154 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
Analysis, Design, and Optimization of Robust Trajectories in Cislunar Environment for Limited-Capability Spacecraft
Nowadays, the space exploration is going in the direction of exploiting small platforms to get high scientific return at significantly lower costs. However, miniaturized spacecraft pose different challenges both from the technological and mission analysis point of view. While the former is in constant evolution due to the manufacturers, the latter is an open point, since it is still based on a traditional approach, not able to cope with the new platforms' peculiarities. In this work, a revised preliminary mission analysis approach, merging the nominal trajectory optimization with a complete navigation assessment, is formulated in a general form and three main blocks composing it are identified. Then, the integrated approach is specialized for a cislunar test case scenario, represented by the transfer trajectory from a low lunar orbit to an halo orbit of the CubeSat LUMIO, and each block is modeled with mathematical means. Eventually, optimal solutions, minimizing the total costs, are sought, showing the benefits of an integrated approach
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
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
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
Thrust continuation of time-optimal orbital transfers with soft terminal conditions
Time-optimal orbital transfers with soft terminal conditions are studied in this work. First, a two-layer thrust continuation method is devised. The unfavorable thrust continuation path is handled by switching between different solution curves. Second, the proposed method is applied to solving time-optimal transfers under two- or three-body dynamics with Cartesian coordinates to verify its effectiveness. The near conservation of the product between the time of flight and the thrust level is observed for general orbital transfers. A linear variation of this quantity with eccentricity is also illustrated when the difference in eccentricity between the initial and terminal orbits is large enough
- …