Feedback control of the general two-trailers system with the Transverse Function approach

The so-called "general two-trailers system" is a nonholonomic system composed of a controlled unicycle-like vehicle and two passive trailers with off-axle hitching. It is not differentially flat and cannot be transformed into the chained form system. Methods developed for this latter class of systems thus do not apply. The Transverse Function (TF) approach is here used to solve the trajectory tracking problem for this system. The proposed control solution yields practical stabilization of any reference motion, whether it is or is not feasible. Practical stabilization of non-feasible trajectories in the case of non-differently flat systems is of particular interest due partly to the difficulty of planning and calculating desired feasible state reference motions. The method is illustrated by simulation results which show that, in addition to the unconditional practical stabilization property evoked above, asymptotic stabilization of feasible and persistently exciting motions can also be achieved with the same performance as local stabilizers derived from a linear approximation of the tracking-error equations

On the transversality of functions at the core of the transverse function approach to control

"The transverse function approach to control, introduced by Morin and Samson in the early 2000s, is based on functions that are transverse to a set of vector fields in a sense formally similar to, although strictly speaking different from, the classical notion of transversality in differential topology. In this paper, a precise link is established between transversality and the functions used in the transverse function approach. It is first shown that a smooth function f : M -> Q is transverse to a set of vector fields which locally span a distribution D on Q if, and only if, its tangent mapping T f is transverse to D, where D is regarded as a submanifold of the tangent bundle T Q. It is further shown that each of these two conditions is equivalent to transversality of T f to D along the zero section of T M. These results are then used to rigorously state and prove that if M is compact and D is a distribution on Q, then the set of mappings of M into Q that are transverse to D is open in the strong (or "Whitney C (a)-") topology on C (a)(M, Q).

The Mechanics and Control of Undulatory Robotic Locomotion

In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle. We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations. The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations. The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields. The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets

First International Symposium on Strain Gauge Balances

The first International Symposium on Strain Gauge Balances was sponsored and held at NASA Langley Research Center during October 22-25, 1996. The symposium provided an open international forum for presentation, discussion, and exchange of technical information among wind tunnel test technique specialists and strain gauge balance designers. The Symposium also served to initiate organized professional activities among the participating and relevant international technical communities. Over 130 delegates from 15 countries were in attendance. The program opened with a panel discussion, followed by technical paper sessions, and guided tours of the National Transonic Facility (NTF) wind tunnel, a local commercial balance fabrication facility, and the LaRC balance calibration laboratory. The opening panel discussion addressed "Future Trends in Balance Development and Applications." Forty-six technical papers were presented in 11 technical sessions covering the following areas: calibration, automatic calibration, data reduction, facility reports, design, accuracy and uncertainty analysis, strain gauges, instrumentation, balance design, thermal effects, finite element analysis, applications, and special balances. At the conclusion of the Symposium, a steering committee representing most of the nations and several U.S. organizations attending the Symposium was established to initiate planning for a second international balance symposium, to be held in 1999 in the UK

The 1995 NASA-ODU American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program

Since 1964, the National Aeronautics and Space Administration (NASA) has supported a program of summer faculty fellowships for engineering and science educators. In a series of collaborations between NASA research and development centers and nearby universities, engineering faculty members spend 10 weeks working with professional peers on research. The Summer Faculty Program Committee of the American Society for Engineering Education supervises the programs. The objectives of this program are: (1) To further the professional knowledge of qualified engineering and science faculty members; (2) To stimulate and exchange ideas between participants and NASA; (3) To enrich and refresh the research and teaching activities of participants' institutions; and (4) To contribute to the research objectives of the NASA center. College or university faculty members will be appointed as Research Fellows to spend 10 weeks in cooperative research and study at the NASA Langley Research Center. The Fellow will devote approximately 90 percent of the time to a research problem and the remaining time to a study program. The study program will consist of lectures and seminars on topics of interest or that are directly relevant to the Fellows' research topics. The lectures and seminar leaders will be distinguished scientists and engineers from NASA, education, or industry

NASA/American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program, 1991

In a series of collaborations between NASA research and development centers and nearby universities, engineering faculty members spent 10 weeks working with professional peers on research. The Summer Faculty Program Committee of the American Society of Engineering Education supervises the programs. The objects were the following: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate and exchange ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA center

Aeronautical engineering: A continuing bibliography with indexes (supplement 304)

This bibliography lists 453 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1994. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

NASA LaRC Workshop on Guidance, Navigation, Controls, and Dynamics for Atmospheric Flight, 1993

This publication is a collection of materials presented at a NASA workshop on guidance, navigation, controls, and dynamics (GNC&D) for atmospheric flight. The workshop was held at the NASA Langley Research Center on March 18-19, 1993. The workshop presentations describe the status of current research in the GNC&D area at Langley over a broad spectrum of research branches. The workshop was organized in eight sessions: overviews, general, controls, military aircraft, dynamics, guidance, systems, and a panel discussion. A highlight of the workshop was the panel discussion which addressed the following issue: 'Direction of guidance, navigation, and controls research to ensure U.S. competitiveness and leadership in aerospace technologies.

Summary of research in progress at ICASE

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1992 through March 31, 1993

The 1993 NASA-ODU American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program

Since 1964, the National Aeronautics and Space Administration has supported a program of summer faculty fellowships for engineering and science educators. In a series of collaborations between NASA research and development centers and nearby universities, engineering faculty members spend 10 weeks working with professional peers on research. The Summer Faculty Program Committee of the American Society for Engineering Education supervises the programs. Objectives are: to further the professional knowledge of qualified engineering and science faculty members; to stimulate and exchange ideas between participants and NASA; to enrich and refresh the research and teaching activities of participants' institutions; and to contribute to the research objectives of the NASA center