Extension of the proximity-quotient control law for low-thrust propulsion

In this paper, the proximity quotient control law, first developed by Petropoulos, is extended to account for both third body effects and solar radiation pressure based on the mission requirements for a hypothetical NEO deflection mission to the asteroid Apophis using a solar sublimation deflection technique. The perturbing effect of solar radiation pressure becomes relevant when dealing with large optics in space. Equations for the disturbing acceleration are derived for the perturbations, then analytically incorporated into the equations determining the rate-of-change in time of the orbital elements, and tested using a Earth-asteroid transfer. Another specific variant of the control law is developed for the orbital maintenance of the spacecraft formation in the vicinity of the NEO

Design of optimal spacecraft-asteroid formations through a hybrid global optimization approach

Purpose – The purpose of this paper is to present a methodology and experimental results on using global optimization algorithms to determine the optimal orbit, based on the mission requirements, for a set of spacecraft flying in formation with an asteroid. Design/methodology/approach – A behavioral-based hybrid global optimization approach is used to first characterize the solution space and find families of orbits that are a fixed distance away from the asteroid. The same optimization approach is then used to find the set of Pareto optimal solutions that minimize both the distance from the asteroid and the variation of the Sun-spacecraft-asteroid angle. Two sample missions to asteroids, representing constrained single and multi-objective problems, were selected to test the applicability of using an in-house hybrid stochastic-deterministic global optimization algorithm (Evolutionary Programming and Interval Computation (EPIC)) to find optimal orbits for a spacecraft flying in formation with an orbit. The Near Earth Asteroid 99942 Apophis (2004 MN4) is used as the case study due to a fly-by of Earth in 2029 leading to two potential impacts in 2036 or 2037. Two black-box optimization problems that model the orbital dynamics of the spacecraft were developed. Findings – It was found for the two missions under test, that the optimized orbits fall into various distinct families, which can be used to design multi-spacecraft missions with similar orbital characteristics. Research limitations/implications – The global optimization software, EPIC, was very effective at finding sets of orbits which met the required mission objectives and constraints for a formation of spacecraft in proximity of an asteroid. The hybridization of the stochastic search with the deterministic domain decomposition can greatly improve the intrinsic stochastic nature of the multi-agent search process without the excessive computational cost of a full grid search. The stability of the discovered families of formation orbit is subject to the gravity perturbation of the asteroid and to the solar pressure. Their control, therefore, requires further investigation. Originality/value – This paper contributes to both the field of space mission design for close-proximity orbits and to the field of global optimization. In particular, suggests a common formulation for single and multi-objective problems and a robust and effective hybrid search method based on behaviorism. This approach provides an effective way to identify families of optimal formation orbits

Relating Catlin and D'Angelo qq-types

We clarify the relationship between the two most standard measurements of the order of contact of q-dimensional complex varieties with a real hypersurface, the Catlin and D'Angelo $q$-types, by showing that the former equals the generic value of the normalized order of contact measured along curves whose infimum is by definition the D'Angelo $q$-type.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1302.229

On the Relationship between D'Angelo q-type and Catlin q-type

We establish inequalities relating two measurements of the order of contact of q-dimensional complex varieties with a real hypersurface.Comment: 18 pages; accepted at the Journal of Geometric Analysis; see arXiv:1102.0356 for the origin of this investigatio

Orbital debris removal with solar concentrators

In 1993 solar concentrators were first proposed to deflect asteroids away from a collision course with the Earth. The original concept was expanded by the authors, and proved to be effective and technologically feasible. One way to deflect the asteroid is to produce a slow decay of its orbit by inducing a thrust via concentrated solar light. Two mechanisms have been investigated: the sublimation of the surface of the asteroid to generate a jet of gas and the induced thrust by light pressure and enhanced Yarkovsky effect. If the concentrators are reduced in size, a similar concept can be adopted to remove orbital debris and inert satellites. In this paper, we present an orbital debris removal system based on concentrated solar light. We will show how enhanced solar pressure, generated by a formation of solar concentrators, can be used to accelerate the decay of small inert objects orbiting the Earth. A set of modified proximal motion equations is proposed to describe the relative dynamics of the solar concentrators with respect to the target piece of debris. The paper will provide an analysis of the cost of the optimal control of the concentrators during the deflection of the debris and a system engineering analysis. In particular, we will show that the concentrator acts as an active solar sail while not deflecting, and as a hybrid solar sail (i.e. the orbit is maintained with an auxiliary low-thrust engine) while deflecting the debris. The results will show that objects with even a small area-to-mass ratio (down to 0.01) can be brought from an 800 km to a 200 km altitude orbit in few hundred days of constant operation. The paper will discuss also the possibility to vaporize some small size targets with high power solar pumped laser

On the detection of nearly optimal solutions in the context of single-objective space mission design problems

When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions – in the design space – but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of e–approximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design

Approximated Computation of Belief Functions for Robust Design Optimization

This paper presents some ideas to reduce the computational cost of evidence-based robust design optimization. Evidence Theory crystallizes both the aleatory and epistemic uncertainties in the design parameters, providing two quantitative measures, Belief and Plausibility, of the credibility of the computed value of the design budgets. The paper proposes some techniques to compute an approximation of Belief and Plausibility at a cost that is a fraction of the one required for an accurate calculation of the two values. Some simple test cases will show how the proposed techniques scale with the dimension of the problem. Finally a simple example of spacecraft system design is presented.Comment: AIAA-2012-1932 14th AIAA Non-Deterministic Approaches Conference. 23-26 April 2012 Sheraton Waikiki, Honolulu, Hawai

Membrane resonance enables stable and robust gamma oscillations

Neuronal mechanisms underlying beta/gamma oscillations (20-80 Hz) are not completely understood. Here, we show that in vivo beta/gamma oscillations in the cat visual cortex sometimes exhibit remarkably stable frequency even when inputs fluctuate dramatically. Enhanced frequency stability is associated with stronger oscillations measured in individual units and larger power in the local field potential. Simulations of neuronal circuitry demonstrate that membrane properties of inhibitory interneurons strongly determine the characteristics of emergent oscillations. Exploration of networks containing either integrator or resonator inhibitory interneurons revealed that: (i) Resonance, as opposed to integration, promotes robust oscillations with large power and stable frequency via a mechanism called RING (Resonance INduced Gamma); resonance favors synchronization by reducing phase delays between interneurons and imposes bounds on oscillation cycle duration; (ii) Stability of frequency and robustness of the oscillation also depend on the relative timing of excitatory and inhibitory volleys within the oscillation cycle; (iii) RING can reproduce characteristics of both Pyramidal INterneuron Gamma (PING) and INterneuron Gamma (ING), transcending such classifications; (iv) In RING, robust gamma oscillations are promoted by slow but are impaired by fast inputs. Results suggest that interneuronal membrane resonance can be an important ingredient for generation of robust gamma oscillations having stable frequency

Custom EMAT Instrumentation: Correlation Receiver and Flaw Detector

New, custom instrumentation is presented which is designed to complement and exploit the unique properties of EMAT\u27s. A two channel correlation receiver is described which allows simultaneous detection of the in-phase and quadrature components of an ultrasonic signal with the optimum noise figure and improved interference rejection. In addition, a prototype, fully self-contained EMAT flaw detector is presented. This is a surface wave device for handheld use and incorporates such features as battery operations, correlation detection, search and inspect modes, and digital readout of flaw position and reflected signal amplitude

New heuristics for multi-objective worst-case optimization in evidence-based robust design

This paper presents a non-nested algorithm for the solution of multi-objective min-max problems (MOMMP) in worst-case optimization. The algorithm has been devised for evidence-based robust optimization, where the lack of a defined probabilistic behaviour of the uncertain parameters makes it impossible to apply sample-based techniques and forces the designer to identify the worst case over the subdomains of the uncertainty space. In evidence theory, the robustness of the solutions is measured in terms of the Belief in the realization of the value of the design budgets, which acts as a lower bound to the unknown cumulative distribution function of the budget. Thus a means of finding robust solutions in preliminary design consists on applying the minimax model, where the worst-case budget over the uncertainty space is optimized over the control space. The paper proposes a novel heuristic to solve MOMMP and demonstrates its capability to approximate the worst-case Pareto front at a very reduced cost with respect to approaches based on nested optimization