Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed by Ordinary Differential Equations

The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. Treatment of small geometric uncertainty in the context of manufacturing tolerances is a well studied topic. Traditional sequential design methodologies have recently been replaced by concurrent optimal design methodologies where optimal system parameters are simultaneously determined along with optimally allocated tolerances; this allows to reduce manufacturing costs while increasing performance. However, the state of the art approaches remain limited in that they can only treat geometric related uncertainties restricted to be small in magnitude. This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems governed by ordinary differential equations. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Additionally, uncertainties are allowed to be large in magnitude and the governing constitutive relations may be highly nonlinear. In the proposed framework, uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments of the uncertain system to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that is off-set from the traditional deterministic optimal trade-off curve. The Pareto off-set is shown to be a result of the additional statistical moment information formulated in the objective and constraint relations that account for the system uncertainties. Therefore, the Pareto trade-off curve from the new framework characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost. A kinematic tolerance analysis case-study is presented first to illustrate how the proposed methodology can be applied to treat geometric tolerances. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost, accounting for the entire family of systems within the associated probability space. This case-study highlights the general nature of the new framework which is capable of optimally allocating uncertainties of multiple types and with large magnitudes in a single calculation

The Marshall Mission, 1946

The purpose of this thesis is to examine the diplomacy of the mission of General George Catlett Marshall to China in 1946. By utilizing material gleaned chiefly from United States Relations with China, with Special Reference to the Period 1944-1949, the Congressional Record, and the New York Times, a step-by-step account of the Marshall Mission is attempted. Moreover, the effort is made to see the mission in its proper setting, against the backdrop of Oriental Communism and of antique Chinese Confucian authoritarianism. Thirdly, the narrative of the mission itself is coupled with the news of developing public opinion in the United States, China, and the Soviet Union, in an endeavor to determine the relationship and impact of the public temper on the mission, or visa versa. In brief, the salient purpose is to observe the power of the democratic practice of diplomacy when it is pitted against the anti- democratic force of ideology. One fully positive correlation is yielded by the study: Marshall followed his directives to the letter. Indeed, his austere, military obedience was so straight and unwavering that the biographical chapter on him seems to have been included, in the last analysis, as a matter of scholarly convention. His directives, moreover, had written into them an element which largely pre-empted any diplomatic battle in China and made it rather one of opposing ideologies. The United States was irrevocably tied to support of Chiang Kai-shek and the Nationalist faction. Stage by stage, this persistent fact inexorably alienated the Chinese Communists from the negotiations and made then more amenable to support from, and collusion with, the Kremlin. When this potentiality was early manifested, Chiang himself became minatory, finally settling upon a policy of force when he had seen that he could obviate Marshall\u27s constraints with impunity and still count on an American sentiment that was growing more and more mono-maniacally anti-Communist in temper. The result was that Chiang went the way of reaction, suppression, and cruelty, and the Chinese population, in the words of Dean G. Acheson, “moved out from under” his despotic leadership. Chinese Communism soon took over the China mainland, felling nationalism in violent struggle which took place as if there had been no diplomatic intervention by the United States. The determining factor seems to have been in an American foreign policy, which, from 1946 through 1949, as Archibald MacLeish notes, was a “mirror image of Soviet foreign policy. It was a policy based on anti-Communist ideology, and one which thereby passed over many of the political, social, military, and exigencies of postwar China-exigencies which needed to have been taken into consideration if diplomacy was to be given a chance to function

Relationship of aging to the shelling and quality of Southern peas, Vigna sinensis

Food processors in Tennessee pack over half of the 50 million pounds of Southern peas processed in the Southeastern states each year. These peas account for almost 11 per cent of the total vegetables packed in the Southeastern states and are exceeded in volume only by green beans and tomatoes. Over two-thirds of the Southern peas are packed in the green pea stage of maturity (27). To be processed in the green pea stage, Southern peas are harvested by hand and hauled to the processor by truck. A major problem at this stage of handling, however, is that the peas that have been picked only a few hours do not shell easily enough to permit mechanical shelling. Processors have found that mechanical hullers can be used if the peas are allowed to age for 24 or more hours. Aging is easily accomplished by either leaving the peas on trucks or loading them onto large wagons furnished by the processor. During the aging period, heat from respiration of the peas and bacterial action causes the product temperature to increase several degrees above the ambient temperature (24). Due to the excessively high temperatures and prolonged storage period usually encountered during this aging period, there is a high degree of probability that the quality of the peas is affected consider-ably. Furthermore, the storage of over 100 tons of peas for 24 hours presents economic and logistic problems. Also more and more economic pressure is being applied on the food industry to convert to continuous flow operations. However, until some means of effecting increased shellout percentages of freshly harvested peas is evolved, continuous flow of Southern peas from field to package cannot be realized. With these factors in mind, this study was made in an attempt to: (1) determine if aging exerts any influence on percentage shellout. (2) study the effect of aging on certain specific quality factors. (3) study certain morphological changes of the Southern pea pod

Handbook of Nonsexist Writing for Writers, Editors and Speakers; Marketing to Women ; Microcomputer Primer (First Edition): A Layman\u27s Guide for Selection and Use of Microcomputers in Developing Countries

Reviews of The Handbook of Nonsexist Writing for Writers, Editors and Speakers by Casey Miller and Kate Swift; Marketing to Women, by Cecelia Reed, Mark Sullivan and Neal Hirschfeld; and Microcomputer Primer (First Edition): A Layman\u27s Guide for Selection and Use of Microcomputers in Developing Countries, by John L. Woods

Leadership and Human Development

This article describes Graves’ theory of sociological development and its applicability to leadership. The interrelationship of the most common levels of functioning, appropriate management techniques, and methods for facilitating the growth of organization members is examined

Pasture Weaning at the McNay Memorial Research and Demonstration Farm: A Progress Report

In September 1995, 225 spring-born calves were weaned on pasture at the McNay Memorial Research and Demonstration Farm to explore procedures necessary to conduct a successful pasture-weaning program. In the two to three week post-weaning period, average daily gains (ADG) for the two groups weaned that year were 1.06 and 3.06 pounds; there were no health problems. In 1996, a research trial utilizing 242 spring-born calves was conducted to compare pastureweaned and feedlot-weaned calves. Half of the calves were weaned on pasture for three weeks and then placed in a feedlot for three more weeks. The other half of the calves were weaned directly into the feedlot for the six week post-weaning period. ADGs during the three week post-weaning period were 1.24 and 2.42 for the pastureweaned and feedlot-weaned calves. For the entire six week trial, ADGs were 1.83 and 2.40 for the pastureweaned and feedlot-weaned calves. There was no sickness in either weaning treatment during the six week trial. Initial experience indicates pasture-weaning is a feasible method of getting calves through a stressful procedure