Nonholonomic motion planning: steering using sinusoids

Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given

THE PROVISION OF RAIL SERVICE: THE IMPACT OF COMPETITION

Grain transportation is one of the most important economic issues for grain producers in the Northern Plains. The reliance on export markets and the long distances to port position means that transportation costs have a significant effect on the price received by farmers. In the prairie region of Canada, rail transportation is undergoing a major transformation that will affect the competitive positions of agriculture in both the United States and Canada and influence the direction of grain flows between the two countries. Rail rates are no longer legislated although a cap is still in place), restrictions on branch line abandonment have been lifted, and further deregulation of price and car allocation is being considered. Some parties, including the railways, argue that a completely deregulated system, similar to the U.S. system, is the only way to achieve transportation efficiencies. Other groups, supporting the status quo, argue that the regulation of rates is essential to control the monopoly power of the railways. There has been very little discussion of other policy options, with the exception of a limited discussion of nationalized railbeds. The U.S. experience provides a stark view of the likely outcome of deregulation. When railways are not faced with competition from other railways or from other forms of transportation such as barges, the evidence suggests railways will price freight services at or near truck competitive rates. Freight rates in Montana, where no effective rail and/or barge competition exists, are approximately twice those at Kansas City and Denver/Commerce City, where such competition exists. The current cost-based regulated rates in Western Canada are similar to those at Kansas City and Denver/Commerce City. Given similar distances to port and the existence of only two railways (and no likelihood of new entrants), deregulation in Western Canada is likely to result in freight rates closer to those in Montana than to the current regulated level. The increase in freight costs will result in transfers from producers to the railways, distort production incentives, and create losses elsewhere in the economy. While maintenance of a regulated freight rate structure would address the freight rate issue, other problems would result. The lack of price signals reduces incentives for industry participants to perform. Branch lines are less likely to be maintained in a regulated environment because railways may be unable to charge the extra amount necessary to make them viable. Railways may also disrupt the system - as a form of bargaining - to create pressure for deregulation. This report explores the option of the government encouraging entry into rail service provision. Just as telecommunication companies are required to allow competitors to use their phone lines, existing railways could be required to make their track and switching equipment available to rail operators who wish to run train service on a line, on the condition that the access price covers the infrastructure cost. The paper examines the case of the British railway system where the ownership of the track has been separated from the operation of the rail equipment and the provision of service, and explores the applicability of this model to grain transportation on the Great Plains. In Britain, ownership of the track rests with a company called Railtrack (although Railtrack was government-owned, it has been privatized). Railtrack leases access to thirty train operators for fees that are regulated by the Office of the Rail Regulator to cover maintenance costs and provide a return on investment. The thirty rail operators then compete to provide service to customers. This model and others similar to it need to be developed and articulated before they can be considered in the public policy forum. Nevertheless, given the importance of rail transportation to the grain industry in the Northern Plains, it is imperative that options such as these be investigated to address the very thorny issue of freight rate and entry regulation.barriers to entry, competition, grain handling, grain transportation, monopoly, railroads, regulation, Public Economics, K2, L1, L9, L5,

Trajectory generation for the N-trailer problem using Goursat normal form

Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included

Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

A Bayesian partial identification approach to inferring the prevalence of accounting misconduct

This paper describes the use of flexible Bayesian regression models for estimating a partially identified probability function. Our approach permits efficient sensitivity analysis concerning the posterior impact of priors on the partially identified component of the regression model. The new methodology is illustrated on an important problem where only partially observed data is available - inferring the prevalence of accounting misconduct among publicly traded U.S. businesses

Storage and hydrolysis of seawater samples for inorganic carbon isotope analysis

Preservation of seawater samples was tested for total inorganic carbon (ΣCO2), stable carbon isotope (δ13C), and radiocarbon (14C) applications using foil bags and storage by refrigeration and freezing. The aim was to preserve representative samples with minimal storage effects but without using toxic methods such as mercuric chloride poisoning. Hydrolysis of samples to CO2 was based on existing methods. Results of IAEA-C2 standard used with deionized water stored in the foil bags showed complete reaction yields, 14C results within 2σ of the consensus value, and δ13C that were internally consistent, indicating that there were no procedural effects associated with the foil bags. 14C results were statistically indistinguishable across the storage times, for frozen and refrigerated seawater samples from a coastal site, Elie Ness, Fife, UK. The scatter of ΣCO2 concentrations and δ13C was within scatter observed in other studies for lake- and seawater samples preserved by acidification or using mercuric chloride. However, both ΣCO2 and δ13C were less variable for frozen samples compared with refrigerated samples. The foil bags are lighter, safer to transport, and similar in cost to glass bottles and allow sample collection in the field and transfer to the hydrolysis vessel without exposure of the sample to atmosphere. Storage of seawater samples in the foil bags was considered a reliable, alternative method to poisoning for ΣCO2, δ13C, and 14C, and freezing the samples is recommended for storage time beyond a week

Steering nonholonomic systems in chained form

The authors introduce a nilpotent form, called a chained form, for nonholonomic control systems. For the case of a nonholonomic system with two inputs, they give constructive conditions for the existence of a feedback transformation which puts the system into chained form, and show how to steer the system between arbitrary states. Examples are presented for steering a car and a car with a trailer attached: other examples can be found in the areas of space robotics and multifingered robot hands. The present results also have applications in the area of nilpotentization of distributions of vector fields on R^n