141 research outputs found
Geometry of Weak Stability Boundaries
The notion of a weak stability boundary has been successfully used to design
low energy trajectories from the Earth to the Moon. The structure of this
boundary has been investigated in a number of studies, where partial results
have been obtained. We propose a generalization of the weak stability boundary.
We prove analytically that, in the context of the planar circular restricted
three-body problem, under certain conditions on the mass ratio of the primaries
and on the energy, the weak stability boundary about the heavier primary
coincides with a branch of the global stable manifold of the Lyapunov orbit
about one of the Lagrange points
Earth--Mars Transfers with Ballistic Capture
We construct a new type of transfer from the Earth to Mars, which ends in
ballistic capture. This results in a substantial savings in capture
from that of a classical Hohmann transfer under certain conditions. This is
accomplished by first becoming captured at Mars, very distant from the planet,
and then from there, following a ballistic capture transfer to a desired
altitude within a ballistic capture set. This is achieved by manipulating the
stable sets, or sets of initial conditions whose orbits satisfy a simple
definition of stability. This transfer type may be of interest for Mars
missions because of lower capture , moderate flight time, and
flexibility of launch period from the Earth
Robust Bang-Off-Bang Low-Thrust Guidance Using Model Predictive Static Programming
Model Predictive Static Programming (MPSP) was always used under the
assumption of continuous control, which impedes it for applications with
bang-off-bang control directly. In this paper, MPSP is employed for the first
time as a guidance scheme for low-thrust transfers with bang-off-bang control
where the fuel-optimal trajectory is used as the nominal solution. In our
method, dynamical equations in Cartesian coordinates are augmented by the mass
costate equation, while the unconstrained velocity costate vector is used as
control variable, and is expressed as a combination of Fourier basis functions
with corresponding weights. A two-loop MPSP algorithm is designed where the
weights and the initial mass costate are updated in the inner loop and
continuation is conducted on the outer loop in case of large perturbations. The
sensitivity matrix (SM) is recursively calculated using analytical derivatives
and SM at switching points is compensated based on calculus of variations. An
sample interplanetary CubeSat mission to an asteroid is used as study case to
illustrate the effectiveness of the method developed
Analysis of ballistic capture in Sun–planet models
Analysis of ballistic capture orbits in Sun–planet systems is conducted in this paper. This mechanism utilizes purely gravitational forces, and may occur in non-Keplerian regimes. Ballistic capture orbits are generated by proper manipulation of sets of initial conditions that satisfy a simple definition of stability. Six Sun–planet systems are considered, including the inner planets, Jupiter, and Saturn. The role of planets orbital eccentricity, their true anomaly, and mass ratios is investigated. Moreover, the influence of the post-capture orbit in terms of inclination and orientation is also assessed. Analyses are performed from qualitative and quantitative perspective. The quality of capture orbits is measured by means of the stability index, whereas the capture ratio gives information on their statistical occurrence. Some underlying principles on the selection of the dynamical model, the initial true anomaly, and inclination are obtained. These provide a reference for practical cases
Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics
A method to solve nonlinear optimal control problems is proposed in
this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the
original, nonlinear problem. Each subproblem is solved by manipulating
the state transition matrix of the state-costate dynamics. Hard, soft,
and mixed boundary conditions are handled. The presented method is
a modified version of an algorithm known as "approximating sequence
of Riccati equations." Sample problems in astrodynamics are treated to
show the effectiveness of the method, whose limitations are also discussed
An Image Processing Pipeline for Autonomous Deep-Space Optical Navigation
A new era of space exploration and exploitation is fast approaching. A
multitude of spacecraft will flow in the future decades under the propulsive
momentum of the new space economy. Yet, the flourishing proliferation of
deep-space assets will make it unsustainable to pilot them from ground with
standard radiometric tracking. The adoption of autonomous navigation
alternatives is crucial to overcoming these limitations. Among these, optical
navigation is an affordable and fully ground-independent approach. Probes can
triangulate their position by observing visible beacons, e.g., planets or
asteroids, by acquiring their line-of-sight in deep space. To do so, developing
efficient and robust image processing algorithms providing information to
navigation filters is a necessary action. This paper proposes an innovative
pipeline for unresolved beacon recognition and line-of-sight extraction from
images for autonomous interplanetary navigation. The developed algorithm
exploits the k-vector method for the non-stellar object identification and
statistical likelihood to detect whether any beacon projection is visible in
the image. Statistical results show that the accuracy in detecting the planet
position projection is independent of the spacecraft position uncertainty.
Whereas, the planet detection success rate is higher than 95% when the
spacecraft position is known with a 3sigma accuracy up to 10^5 km.Comment: 26 pages, 7 figure
Qualitative study of ballistic capture at Mars via Lagrangian descriptors
Lagrangian descriptors reveal the dynamical skeleton governing transport
mechanisms of a generic flow. In doing so, they unveil geometrical structures
in the phase space that separate regions with different qualitative behavior.
This work investigates to what extent Lagrangian descriptors provide
information about non-Keplerian motion in Mars proximity, which is modeled
under the planar elliptic restricted three-body problem. We propose a novel
technique to reveal ballistic capture orbits extracting separatrices of the
phase space highlighted by Lagrangian descriptor scalar fields. The Roberts'
operator to approximate the gradient is used to detect the edges in the fields.
Results demonstrate the chaos indicator ability to distinguish sets of initial
conditions exhibiting different dynamics, including ballistic capture ones.
Separatrices are validated against reference weak stability boundary derived on
similar integration intervals. Compared to other techniques, Lagrangian
descriptors provide dynamics insight bypassing the propagation of the
variational equations.Comment: Post-print submitted to "Communications in Nonlinear Science and
Numerical Simulation". EXTREMA - Engineering Extremely Rare Events in
Astrodynamics for Deep-Space Missions in Autonomy, European Research Council
(ERC), European Union (EU), Horizon 2020. The content of this document
reflects only the author's view. ERC is not responsible for any use that may
be made of the information it contain
Application of Pulsar-Based Navigation for Deep-Space CubeSats
This paper investigates the use of pulsar-based navigation for deep-space CubeSats. A novel approach for dealing with the onboard computation of navigational solutions and timekeeping capabilities of a spacecraft in a deep-space cruise is shown, and the related implementation and numerical simulations are discussed. The pulsar’s signal detection, processing, and exploitation are simulated for navigation onboard a spacecraft, thus showing the feasibility of autonomous state estimation in deep space even for miniaturized satellites
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