The problem of reorienting a spacecraft to acquire a moving target is investigated. The spacecraft is modeled as a rigid body with N axisymmetric wheels controlled by axial torques, and the kinematics are represented by Modified Rodriques Parameters. The trajectory, denoted the reference trajectory, is one generated by a virtual spacecraft that is identical to the actual spacecraft. The open-loop reference attitude, angular velocity, and angular acceleration tracking commands are constructed so that the solar panel vector is perpendicular to the sun vector during the tracking maneuver. We develop a nonlinear feedback tracking control law, derived from Lyapunov stability and control theory, to provide the control torques for target tracking. The controller makes the body frame asymptotically track the reference motion when there are initial errors in the attitude and angular velocity. A spacecraft model, based on the X-ray Timing Explorer spacecraft, is used to demonstrate the effectiveness of the Lyapunov controller in tracking a given target. / Master of Science

The word 'rendezvous' implies a pre-arranged meeting between two entities for a specific purpose. This term is used in the study of spacecraft operations, to describe a set of maneuvers performed by two spacecraft in order to achieve a match in position and velocity. The term 'orbital rendezvous' applies to rendezvous between spacecraft in earth-centered orbits. Considering its obvious scope for application in the assembly, maintenance and retrieval of earth satellites, the importance of orbital rendezvous towards maintaining a sustained presence in space can be easily appreciated. This particular study deals with the development of a guidance scheme for an orbital rendezvous operation, wherein only one of the spacecraft, called the chaser, is assumed to be provided with a capability to maneuver, while the other spacecraft, the target, is assumed to be thrust-free or passive. There is presently a lot of interest in autonomous trajectory planning and guidance schemes for orbital rendezvous missions. Autonomy here, refers to the absence of ground supervision and control over the on-board planning and guidance process, and is expected to result in greater mission flexibility and lower operating costs. The terms trajectory planning and guidance collectively refer to the optimization process used to determine minimum-fuel trajectories, and the means employed to make the spacecraft follow them, based on navigational updates. The challenge lies mainly in making the autonomous scheme real-time implementable, and at the same time compatible with the limited computational capabilities available on-board. It is well known that a large part of the computation times and costs, when determining optimal trajectories, are taken up by (1) the prediction of spacecraft motion using numerical integration schemes, and (2) the use of iterative numerical techniques to solve the non-linear, coupled system of equations obtained as boundary conditions in the trajectory optimization problem. There exists on the other hand, a wealth of results from analytical investigations into the motion of spacecraft, that can be profitably utilized by use of suitable assumptions, to reduce computation times and costs relating to trajectory prediction. The present thesis seeks to follow this course, while trying to ensure that the assumptions made do not influence in a negative manner the accuracy of the guidance scheme. The assumptions to be described below are based on the division of the total rendezvous maneuver into sub-phases. The trajectory optimization problems for the individual sub-phases are first considered independent of one another. A method is then found to combine the two sub-phases in an optimal manner. The initial or the homing phase of the rendezvous maneuver, consists of an open-loop orbit transfer, intended to place the chaser within a 'window of proximity' spanning a few hundreds of kilometers, of the target. In order to avoid time consuming numerical integration of the non-homogeneous, non-linear central force-field equations of motion, an impulsive thrust model is assumed. A parametric optimization method is used to determine the location, orientation and magnitude of the impulses for a minimum-fuel rendezvous transfer, as it is well known that parametric optimization methods are robust compared to the more general functional optimization methods. A two-impulse transfer is selected, knowing that at least two-impulses are required for a rendezvous maneuver, and that methods are available if necessary, to obtain optimal multi-impulse trajectories from a two-impulse solution. The total characteristic velocity, a scalar cost function related to fuel-consumption, is minimized with respect to a set of independent variables. The variables chosen in this case to determine the rendezvous transfer are (1) the transfer angle θc defining an initial coast in the chaser orbit C by the chaser, (2) the transfer angle θs defining a coast by the target to the position of the second impulse in the target orbit S and (3) a parameter (say p ) that determines the shape of the transfer orbit T between the first and second impulses.

While human presence in cislunar space continues to expand, so too does the demand for `lightweight' automated on-board processes. In nonlinear dynamical environments, computationally efficient guidance strategies are challenging. Many traditional approaches rely on either simplifying assumptions in the dynamical model or on abundant computational resources. This research employs reinforcement learning, a subset of machine learning, to produce a controller that is suitable for on-board low-thrust guidance in challenging dynamical regions of space. The proposed controller functions without knowledge of the simplifications and assumptions of the dynamical model, and direct interaction with the nonlinear equations of motion creates a flexible learning scheme that is not limited to a single force model. The learning process leverages high-performance computing to train a closed-loop neural network controller. This controller may be employed on-board, and autonomously generates low-thrust control profiles in real-time without imposing a heavy workload on a flight computer. Control feasibility is demonstrated through sample transfers between Lyapunov orbits in the Earth-Moon system. The sample low-thrust controller exhibits remarkable robustness to perturbations and generalizes effectively to nearby motion. Effective guidance in sample scenarios suggests extendibility of the learning framework to higher-fidelity domains.

In this report we present a graphical tool, Behavioral Analysis of Spacecraft Systems (BASS), that can be used by spacecraft designers to perform system-level behavioral analysis of small satellites. The domain-specific spacecraft meta-model is created in the visual modeling tool Generic Modeling Environment (GME) such that spacecraft designs created using the meta-model appear familiar to the spacecraft designers. Users can model scenarios that are to be verified for the design in BASS. The graphical models are assigned formal semantics facilitating the creation of formally verifiable spacecraft models. The C++ application that translates the modeling objects to equivalent mathematical representation of interest is called BASS Interpreter and is bound to the meta-model. BASS Interpreter that generates Communicating Sequential Processes (CSP) semantics for the visual spacecraft models is supported in the current work. The model-checker for CSP called Failures Divergences and Refinement (FDR) is run to explore the state-space of the spacecraft process model to comment on the design. We demonstrate the feasibilty and advantage of incorporating BASS into initial design phases of small satellite development by successfully verifying the design of Tomographic Remote Observer of Ionospheric Disturbances (TOROID).

Spacecraft trajectory optimization is a near-infinite problem space with a wide variety of models and optimizers. As trajectory complexity increases, so too must the capabilities of modern optimizers. Common objective cost functions for these optimizers include the propellant utilized by the spacecraft and the time the spacecraft spends in flight. One effective method of minimizing these costs is the utilization of one or multiple gravity assists. Due to the phenomenon known as the Oberth effect, fuel burned at a high velocity results in a larger change in orbital energy than fuel burned at a low velocity. Since a spacecraft is flying fastest at the periapsis of its orbit, application of impulsive thrust at this closest approach is demonstrably capable of generating a greater change in orbital energy than at any other location in a trajectory. Harnessing this extra energy in order to lower relevant cost functions requires the modeling of these “powered flybys” or “powered gravity assists” (PGAs) within an interplanetary trajectory optimizer. This paper will discuss the use and modification of the Spacecraft Trajectory Optimization Suite, an optimizer built on evolutionary algorithms and the island model paradigm from the Parallel Global Multi-Objective Optimizer (PaGMO). This variant of STOpS enhances the STOpS library of tools with the capability of modeling and optimizing single and multiple powered gravity assist trajectories. Due to its functionality as a tool to optimize powered flybys, this variant of STOpS is named the Spacecraft Trajectory Optimization Suite - Flybys with Impulsive Thrust Engines (STOpS-FLITE). In three test scenarios, the PGA algorithm was able to converge to comparable or superior solutions to the unpowered gravity assist (uPGA) modeling used in previous STOpS versions, while providing extra options of trades between time of flight and propellant burned. Further, the PGA algorithm was able to find trajectories utilizing a PGA where uPGA trajectories were impossible due to limitations on time of flight and flyby altitude. Finally, STOpS-FLITE was able to converge to a uPGA trajectory when it was the most optimal solution, suggesting the algorithm does include and properly considers the uPGA case within its search space.

In this dissertation, we discuss the Distributed Spacecraft Attitude Control System Simulator (DSACSS) testbed developed at Virginia Polytechnic Institute and State University for the purpose of investigating various control techniques for single and multiple spacecraft. DSACSS is comprised of two independent hardware-in-the-loop simulators and one software spacecraft simulator. The two hardware-in-the-loop spacecraft simulators have similar subsystems as flight-ready spacecraft (e.g. command and data handling; communications; attitude determination and control; power; payload; and guidance and navigation). The DSACSS framework is a flexible testbed for investigating a variety of spacecraft control techniques, especially control scenarios involving coupled attitude and orbital motion. The attitude hardware simulators along with numerical simulations assist in the development and evaluation of Lyapunov based asymptotically stable, nonlinear attitude controllers with three reaction wheels as the control device. The angular rate controller successfully tracks a time varying attitude trajectory. The Modified Rodrigues Parmater (MRP) attitude controller results in successfully tracking the angular rates and MRP attitude vector for a time-varying attitude trajectory. The attitude controllers successfully track the reference attitude in real-time with hardware similar to flight-ready spacecraft. Numerical simulations and the attitude hardware simulators assist in the development and evaluation of a robust, asymptotically stable, nonlinear attitude controller with three reaction wheels as the actuator for attitude control. The MRPs are chosen to represent the attitude in the development of the controller. The robust spacecraft attitude controller successfully tracks a time-varying reference attitude trajectory while bounding system uncertainties. The results of a Global Positioning System (GPS) hardware-in-the-loop simulation of two spacecraft flying in formation are presented. The simulations involve a chief spacecraft in a low Earth orbit (LEO), while a deputy spacecraft maintains an orbit position relative to the chief spacecraft. In order to maintain the formation an orbit correction maneuver (OCM) for the deputy spacecraft is required. The control of the OCM is accomplished using a classical orbital element (COE) feedback controller and simulating continual impulsive thrusting for the deputy spacecraft. The COE controller requires the relative position of the six orbital elements. The deputy communicates with the chief spacecraft to obtain the current orbit position of the chief spacecraft, which is determined by a numerical orbit propagator. The position of the deputy spacecraft is determined from a GPS receiver that is connected to a GPS hardware-in-the-loop simulator. The GPS simulator creates a radio frequency (RF) signal based on a simulated trajectory, which results in the GPS receiver calculating the navigation solution for the simulated trajectory. From the relative positions of the spacecraft the COE controller calculates the OCM for the deputy spacecraft. The formation flying simulation successfully demonstrates the closed-loop hardware-in-the-loop GPS simulator. This dissertation focuses on the development of the DSACSS facility including the development and implementation of a closed-loop GPS simulator and evaluation of nonlinear feedback attitude and orbit control laws using real-time hardware-in-the-loop simulators. / Ph. D.

In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.

Presently, most spacecraft are controlled from ground involving activities such as up-linking the schedule of daily operations and monitoring health parameters. These activities lead to a cognitive overload on human operators. Imaging/science opportunities are lost, if any discrepancies occur during the execution of pre-planned sequences. Consequently, advanced space exploration systems for future needs demand on-board intelligence and autonomy. This thesis attempts to solve the problem of providing an adequate degree of autonomy in future generation of spacecraft. The autonomous spacecraft accept high-level goals from users and make decisions on-board to generate detailed command schedules satisfying stringent constraints posed by the harsh environment of the space, visibility criteria and scarce on-board resources. They reconfigure themselves in case of any failure and re-plan when needed. Autonomy concepts are derived in the context of complex systems by drawing analogy to living organisms and social organisations. A general autonomy framework may be defined with a six level structure comprising of the following capabilities -reflexes, awareness, self-regulation, self-healing, self-adaptation and self-evolution. A generic and reusable software architecture is proposed using hybrid multi-agent systems, which are arranged in a hierarchical manner using two types of decomposition viz. stratum and layer. The software architecture of the autonomous spacecraft is modeled as a stratified agent with a deliberative stratum, which achieves adaptive behaviour and a reactive stratum, which achieves reactive behaviour. Each individual agent has a generic structure comprising of perception, action, communication and knowledge components. It achieves the specialist capability through model-based reasoning. The knowledge models encompass: Planning knowledge describing higher-level goals, task structure and method of achieving the goals, Control knowledge encompassing the static and dynamic models of the spacecraft and Diagnostic knowledge incorporating the cause-effect relationships. The deliberative stratum is capable of planning in different time horizons and is, in turn, organised into a hierarchical agent system with three layers corresponding to different time horizons. It is composed of a long-term, medium-term and short-term planning agents, focusing on strategic issues, spacecraft level resources and specific spacecraft states respectively. The power of Petri nets is exploited for knowledge modeling as well as for plan representation. The ability of Petri nets to represent causality, concurrency and conflict relations explicitly makes it an excellent tool for representing the planning problem. Hierarchical Timed Petri Net is chosen for our modeling, since it captures the temporal requirements of the real-time spacecraft operations as well as facilitates the modeling of the system with multiple levels of abstraction. The necessary primitives for the plan representation are defined. In hierarchical modeling using Petri nets, refinement is done by a compound (high-level) transition. A compound transition models either a complex activity, which corresponds to high-level operation on spacecraft or a method, which corresponds to the agent capability. At the lowest layer, a transition in the plan represents a primitive command to the spacecraft, such as ‘switch on camera’. The Petri net unfolding technique, which is a partial order approach, is applied to derive the plans from the dynamic knowledge models. This tackles the problem of combinatorial explosion. A hierarchical planning approach is followed, in which the abstract plan is recursively decomposed using the unfolding technique and refined by way of exercising the appropriate decisions in each layer. The reactive stratum is configured with three peer level agents. The control agent executes the command schedule and has the capability for reflex action. Structural properties of Petri nets are exploited by the execution-monitoring agent and the diagnostic agent for system level diagnosis. Fault tree method is applied for fine granularity diagnosis. The resultant architecture is a cost-effective solution, since it permits reusability of knowledge models across similar missions. The knowledge models are formally verified for ensuring the absence of deadlocks, buffer overflows, recoverability and detection of unreachable modules using Petri net properties such as reachability, liveness, boundedness, safeness, reversibility and home state. The high-risk components are subjected to safety property verification, which makes the system rugged. The hierarchical composition of Petri net models (which are independently verified), preserves liveness and boundedness characteristics and thus ensuring the reliability of the integrated models. This, in turn, ensures that reliable plans are generated on-board using these good quality models. The models of the system components viz. partial order plan, conditional plan, dynamic world model, reflex model, resource model and the hierarchical models are developed and demonstrated using HPSIM and Moses Tool Suite, using examples from spacecraft domain. The long-term planning agent, with hierarchical world models, for handling high-level goals is developed and simulated using Moses Tool Suite. The plan generation using unfolding approach is demonstrated using VIPTool, which has the partial order analysis capability. In summary, the main contributions include (a) Definition of a general framework for spacecraft autonomy; (b) design of a generic and reusable architecture for autonomous spacecraft using hybrid multi-agent concepts; (c) unified knowledge representation and reasoning using Petri nets across various strata/layers; (d) application of Petri net unfolding technique in a hierarchical manner for plan generation; (e) use of structural properties of Petri nets for fault identification and location; (f) verification and validation of Petri net models using Petri net properties and (g) simulation and demonstration of the system components viz. partial order plan, conditional plan, dynamic world model, reflex model, resource model and hierarchical models, by developing examples from spacecraft domain, using HPSIM and Moses Tool Suite and demonstration of plan generation using unfolding technique using VIPTool.

ITC/USA 2005 Conference Proceedings / The Forty-First Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2005 / Riviera Hotel & Convention Center, Las Vegas, Nevada / This paper presents an approach to development of generic ground systems to be used for spacecraft testing and operations. This method makes use of a standard modeling method, which enables virtualization of spacecraft. By virtualizing spacecraft, development of generic systems that are applicable to different spacecraft becomes possible even if spacecraft themselves are not standardized. This is because systems can utilize (1) a standard database that can store information on any virtual spacecraft and (2) standard software tools that can be used for any virtual spacecraft. This paper explains the concept of virtualization of spacecraft, introduces the standard model used for virtualization of spacecraft, shows how to manipulate virtual spacecraft with software tools, and presents the core elements of generic ground systems.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Wireless interfaces are becoming ubiquitous in terrestrial applications ranging from local area networking in business and commercial environments to large scale factory automation and process control. The pressure to develop these wireless interfacing techniques has come from the need to reduce cabling, reduce installation costs, and make it easier to extend network infrastructures. Concerns about electromagnetic compatibility, safety, reliability, and security have lead to the development of techniques and protocols that enable such wireless interfaces to be operated in electromagnetically harsh environments, without generating unacceptable interference, and providing reliable, dependable and secure data communications. On the face of it, the use of wireless interfaces onboard spacecraft looks like a good way of reducing the spacecraft harness mass and bulk. However, recent work by the European Space Agency has shown that, while harness reduction will undoubtedly be one benefit of using wireless interfaces, they offer many other benefits that will be more significant in the near future. Amongst these are significant advantages during integration and testing, the ability to retrofit and upgrade facilities, and cable replacement in moving structures such as robotic arms. In this paper we briefly survey the benefits of wireless interface technologies for spacecraft onboard use, and identify the challenges involved in adapting them for flight use. We then look at the considerations that should be taken into account in establishing the financial case for developing wireless interface technologies for flight applications.