1,721,332 research outputs found
Fast Numerical Approximation of Invariant Manifolds in the Circular Restricted Three-Body Problem
Full text linkIn this paper a two-step approach to approximate the invariant manifolds in the circular restricted three-body problem is presented. The method consists in a two-dimensional interpolation, followed by a nonlinear correction. A two-dimensional cubic convolution interpolation is implemented to reduce the computational effort. A nonlinear correction is applied to enforce the energy level of the approximated state. The manifolds are parameterized by using two scalars. Results show efficiency and moderate accuracy. The present method fits the needs of trajectory optimization algorithms, where a great number of manifold insertion points has to be evaluated online
Earth-Mars Transfers with Ballistic Capture
Full text linkWe construct a new type of transfer from the Earth to Mars, which ends in ballistic capture. This results in substantial savings in capture (Formula presented.) from that of a classical Hohmann transfer under certain assumptions as well as an alternate way for spacecraft to transfer to Mars. 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 using stable sets, which are sets of initial conditions whose orbits satisfy a definition of orbital stability. This transfer type may be of interest for Mars missions because of low capture (Formula presented.), flexibility of launch period from the Earth, moderate flight time, and the benign nature of the capture process
The EXTREMA Thruster-In-The-Loop Experiment: a facility for hands-on testing of spacecraft guidance algorithms
Full text linkThe EXTREMA THruster-In-the-Loop Experiment (ETHILE) is a facility designed for testing the effectiveness and robustness of spacecraft guidance algorithms through hardware actuation. Initially designed to simulate in an accelerated framework the actuation of interplanetary transfers with low-thrust, the system is highly configurable as it can simulate different thruster behaviours with a thruster balance equipped with a compressed air nozzle. An overview of the system and its performance is given, highlighting through a practical example its possible use for research and educational purposes
On Optimal Two-Impulse Earth-Moon Transfers in a Four-Body Model
Full text linkIn this paper two-impulse Earth-Moon transfers are treated in the restricted four-body problem with the Sun, the Earth, and the Moon as primaries. The problem is formulated with mathematical means and solved through direct transcription and multiple shooting strategy. Thousands of solutions are found, which make it possible to frame known cases as special points of a more general picture. Families of solutions are defined and characterized, and their features are discussed. The methodology described in this paper is useful to perform trade-off analyses, where many solutions have to be produced and assessed
Trade-Off Between Cost and Time in Lunar Transfers: a Quantitative Analysis
No full textIn this paper, two-impulse Earth-Moon transfers are studied in a four-body model. For given departure, arrival orbits, the focus is on reconstructing the total set of possible solutions within a specified maximum transfer time. This is done by formulating the transfer as a nonlinear programming problem, and by solving it with direct transcription and multiple shooting. The outcome is analyzed in a cost vs. transfer time plane, where orbits showing their best balance are studied. With this approach, Hohmann, interior, and exterior transfers, as well as the existing literature, can be viewed as special points of a more general picture, where new solutions emerge
Advances in Ballistic Capture Orbits Computation with Applications
No full textIn this paper, recent developments on the computation of ballistic capture orbits are discussed, together with a presentation on their applications to practical cases. The paper focuses on the method used to derive the stable sets. These are sets of initial conditions that generate orbits satisfying a simple definition of stability, whose manipulation produces ballistic capture orbits. The way this method has evolved over the years will be illustrated, from the simple planar circular restricted three-body model to a three-dimensional high-fidelity context. Applications involve interplanetary trajectory design, lunar missions, and asteroid retrieval scenarios
Aeroballistic Capture at Mars: Modeling, Optimization, and Assessment
Full text linkIn this paper a novel paradigm for Mars missions is modeled, optimized, and assessed. This concept consists of a maneuver that combines aerocapture and ballistic capture upon Mars arrival, labeled aeroballistic capture. The idea is reducing the overall cost and mass by exploiting the interaction with the planet atmosphere as well as the complex sun–Mars gravitational field. The aeroballistic capture paradigm is first formulated. This is then split into a number of phases, each of them is modeled with mathematical means. The problem is then stated by using optimal control theory, and optimal solutions are sought. These are specialized to four application cases. An assessment of aeroballistic capture shows their superiority compared to classical injection maneuvers when medium-to-high final orbits about Mars are targeted
Robust Bang-Off-Bang Low-Thrust Guidance Using Model Predictive Static Programming
Full text linkModel Predictive Static Programming (MPSP) has been always used under the assumption of continuous or impulsive control, but never in low-thrust transfers featuring bang-off-bang control. Following the observation that the sensitivity matrix (SM) is discontinuous across the switching time, this work introduces a two-loop MPSP guidance scheme using fuel-optimal trajectories as nominal solutions. In our method, the equations of motion are augmented by the mass costate equation, while the velocity costate is the MPSP control, expressed by a weighted sum of Fourier basis functions. The SM is computed at the switching time by using calculus of variations. Both the MPSP control and the initial mass costate are updated in an inner loop using Newton's method, and continuation is employed in an outer loop to face large perturbations. A sample interplanetary CubeSat mission to an asteroid is used as study case to illustrate the effectiveness and robustness of the method developed
A TFC-based homotopy continuation algorithm with application to dynamics and control problems
Full text linkA method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge, due to manually, inherently selected homotopy paths. This work introduces a homotopy method based on the Theory of Functional Connections (TFC). The TFC-based method implicitly defines infinite homotopy paths, from which the most promising ones are selected. A two-layer continuation algorithm is devised, where the first layer tracks the homotopy path by monotonously varying the continuation parameter, while the second layer recovers possible failures resorting to a TFC representation of the homotopy function. Compared to pseudo-arclength methods, the proposed TFC-based method retains the simplicity of direct continuation while allowing a flexible path switching. Numerical simulations illustrate the effectiveness of the presented method
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