Lunar Ascent and Orbit Injection via Neighboring Optimal Guidance and Constrained Attitude Control

Future human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent phases of spaceflight. This research focuses on the original combination of two techniques applied to lunar ascent modules, i.e., (1) the recently introduced variable-time-domain neighboring optimal guidance (VTD-NOG), and (2) a constrained proportional-derivative (CPD) attitude control algorithm. VTD-NOG belongs to the class of feedback implicit guidance approaches aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory. CPD pursues the desired attitude using thrust vector control while constraining the rate of the thrust deflection angle. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and CPD represents an accurate and effective methodology for guidance and control of lunar ascent path and orbit injection in the presence of nonnominal flight conditions

Design Methodology and Performance Evaluation of New Generation Sounding Rockets

Sounding rockets are currently deployed for the purpose of providing experimental data of the upper atmosphere, as well as for microgravity experiments. This work provides a methodology in order to design, model, and evaluate the performance of new sounding rockets. A general configuration composed of a rocket with four canards and four tail wings is sized and optimized, assuming different payload masses and microgravity durations. The aerodynamic forces are modeled with high fidelity using the interpolation of available data. Three different guidance algorithms are used for the trajectory integration: constant attitude, near radial, and sun-pointing. The sun-pointing guidance is used to obtain the best microgravity performance while maintaining a specified attitude with respect to the sun, allowing for experiments which are temperature sensitive. Near radial guidance has instead the main purpose of reaching high altitudes, thus maximizing the microgravity duration. The results prove that the methodology at hand is straightforward to implement and capable of providing satisfactory performance in term of microgravity duration

Low-thrust lunar capture leveraging nonlinear orbit control

Nonlinear orbit control with the use of low-thrust propulsion is proposed as an effective strategy for autonomous guidance of a space vehicle directed toward the Moon. Orbital motion is described in an ephemeris model, with the inclusion of the most relevant perturbations. Unfavorable initial conditions, associated with weak, temporary lunar capture, are considered, as representative conditions that may be encountered in real mission scenarios. These may occur when the spacecraft is released in nonnominal flight conditions, which would naturally lead it to impact the Moon or escape the lunar gravitational attraction. To avoid this, low-thrust propulsion, in conjunction with nonlinear orbit control, is employed, to drive the space vehicle toward two different, prescribed, low-altitude lunar orbits. Nonlinear orbit control leads to identifying a saturated feedback law (for the low-thrust magnitude and direction) that is proven to enjoy global stability properties. The guidance strategy at hand is successfully tested on three different mission scenarios. Then, the capture region is identified, and includes a large set of initial conditions for which nonlinear orbit control with low-thrust propulsion is effective to achieve lunar capture and final orbit acquisition. For the purpose of achieving lunar capture, low-thrust propulsion is shown to be more effective if ignited at aposelenium

Neighboring optimal guidance and proportional-derivative attitude control applied to low-thrust orbit transfers

This work presents a unified guidance and control architecture, termed VTD-NOG & PD-RM, and describes its application to low-thrust orbit transfer from a low Earth orbit to a geostationary orbit. The variable time-domain neighboring optimal guidance (VTD-NOG) is a feedback guidance technique based upon minimizing the second differential of the objective function along the perturbed trajectory, and was proven to avoid the numerical difficulties encountered with alternative neighboring optimal algorithms. VTD-NOG identifies the trajectory corrections assuming the thrust direction as the control input. A proportional-derivative attitude control based on rotation matrices (PD-RM) is used to drive the actual thrust direction toward the desired one, determined by VTD-NOG. Reaction wheels are employed to perform the attitude control action. In the dynamical simulations, thrust oscillations, errors on the initial conditions, and gravitational perturbations are considered. Extensive Monte Carlo simulations point out that orbit injection occurs with very satisfactory accuracy, even in the presence of nonnominal flight conditions

Ascent Trajectories of Multistage Launch Vehicles: Numerical Optimization with Second-Order Conditions Verification

Multistage launch vehicles are employed to place spacecraft and satellites in their operational orbits. Trajectory optimization of their ascending path is aimed at defining the maximum payload mass at orbit injection, for specified structural, propulsive, and aerodynamic data. This work describes and applies a method for optimizing the ascending path of the upper stage of a specified launch vehicle through satisfaction of the necessary conditions for optimality. The method at hand utilizes a recently introduced heuristic technique, that is, the particle swarm algorithm, to find the optimal ascent trajectory. This methodology is very intuitive and relatively easy to program. The second-order conditions, that is, the Clebsch-Legendre inequality and the conjugate point condition, are proven to hold, and their fulfillment enforces optimality of the solution. Availability of an optimal solution to the second order is an essential premise for the possible development of an efficient neighboring optimal guidance

Mars Constellation Design and Low-Thrust Deployment Using Nonlinear Orbit Control

This research addresses the design of a Mars constellation composed of 12 satellites and devoted to telecommunications. While 3 satellites travel areostationary orbits, the remaining 9 satellites are placed in three distinct quasi-synchronous, inclined, circular orbits. The constellation at hand provides continuous global coverage, over the entire Martian surface. The use of 4 carrier vehicles, departing from a 4-sol orbit, is proposed as an affordable option for the purpose of deploying the entire constellation, even starting from dispersed initial conditions. Each carrier is driven toward the respective operational orbit using steerable and throttleable low-thrust propulsion, in conjunction with nonlinear orbit control. Lyapunov stability analysis leads to defining a feedback law that enjoys quasi-global stability properties. Orbit phasing concludes the constellation deployment, and is carried out by each satellite. The tradeoff between phasing time and propellant expenditure is characterized

Low-thrust transfer to quasi-synchronous Martian elliptic orbit via nonlinear feedback control

This study considers the problem of injecting a spacecraft into an elliptic, repeating-ground-track orbit about Mars, starting from a 4-sol highly elliptical orbit, which is a typical Martian capture orbit, entered at the end of the interplanetary transfer. The final operational orbit has apoares corresponding to the maximum (or minimum) latitude, and nine nodal periods are flown in 5 Martian nodal days. The orbit at hand is proven to guarantee coverage properties similar to the Molniya orbit about Earth; therefore, it is especially suitable for satellites that form constellations. Low-thrust nonlinear orbit control is proposed as an affordable and effective option for orbit injection, capable of attaining significant propellant reduction if compared to alternative strategies based on chemical propulsion. This work introduces a new, saturated feedback law for the low-thrust direction and magnitude that is capable of driving the spacecraft of interest toward the operational orbit. Remarkable stability properties are proven to hold using the Lyapunov stability theory. Because no reference path is to be identified a priori, this technique represents a viable autonomous guidance strategy, even in the case of temporary unavailability of the low-thrust propulsion system or in the presence of widely dispersed initial conditions and errors on estimating orbit perturbations. Monte Carlo simulations prove that the feedback guidance strategy at hand is effective and accurate for injecting a spacecraft into the desired, repeating-ground-track operational orbit without requiring any reference transfer path

Statistical Study of Uncontrolled Geostationary Satellites Near an Unstable Equilibrium Point

The growth of the population of space debris in the geostationary ring and the resulting threat to active satellites require insight into the dynamics of uncontrolled objects in the region. A Monte Carlo simulation analyzed the sensitivity to initial conditions of the long-term evolution of geostationary spacecraft near an unstable point of the geopotential, where irregular behavior (e.g., transitions between long libration and continuous circulation) occurs. A statistical analysis unveiled sudden transitions from order to disorder, interspersed with intervals of smooth evolution. There is a periodicity of approximately half a century in the episodes of disorder, suggesting a connection with the precession of the orbital plane, due to Earth's oblateness and lunisolar perturbations. The third-degree harmonics of the geopotential also play a vital role. They introduce an asymmetry between the unstable equilibrium points, enabling the long libration mode. The unpredictability occurs just in a small fraction of the precession cycle, when the inclination is close to zero. A simplified model, including only gravity harmonics up to degree 3 and the Earth and Moon in circular coplanar orbits is capable of reproducing most features of the high-fidelity simulation

Using Space Manifolds Dynamics to deploy a small satellite constellation around the Moon

Negli ultimi anni la analisi per missioni spaziali interplanetarie e Terra-Luna ha avuto un nuovo e interessante impulso. La tecnica utilizzata da circa un secolo era quella delle “coniche raccordate”, ovvero la traiettoria interplanetaria veniva approssimata collegando archi di traiettoria nei quali l’effetto gravitazionale era esercitato da un corpo celeste alla volta, quindi trattasi di archi di coniche kepleriane, e le coniche raccordate passando dalla sfera di influenza di un corpo celeste all’altro. Viceversa, proprio a partire dalle missioni Terra-Luna si è trovato molto interessante esplorare regioni dinamiche dove fosse rilevante, e in sorta di equilibrio, il contributo gravitazionale di più corpi celesti. In questo caso si tratta di esplorare traiettorie a bassa energia che hanno il grande vantaggio di trarre pieno vantaggio degli aiuti gravitazionali di più corpi, con notevole riduzione del propellente necessario a realizzare i trasferimenti e al prezzo di allungare i tempi di trasferimento. I diversi livelli di energia utilizzabili sono tali da poter effettuare missioni notevolmente diverse tra loro a prezzo di piccole variazioni di velocità: ad esempio alcuni trasferimenti Terra-Luna possono virare con poca variazione di energia in tour tra i punti di equilibrio lagrangiani oppure, mediante tecniche di trasferimento esterno, in trasferimenti su altri pianeti. Tutto ciò è realizzato sfruttando appieno la complessità della dinamica di sistemi a più corpi, che ha portato al riconoscimento di “autostrade spaziali”, ovvero a un insieme di traiettorie di interesse nella analisi di missione e che possono essere percorse passando dall’una all’altra con poca variazione di velocità. In particolare questa tecnica è ripercorsa per il dispiegamento di una costellazioni di satelliti attorno alla Luna. La dinamica del trasferimento è compresa con una certa nettezza utilizzando dapprima una rappresentazione linea rizzata attorno alla regione cruciale del trasferimento (il punto di equilibrio intermedio del sistema Terra-Luna) e quindi sfruttando le proprietà della dinamica non lineare