Determination Of Optimal Trajectories Research Articles

Bucket Trajectory Optimization under the Automatic Scooping of LHD

We propose an optimal planning scheme of the bucket trajectory in the LHD (Load-Haul-Dump) automatic shoveling system to improve the effectiveness of the scooping operation. The research involves simulation of four typical shoveling methods, optimization of the scooping trajectory, establishment of a reaction force model in the scooping process and determination of optimal trajectory. Firstly, we compared the one-step, step-by-step, excavation and coordinated shoveling method by the Engineering Discrete Element Method (EDEM) simulation. The coordinated shoveling method becomes the best choice on account of its best comprehensive performance among the four methods. Based on the coordinated shoveling method, the shape of the optimized trajectory can be roughly determined. Then, we established a model of bucket force during the shoveling process by applying Coulomb’s passive earth pressure theory for the purpose of calculating energy consumption. The trajectory is finally determined through optimizing the minimum energy consumption in theory. The theoretical value is verified by the EDEM simulation.

Usefulness of Ultrasound-Guided Microsurgery in Cavernous Angioma Removal

Primary elements of surgical treatment of cavernous angiomas (CAs) are precise lesion identification and optimal trajectory determination. Navigation techniques allow for better results compared to microsurgery alone. In this study, we examined the benefits of intraoperative ultrasound (IOUS) use as an adjunct to standard localization systems. We retrospectively analyzed 59 CAs, comparing outcomes in 2 groups of patients: 34 who underwent frame-based or frameless navigation-assisted microsurgery (no-IOUS group) and 25 who underwent IOUS-guided microsurgery associated with these techniques (IOUS group). The use of IOUS did not significantly increase the surgery time (mean, 172 ± 1.7 minutes in the IOUS group and 192.6 ± 11.5 in no-IOUS group; P= 0.08). In all 25 patients in the IOUS group, IOUS allowed for ready identification of CA as a hyperechoic mass. At the last follow-up (mean, 41.7 ± 3.5 months postsurgery), 95.2% of the IOUS group and 80.8% of the no-IOUS group had a modified Rankin Scale score of 0-1 and an Extended Glasgow Outcome Scale score of 7-8 (P= 0.2), with 100% and 64%, respectively, included in Engel outcome scale class IA (P= 0.006). Complete removal, as confirmed on postoperative magnetic resonance imaging, was achieved in all patients in the IOUS group and in almost all (97.1%; P=0.4) patients in the no-IOUS group. IOUS is a valid tool for the intraoperative identification of CAs. Implementation of standard localization methods with IOUS guidance was associated with complete resection in all cases, without increasing surgical time. Compared with microsurgery without IOUS guidance, long-term functional outcomes showed better trends, and the epilepsy-free rate was significantly higher.

TIME ALLOCATION, THE DYNAMICS OF INTERACTION, AND TECHNOLOGY ADOPTION

Inspired by recent literature that approaches the dissemination of knowledge from a social interaction perspective, the article explores the dynamics of a prototypical optimal control growth problem structured upon the following features: (i) the model economy is populated by a large number of rational agents; (ii) each agent allocates time, optimally, among production and social interaction; (iii) knowledge spreads through the contact with others; (iv) the propagation of ideas follows two steps—in a first stage, interaction promotes the acquisition of theoretical knowledge and, in a second stage, it works as a catalyst for the successful implementation of the theory to practical productive uses; (v) interaction contributes not only to the diffusion of a given state of technical knowledge—it fosters, as well, the growth of ideas and techniques. The model allows for the endogenous determination of optimal trajectories concerning the allocation of time and the intensity of interaction; moreover, a long-term endogenous growth rate for the economy is derived, with optimal growth being essentially driven by the state of techniques and by the forces that shape the human interaction process.

ІМІТАЦІЙНО-КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ БІОМЕХАНІЧНИХ СИСТЕМ ДЛЯ ДОСЛІДЖЕННЯ ФУНКЦІОНАЛЬНИХ МОЖЛИВОСТЕЙ АПАРАТІВ ЗОВНІШНЬОЇ ФІКСАЦІЇ

Представлений алгоритм дій при створенні тривимірних комп‘ютерних динамічних моделей для дослідження репозиційних можливостей апаратів зовнішньої фіксації (АЗФ). З використанням запропонованого алгоритму в програмі Autodesk Inventor 11 створені три моделі біомеханічних систем: I – «кістка – компонування апарата Ілізарова для корекції кутових зміщень»; IІ – «кістка – компонування апарата Ілізарова для корекції багатокомпонентних зміщень»; ІII – «кістка – апарат для корекції деформації кісток і суглобів».
 Встановлено, що тривимірні комп’ютерні моделі систем для черезкісткового остеосинтезу (ЧО) найбільш доцільно будувати з застосуванням способу шаблонів, що дозволяє здійснювати корекцію геометричних параметрів деталей в зборці моделі та забезпечує можливість швидкої зміни компонування АЗФ.
 Застосування розроблених тривимірних динамічних моделей забезпечує можливість моделювання репозиції кісткових фрагментів за різних типів переломів та будь-якої площини зламу; моделювання корекції деформації кісток; визначення оптимальної траєкторії переміщення фрагментів; вибору оптимального типу репозиційних елементів та компонування АЗФ.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

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Analytical Techniques for the Optimisation of Rocket Trajectories

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

Applications of dynamic programming to space guidance, satellites and trajectories

Abstract : The feasibility of space travel and man-made satellites has triggered a rash of interest in the determination of optimal trajectories and generally in guidance and control processes. These problems, for so long of purely mathematical and astronomical concern, have now become part of the engineering domain. The result is that there is a great demand for feasible numerical solutions of the associated analytic problems. Many of these are classically of great difficulty. As a result of the intensive study of these questions, it is now well appreciated that the classical techniques of the calculus of variations are inoperative unless the problem is rather carefully selected. The applicability is shown of a new mathematical technique, based on the theory of dynamic programming, to the computational solution of trajectory problems. Many problems, seemingly inaccessible to the conventional methods of the calculus of variations, have already been resolved.