Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

Global trajectory optimisation: can we prune the solution space when considering deep space manoeuvres?

This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvres (DSM). The study was performed by a joint team of scientists from the University of Reading and the University of Glasgow.

Earth-Venus trajectories.

Includes bibliographies.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

POCS-based reconstruction of multiplexed sensitivity encoded MRI (POCSMUSE): A general algorithm for reducing motion-related artifacts.

PURPOSE: A projection onto convex sets reconstruction of multiplexed sensitivity encoded MRI (POCSMUSE) is developed to reduce motion-related artifacts, including respiration artifacts in abdominal imaging and aliasing artifacts in interleaved diffusion-weighted imaging. THEORY: Images with reduced artifacts are reconstructed with an iterative projection onto convex sets (POCS) procedure that uses the coil sensitivity profile as a constraint. This method can be applied to data obtained with different pulse sequences and k-space trajectories. In addition, various constraints can be incorporated to stabilize the reconstruction of ill-conditioned matrices. METHODS: The POCSMUSE technique was applied to abdominal fast spin-echo imaging data, and its effectiveness in respiratory-triggered scans was evaluated. The POCSMUSE method was also applied to reduce aliasing artifacts due to shot-to-shot phase variations in interleaved diffusion-weighted imaging data corresponding to different k-space trajectories and matrix condition numbers. RESULTS: Experimental results show that the POCSMUSE technique can effectively reduce motion-related artifacts in data obtained with different pulse sequences, k-space trajectories and contrasts. CONCLUSION: POCSMUSE is a general post-processing algorithm for reduction of motion-related artifacts. It is compatible with different pulse sequences, and can also be used to further reduce residual artifacts in data produced by existing motion artifact reduction methods.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.

Sub-Optimal Orbital Maneuvers for Artificial Satellites

The determination of a specific orbit and the procedure to calculate orbital maneuvers of artificial satellites are problems of extreme importance in the study of orbital mechanics. Therefore, the transferring problem of a spaceship from one orbit to another, and the attention due to this subject has in increased during the last years. Many applications can be found in several space activities, for example, to put a satellite in a geostationary orbit, to change the position of a spaceship, to maintain a specific satellite's orbit, in the design of an interplanetary mission, and others. The Brazilian Satellite SCD-1 (Data Collecting Satellite) will be used as example in this paper. It is the first satellite developed entirely in Brazil, and it remains in operation to this date. SCD-1 was designed, developed, built, and tested by Brazilian scientists, engineers, and technicians working at INPE (National Institute for Space Research, and in Brazilian Industries. During the lifetime, it might be necessary do some complementary maneuvers, being this one either an orbital transferring, or just to make periodical corrections. The purpose of transferring problem is to change the position, velocity and the satellite's mass to a new pre determined state. This transfer can be totally linked (in the case of "Rendezvous") or partially free (free time, free final velocity, etc). In the global case, the direction, the orientation and the magnitude of the thrust to be applied must be chosen, respecting the equipment's limit. In order to make this transferring, either sub-optimal or optimal maneuvers may be used. In the present study, only the sub-optimal will be shown. Hence, this method will simplify the direction of thrust application, to allow a fast calculation that may be used in real time, with a very fast processing. The thrust application direction to be applied will be assumed small and constant, and the purpose of this paper is to find the time interval that the thrust is applied. This paper is basically divided into three parts: during the first one the sub-optimal maneuver is explained and detailed, the second presents the Satellite SCD-1, and finally the last part shows the results using the sub-optimal maneuver applied to the Brazilian Satellite.

Event-related potential P300 microstate topography during visual one- and two-dimensional tasks in chronic schizophrenics

Reports on left-lateralized abnormalities of component P300 of event-related brain potentials (ERP) in schizophrenics typically did not vary task difficulties. We collected 16-channel ERP in 13 chronic, medicated schizophrenics (25±4.9 years) and 13 matched controls in a visual P300 paradigm with targets defined by one or two stimulus dimensions (C1: color; C2: color and tilt); subjects key-pressed to targets. The mean target-ERP map landscapes were assessed numerically by the locations of the positive and negative map-area centroids. The centroids' time-space trajectories were searched for the P300 microstate landscape defined by the positive centroid posterior of the negative centroid. At P300 microstate centre latencies in C1, patients' maps tended to a right shift of the positive centroid (p<0.10); in C2 the anterior centroid was more posterior (p<0.07) and the posterior (positive) centroid more anterior (p<0.03), but without leftright difference. Duration of P300 microstate in C2 was shorter in patients (232 vs 347 ms;p<0.03) and the latency of maximal strength of P300 microstate increased significantly in patients (C1: 459 vs 376 ms; C2: 585 vs 525 ms). In summary only the one-dimensional task C1 supported left-sided abnormalities; the two-dimensional task C2 produced abnormal P300 microstate map landscapes in schizophrenics, but no abnormal lateralization. Thus, information processing involved clearly aberrant neural populations in schizophrenics, different when processing one and two stimulus dimensions. The lack of lateralization in the two-dimensional task supported the view that left-temporal abnormality in schizophrenics is only one of several task-dependent aberrations.

Analysis of missile trajectory measurement accuracy for data processing

"Contract no. AF 30(602)-2138, Project 5554, Task 55102."

Dispersal of reactor core materials by reentry processes; preliminary analysis,

"Project no. AA-1506-W. Contract no. P.O. no.51-1136. Sub order no. 7, Sandia Corporation."

Generation of parabolic trajectories for current error space phasor similar to an SVPWM controller for control of switching frequency variation in current hysteresis PWM controlled IM drives

Switching frequency variation over a fundamental period is a major problem associated with hysteresis controller based VSI fed IM drives. This paper describes a novel concept of generating parabolic trajectories for current error space phasor for controlling the switching frequency variation in the hysteresis controller based two-level inverter fed IM drives. A generalized algorithm is developed to determine unique set of parabolic trajectories for different speeds of operation for any given IM load. Proposed hysteresis controller provides the switching frequency spectrum of inverter output voltage, similar to that of the constant switching frequency VC-SVPWM based IM drive. The scheme is extensively simulated and experimentally verified on a 3.7 kW IM drive for steady state and transient performance.

Trajectories of charged particles in the static Ernst space-time

The authors study the trajectories of charged particles in Ernst's space-time representing a static black hole immersed in a magnetic field. They find bound orbits always exist for realistic magnetic field strengths. A similar investigation is carried out for the case of Melvin's magnetic universe and for a corresponding test field superposed on a flat space-time.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.