Trajectory tracking for nonholonomic systems. Theoretical background and applications

The problem of stabilizing reference trajectories for nonholonomic systems, often referred to as the trajectory tracking problem in the literature on mobile robots, is addressed. The first sections of this report set the theoretical background of the problem, with a focus on controllable driftless systems which are invariant on a Lie group. The interest of the differential geometry framework here adopted comes from the possibility of taking advantage of ubiquitous symmetry properties involved in the motion of mechanical bodies. Theoretical difficulties and impossibilities which set inevitable limits to what is achievable with feedback control are surveyed, and basic control design tools and techniques are recast within the approach here considered. A general method based on the so-called Transverse Function approach --developed by the authors--, yielding feedback controls which unconditionnally achieve the {\em practical} stabilization of arbitrary reference trajectories, including fixed points and non-admissible trajectories, is recalled. This property singles the proposed solution out of the abundant literature devoted to the subject. It is here complemented with novel results showing how the more common property of asymptotic stabilization of persistently exciting admissible trajectories can also be granted with this type of control. The last section of the report concerns the application of the approach to unicycle-type and car-like vehicles. The versatility and potentialities of the Transverse Function (TF) control approach are illustrated via simulations involving various reference trajectory properties, and a few complementary control issues are addressed. One of them concerns the possiblity of using control degrees of freedom to limit the vehicle's velocity inputs and the number of transient maneuvers associated with the reduction of initially large tracking errors. Another issue, illustrated by the car example, is related to possible extensions of the approach to systems which are not invariant on a Lie group

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).

NASA Tech Briefs, February 1988

Topics covered include: New Product Ideas; NASA TU Services; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Systems; and Life Sciences

Whoever Said Change Was Good: The Transforming Body of the Disney Villainess

This dissertation examines female figures in Disney animation through the lens of Laban Movement Analysis (LMA), a system for observing and articulating movement qualities. Drawing from six major films released between 1937 and 2010, I focus my inquiry on how the bodies and movement of Disneys villainesses reflect and/or perpetuate cultural imaginaries of women. I identify the influence of several cultural tropes of femininity, including fairy-tale archetypes, ballet conventions, and the Hollywood femme fatale, and explore how they constellate social understandings of age, beauty, and desirability. Coalescing around the theme of physical transformation, the study investigates how consistent movement patterns both support character animation and reflect gender ideologies encoded in the bodies of these wicked women. Through a methodology grounded in LMA and drawing from dance studies, feminist theory, and Disney scholarship, I interrogate popular conceptions of women and evil, articulate how movement contributes to cultural meaning, and demonstrate LMAs value to cultural analysis and animation

SPACE: Vision and Reality: Face to Face. Proceedings Report

The proceedings of the 11th National Space Symposium entitled 'Vision and Reality: Face to Face' is presented. Technological areas discussed include the following sections: Vision for the future; Positioning for the future; Remote sensing, the emerging era; space opportunities, Competitive vision with acquisition reality; National security requirements in space; The world is into space; and The outlook for space. An appendice is also attached