1,721,258 research outputs found
Low-thrust minimum-fuel trajectory optimization for the Sun-Earth inclined L4 mission
No full textThis study focuses on optimizing low-thrust trajectories for a spacecraft to achieve an inclined Sun-Earth L4 periodic orbit. The optimization is formulated as an indirect optimization problem, based on the Euler-Lagrange equations of motion. The objective is to minimize the total propellant mass, following the Pontryagin Minimum Principle, which maximizes the spacecraft's mass upon arrival at the Sun-Earth L4 point. The analysis includes two key optimal control problems: Sun-Earth L4 insertion and inclination-pumping optimal control problem. The Sun-Earth L4 insertion optimal control problem solves the optimal thrusting direction and throttling required to stop at the Sun-Earth L4 with the desired ecliptic inclination after launch. The inclination-pumping optimal control problem solves the optimal thrusting direction and throttling required to move the spacecraft from a low to a high-inclination orbit about Sun-Earth L4. The first continuation strategy is transitioning the spacecraft trajectory from energy-optimal to fuel-optimal solutions. Then, a second continuation strategy is employed to decrease and increase the maximum thrust level, which generates the control surfaces that reveal the relationship between fuel-optimal trajectories and thrust levels. The test cases involve a 1,500 kg spacecraft equipped with a 200 mN electric thruster powered by solar arrays that provide 3 kW end-of-life-2-kW of which is required, leaving a steady 1 kW margin. These cases analyze the mass at arrival for various initial inclinations and maneuver sequences. The analysis performed in the case study section targets 14 5 inclined Sun-Earth L4 periodic orbit with several intermediate inclinations. Optimal launch windows for high-latitude solar surface observations are calculated for each trajectory type, accounting for the tilt angle of the Sun's rotational axis from the ecliptic frame. (c) 2025 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Multiple Mars gravity-assist trajectory to inclined Sun-Earth L4
No full textThe multiple Mars gravity-assist trajectory is compared to the phasing trajectory for placing a spacecraft in a circular Sun-Earth L4 orbit with a 1 AU semi-major axis and inclinations of 10 degrees and 14.5 degrees relative to the ecliptic plane. The gravity-assist maneuvers are treated as instantaneous velocity changes using a zero-sphere-of-influence model. The trajectory is optimized for two potential launch vehicles (Falcon 9 and Falcon Heavy) to achieve the desired orbit with minimal C3 energy. Through trajectory analysis based on various launch vehicles and their C3-based payload capacities, it was found that the multiple Mars gravity-assist trajectories are outperformed by the phasing trajectory at a 10 degrees inclination but are additions to the Pareto optimal solutions for 14.5 degrees inclination mission when considering the spacecraft's arrival mass at the Sun-Earth L4.
YORP-Yarkowski evolution of asteroid families: the effects of collisions
Get PDFThe depletion of objects in the central part of an asteroid family, which can be observed in the absolute magnitude vs. semimajor axis, can be explained in terms of a coupling of the YORP and Yarkovsky effects (Paolicchi and Knezevic, Icarus, 2016). In particular, it can be ascribed to the obliquity evolution caused by YORP and on how it influeces the Yarkovsky drift.With this work we intend to improve the modeling of YORP-Yarkovsky evolution of asteroid families exploiting a model which tracks the evolution of the spin vector of small asteroids, including also the effects of collisions on the YORP induced obliquity evolution. This allows a better modeling of the asteroid spin evolution.In these preliminary steps, we will first consider a few model families simulating their time evolution in the magnitude vs. semimajor axis plots. The obtained results will be then compared with observed families to determine and tune the intensity of the effect
Orbit design and control of planetary satellite orbiters in the Hill 3 -body problem.
No full textThe exploration of planetary satellites by robotic spacecraft is currently of strong scientific interest. However, sending a spacecraft to a planetary satellite can be challenging due to strong perturbations from the central planet. The primary goal of this dissertation is to identify and utilize the main dynamical features of the system in the orbit design process. The system is modeled using a modified form of Hill's 3-body problem, where the effect of the planetary satellite's gravity field is included in the low-altitude analysis. A thorough study of the dynamics of the system is performed by applying averaging theory to reduce the complexity and degrees of freedom of the system. The reduced system has one degree of freedom (DOF) and has equilibrium solutions called frozen orbits. These frozen orbits are first used as targets for transfers from capture trajectories in 'safe zones'. The 'safe zones' in phase space are numerically determined; they contain trajectories that enter the Hill region and allow an uncontrolled spacecraft to remain in orbit without impact or escape for specified time periods. Transfers from safe trajectories to frozen orbits are identified and criteria on their costs evaluated. Unstable low-altitude, near-polar frozen orbits are the basis for the design of long lifetime science orbits. The stable and unstable manifolds of these frozen orbits in the 1-DOF system are investigated and the desired path for long lifetime orbits is identified. An algorithm is developed to systematically compute initial conditions in the full system such that the orbits follow the desired path and have sufficiently long lifetimes to be practical as science orbits about planetary satellites. The analysis of the control of a planetary satellite orbiter begins with the evaluation of the effect of orbit uncertainty on the science orbits and the identification of criteria to ensure that the orbits have the desired behavior. Then, two control schemes are developed: (a) given the terminal conditions of a science orbit, redesign a new science orbit and execute a low-cost transfer to it, (b) return the spacecraft to its nominal trajectory via a two-sequence set of maneuvers.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126542/2/3253387.pd
Orbital motion in uniformly rotating second degree and order gravity fields.
No full textThis dissertation studies the orbital motion of a spacecraft about a rotating second degree and order gravity field, with its main application to orbital motion about uniformly rotating, irregular-shape asteroids. Such dynamical systems are non-integrable in general. Our goal is to understand how the orbital dynamics change as a function of the central body's rotation rate and mass distribution. To carry out this analysis we use three different approaches: averaging, resonance analysis, and periodic orbit computation. By using these analyses, we can better understand the character of a spacecraft's motion around an asteroid, which is much different from spacecraft motion around the Earth or other planets in the Solar system. Specifically, the main contributions of this dissertation are as follows. First a definition for size-shape stability of orbital motion is proposed and two facts are presented, which are related to the orbital stability of spacecraft motion in the rotating second degree and order gravity field. Second, the secular motions of a spacecraft are studied for three cases: when the central body does not rotate, rotates slowly, and rotates rapidly. The averaged Lagrange equations are derived and analyzed for these cases. Third, the short-period motions related to resonance are analyzed using the elliptic expansions of semi-major axis and eccentricity, and averaging near a resonance between the asteroid rotational and orbital motion. Fourth, periodic orbits are studied, including search methods, existence and stability analyses; five basic families of periodic orbits are found. Finally, a summary of the results in this dissertation is given, and their relations to our size-shape stability definition are discussed.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132033/2/3057964.pd
Solar sails: Modeling, estimation, and trajectory control.
No full textThere has been great interest in developing solar sail technology and missions by several international space agencies in recent years. However, at present there is no consensus on how one can mathematically model forces and moments acting on a solar sail. Traditional analytical models and finite element methods are not feasible for integration into a precise navigation system. This dissertation takes a step toward resolving this issue by developing tools and concepts that can be integrated into a precise solar sail navigation system. These steps are the derivation of a generalized sail model, a linear estimation method for estimating and predicting forces and moments acting on a solar sail, and a new trajectory control methodology for tracking a nominal trajectory when the sail performance exceeds the nominal design performance. The main contributions of this dissertation follow. First, the generalized sail model (GSM) is defined to analytically describe the forces and moments acting on a solar sail of arbitrary shape. The GSM is derived by performing an integration, of all the differential forces and moments acting on the sail, over the sail surface. Next, the GSM is applied to several examples to illustrate the use of the GSM's analytic equations. These examples allow comparisons of forces and moments generated by different solar sails, the computation of force derivatives, and the application of the model to orbital mechanics problems. Since it is difficult to model the sail geometry based on ground measurements; errors in the sail model are expected once the sail is deployed in space. Due to this difficulty; a least-squares estimation method for the force and moment coefficients of the GSM is derived. For realistic implementation of a sail trajectory, the deployed sail must have an excess thrust capacity. We develop and implement a control methodology for flying a nominal mission profile with such an excess capacity. Control laws for maintaining a flat, ideal solar sail orbiting an equilibrium point of the circular restricted three-body problem and tracking neighboring halo orbits are, provided. The control laws are tested under several conditions including solar sail surface degradation.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126275/2/3238071.pd
The Hamilton -Jacobi theory for solving optimal feedback control problems with general boundary conditions.
No full textThis dissertation presents a general methodology for solving the optimal feedback control problem in the context of Hamiltonian system theory. It is first formulated as a two point boundary value problem for a standard Hamiltonian system, and the associated phase flow is viewed as a canonical transformation. Then relying on the Hamilton-Jacobi theory, we employ generating functions to develop a unified methodology for solving a variety of optimal feedback control formulations with general types of boundary conditions. The major accomplishment is to establish a theoretical connection between the optimal cost function and a special kind of generating function. Guided by this recognition, we are ultimately led to a new flexible representation of the optimal feedback control law for a given system, which is adjustable to various types of boundary conditions by algebraic conversions and partial differentiations. This adaptive property provides a substantial advantage over the classical dynamic programming method in the sense that we do not need to solve the Hamilton-Jacobi-Bellman equation repetitively for varying types of boundary conditions. Furthermore for a special type of boundary condition, it also enables us to work around an inherent singularity of the Hamilton-Jacobi-Bellman equation by a special algebraic transformation. Taking full advantage of these theoretical insights, we develop a systematic algorithm for solving a class of optimal feedback control problems represented by smooth analytic Hamiltonians, and apply it to problems with different characteristics. Then, broadening the practical utility of generating functions for problems where the relevant Hamiltonian is non-smooth, we construct a pair of Cauchy problems from the associated Hamilton-Jacobi equations. This alternative formulation is justified by solving problems with control constraints which usually feature non-smoothness in the control logic. The main result of this research establishes that the optimal feedback control problem can be solved by the generating functions of the canonical solution flow corresponding to the necessary conditions. This result demonstrates the power of analyzing the optimal feedback control problem within the comprehensive field of classical Hamiltonian system theory.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125730/2/3208529.pd
Close proximity spacecraft maneuvers near irregularly shaped small bodies: Hovering, translation, and descent.
No full textRecently there has been significant interest in sending spacecraft to small-bodies in our solar system, such as asteroids, comets, and small planetary satellites, for the purpose of scientific study. It is believed that the composition of these bodies, unchanged for billions of years, can aid in understanding the formative period of our solar system. However, missions to small-bodies are difficult from a dynamical standpoint, complicated by the irregular shape and gravitational potential of the small-body, strong perturbations from solar radiation pressure and third body gravity, and significant uncertainty in the small-body parameters. This dissertation studies the spacecraft maneuvers required to enable a sampling mission in this unique dynamical environment, including station-keeping (hovering), translation, and descent. The bulk of this work studies hovering maneuvers, where equilibrium is created at an arbitrary position by using thrusters to null the nominal spacecraft acceleration. Contributions include a numerical study of previous results on the stability of hovering, a definition of the zero-velocity surface that exists in the vicinity of hovering spacecraft (for time-invariant dynamics), and a dead-band hovering controller design that ensures the trajectory is bounded within a prescribed region. It is found that bounded hovering near the surface of a small-body can often be achieved using dead-band control on only one direction of motion; altitude measurements alone are often sufficient to implement this control. A constant thrust strategy for translation and descent maneuvers appropriate for autonomous implementation is also presented and shown to accurately complete maneuvers in the vicinity of the initial position. Sensitivity analysis studies the effects of parameter uncertainty on these maneuvers. The theory presented within is supported throughout with numerical analysis (software tools are described within) and test cases using models of real small-bodies.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126101/2/3237910.pd
Dynamics in the Hill problem with applications to spacecraft maneuvers.
No full textThe Hill problem models the motion of two gravitationally interacting small masses perturbed by a large body. It covers several astrodynamical systems of interest, one of which is a spacecraft orbiting a planetary satellite (or planet) and perturbed by a Giant planet (or Sun). While previous studies mainly considered a limited set of initial conditions, this dissertation investigates a larger class of motions for the Hill problem by using the notion of periapsis Poincare maps. By reduction of the dynamics of the Hill problem to a sequence of close approaches to the primary, we can partition the phase space into periapsis or apoapsis exclusive regions and locate the regions of quasi-circular motion. First order estimates of these maps have been derived showing that the dynamics strongly depend on the orientation of the orbits with respect to the disturbing body and indicating how they can be used to reduce the cost of orbital transfer maneuvers. As a first application, a new class of plane change maneuvers has been derived. These transfers resemble classical bi-elliptic transfers with the apoapsis maneuver suppressed by the use of the third body forces. These transfers are shown to be preferable to classical approaches over a large range of initial conditions, realizing 70% fuel savings in the case of +/-180° plane changes. As a second application, escape and capture trajectories have been investigated, showing the possibility of low energy direct escape from the surface of certain planetary satellites of the solar system, as well as constraints on low energy capture maneuvers. The problem of one impulse, direct escape and capture maneuvers has also been investigated, yielding an optimal result in the planar case and a practical approach otherwise. Fuel savings on the order of 17% in the case of a Europa orbiter have been obtained. These results should be useful for mission design and planning in the case of orbital environments that can be modeled using the Hill problem.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123971/2/3106179.pd
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