (ESA): it focuses on the development of the Guidance Navigation Control technologies (GNC) suitable to be applied to both In-Orbit Servicing (IOS) and Active Debris Removal (ADR) missions conducted by a chaser spacecraft equipped with a robotic arm that can grab space debris and lock onto other satellites; in particular, the research activity under contract is a simulator of the dynamics of Close Proximity Operations (CPOs) scenarios, called Functional Engineering Simulator (FES). The solar panel and robotic arm mounted on the spacecraft behave as flexible bodies and need to be studied because their deformations may occasionally become severe enough to affect the performance of their respective systems. If these effects occur, vibrations are significantly amplified, accelerating the rate of mechanical wear, increasing power consumption, and interfering with high-precision tasks. The goals of this Master Thesis are: (1) to create a reliable simulation tool to study the dynamic response of the solar panel subject to external perturbations and the effects of the flexible elements of the robotic arm during its motion, (2) to compare the two flexible body methods in terms of accuracy of results and execution time, (3) to find the mathematical model that can adequately represent the flexible body theory so that it can be used to model a real-time simulator. The solar panel is modeled according to two different scenarios, which represent two examples of space mission architectures requiring robotic operations in the near future. Its behavior is studied by analyzing the response to impulses caused by external perturbations acting on the solar panel surface. On the other hand, the robotic arm is modeled to follow a rectilinear path from a starting point to an end point and the behavior of its flexible elements is studied at each time-step of this motion. The flexible-beam method consists of using an existing Simscape Multibody block to model the spacecraft element. Hence, it has been considered as a benchmark in order to verify the reliability of the lumped-parameter method, for which the results demonstrated that it is a valid tool for describing the behavior of flexible bodies of a spacecraft, mainly due to its fast execution times, which make it suitable for modeling in a real-time simulator

Autonomous rendezvous and docking maneuvers with Model Predictive Control strategies

Since the beginning of space era, rendezvous and docking maneuvers have been of great importance for the success of numerous missions. The operation of meeting two or more space vehicles in orbit is a need for many missions which require the assembly or supply of orbital platforms, debris removal, or sample return for interplanetary missions. Such maneuvers can be performed automatically in a feedback way, with numerous advantages over manual control. The objective of this thesis is to present the Model Predictive Control (MPC), an advanced controller, for rendezvous and docking maneuvers between two cooperative satellites in orbit and compare its behaviors and performances with those of a classical PID controller. After the description of the operating principle of MPC and PID control strategies and the dynamics equations of the relative motion between satellites in orbit, a realistic rendezvous and docking scenario is considered. The scenario involves a 3U CubeSat performing autonomously the final approach to a target orbiting station along the V-bar direction, and includes some of the typical environmental disturbances at LEO orbits (differential drag and J2). A software developed in Matlab has been used to carry out the numerical simulations with the two kinds of controller. Once the optimal parameters of the controllers have been found and verified, a 1000-run Montecarlo simulation for both types of controller has been carried out and results have been compared in terms of quality of the trajectory inside the approach cones, respect of docking requirements, and use of delta-V.Since the beginning of space era, rendezvous and docking maneuvers have been of great importance for the success of numerous missions. The operation of meeting two or more space vehicles in orbit is a need for many missions which require the assembly or supply of orbital platforms, debris removal, or sample return for interplanetary missions. Such maneuvers can be performed automatically in a feedback way, with numerous advantages over manual control. The objective of this thesis is to present the Model Predictive Control (MPC), an advanced controller, for rendezvous and docking maneuvers between two cooperative satellites in orbit and compare its behaviors and performances with those of a classical PID controller. After the description of the operating principle of MPC and PID control strategies and the dynamics equations of the relative motion between satellites in orbit, a realistic rendezvous and docking scenario is considered. The scenario involves a 3U CubeSat performing autonomously the final approach to a target orbiting station along the V-bar direction, and includes some of the typical environmental disturbances at LEO orbits (differential drag and J2). A software developed in Matlab has been used to carry out the numerical simulations with the two kinds of controller. Once the optimal parameters of the controllers have been found and verified, a 1000-run Montecarlo simulation for both types of controller has been carried out and results have been compared in terms of quality of the trajectory inside the approach cones, respect of docking requirements, and use of delta-V

Design of sliding mode controller based on radial basis function neural network for spacecraft autonomous proximity

Since the dynamic model of spacecraft has the characteristics of non-linear, kinematic couplings, uncertainties and nonstationary disturbance, it has become a challenging problem to accurately control the relative position and attitude of the spacecraft. A radial basis function neural network (RBFNN)-based sliding mode controller (SMC) is proposed for trajectory tracking of spacecraft autonomous proximity in this paper. Firstly, a six degree-of-freedom (DOF) relative motion dynamics model is developed for close proximity operations. The modified Rodrigues parameters are applied to solve the problem of singularity. Then, a SMC that does not require accurate model information is designed. RBFNN is used to adaptively eliminated the model uncertainty impacts on the system. Finally, the stability of the relative motion dynamics is proved via Lyapunov stability theory. Simulation results illustrate that the method can attenuate the attitude and position errors, reduce the chattering of the input and decrease the overshoot of the control torque effectively

Experimental Investigation of Spacecraft Rendezvous and Docking by Development of a 3 Degree of Freedom Satellite Simulator Testbed

This thesis developed a 3 degree of freedom air bearing satellite simulator testbed. The major components of this testbed are a 2-meter by 4-meter granite table, a pair of satellite simulators, and a passive infrared marker array. The goal of this implementation was to achieve soft docking between 2 satellite simulators while relying only on hardware and systems onboard the satellite simulator. The satellite simulators make use of compressed air stored onboard in tanks to supply the air bearing and gas thrusters. The air bearing system provides a thin cushion of air for the satellite simulator to float on, removing surface contact and friction between the satellite simulator and the granite table. This produces a 3 degree of freedom system which is effectively free of the effects of gravity. The infrared marker array is used to provide reference points similar to stars to enable an onboard positioning system using a single observer. The experimental results obtained here demonstrate the successful implementation of this testbed

Rendezvous in cislunar halo orbits: Hardware-in-the-loop simulation with coupled orbit and attitude dynamics

Space missions to Near Rectilinear Halo Orbits (NRHOs) in the Earth-Moon system are upcoming. A rendezvous technique in cislunar space is proposed in this investigation, one that leverages coupled orbit and attitude dynamics in the Circular Restricted Three-body Problem (CR3BP). An autonomous Guidance, Navigation, and Control (GNC) technique is demonstrated in which a chaser spacecraft approaches a target spacecraft in a sample southern 9:2 synodic-resonant L2 NRHO, one that currently serves as the baseline for NASA's Gateway. A two-layer guidance and control approach is contemplated. First, a nonlinear optimal controller identifies an appropriate baseline rendezvous path for guidance, both in position and orientation. As the spacecraft progresses along the pre-computed baseline path, navigation is performed through optical sensors that measure the relative pose of the chaser relative to the target. A Kalman filter processes these observations and offers state estimates. A linear controller compensates for any deviations identified from the predetermined rendezvous path. The efficacy of the GNC technique is tested by considering a complex scenario in which the rendezvous operation is conducted with an uncontrolled tumbling target. Hardware-in-the-loop laboratory experiments are conducted as a proof-of-concept to validate the guidance algorithm, with observations supplemented by optical navigation techniques

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