Almost-global tracking of simple mechanical systems on a general class of Lie Groups

We present a general intrinsic tracking controller design for fully-actuated simple mechanical systems, when the configuration space is one of a general class of Lie groups. We first express a state-feedback controller in terms of a function-the "error function"-satisfying certain regularity conditions. If an error function can be found, then a general smooth and bounded reference trajectory may be tracked asymptotically from almost every initial condition, with locally exponential convergence. Asymptotic convergence from almost every initial condition is referred to as "almost-global" asymptotic stability. Error functions may be shown to exist on any compact Lie group, or any Lie group diffeomorphic to the product of a compact Lie group and R/sup n/. This covers many cases of practical interest, such as SO(n), SE(n), their subgroups, and direct products. We show here that for compact Lie groups the dynamic configuration-feedback controller obtained by composing the full state-feedback law with an exponentially convergent velocity observer is also almost-globally asymptotically stable with respect to the tracking error. We emphasize that no invariance is needed for these results. However, for the special case where the kinetic energy is left-invariant, we show that the explicit expression of these controllers does not require coordinates on the Lie group. The controller constructions are demonstrated on SO(3), and simulated for the axi-symmetric top. Results show excellent performance.     

Feedback transformations on tori

Here we investigate the problem of transforming a nonlinear system on the torusT ⁿ by using global feedback and global changes of coordinates into an invariant system (i.e., a control system of whichf andg _i are (left and right) invariant vector fields whenT ² is considered as a Lie group). We provide a complete answer whenn=2 and give a sufficient condition and necessary conditions in the more general case.     

Geometry and Control of Human Eye Movements

In this paper, we study the human oculomotor system as a simple mechanical control system. It is a well known physiological fact that all eye movements obey Listing's law, which states that eye orientations form a subset consisting of rotation matrices for which the axes are orthogonal to the normal gaze direction. First, we discuss the geometry of this restricted configuration space (referred to as the Listing space). Then we formulate the system as a simple mechanical control system with a holonomic constraint. We propose a realistic model with musculotendon complexes and address the question of controlling the gaze. As an example, an optimal energy control problem is formulated and numerically solved     

Development of an evanescent wave fiber optic biosensor

Biosensors are uniquely qualified to meet the need for rapid, inexpensive analytical procedures. The authors' intent was to develop a simple, real-time immunoassay that could process multiple samples in a semi-automated manner, while maintaining maximum versatility to permit its application under various conditions. To achieve this goal, the authors have developed a biosensor which detects antibody-antigen binding within the evanescent wave of an optical biosensor     

Stress relieving and its effect on life of welded tubular joints

This paper describes investigations into the fabrication and repair of large welded tubular joints and how the processes used affect fatigue life. Research has been conducted to determine the benefit of local post weld heat treatment (PWHT) of the connections in terms of hardness and residual stress. The use of hole drilling and trepanning techniques for residual stresses measurements in the clusters are described. The results are compared with fitness-for-service assessments and considered in relation to the fatigue performance of the welded connections. Very substantial theoretical improvement in fatigue life can be expected after PWHT.     

Theoretical investigation on the behaviour of a plate strip undergoing local and global deformation

The behaviour of a plate strip with local as well as global imperfections is investigated in this paper. The function used to describe the deformation of the plate was based on a previously conducted experimental investigation. The behaviour of the plate well into the large-deflection post-buckling range has been considered. It is shown that various buckling modes are possible and the effects of the imperfections on the buckling and post-buckling behaviour are presented.     

A necessary and sufficient condition for the perspective observability problem

In this paper we derive a necessary and sufficient condition for observing the initial condition of a new class of system known as the perspective system. Such a system has already been applied in the field of computer vision especially in the area of motion estimation problems. Our result generalizes an earlier result by Popov-Belevitch-Hautus on the problem of observing a linear dynamical system.     

Observing linear dynamics with polynomial output functions

We address the problem of observing a linear system by a scalar polynomial output function. We show that if the null space of A has dimension at most one, then one can always find such an output function which observes the system and when all the eigenvalues of A are real, then a necessary condition for the observability of the system is that the degree of the polynomial is greater than a certain integer which is related to the maximum number of Jordan blocks corresponding to any eigenvalue.     

A hybrid parameterization of linear single input single output systems

We obtain a parameterization of the set of finite dimensional linear dynamical systems of unbounded McMillan degree. In this parameterization a given system is represented in a nonunique way. However, a certain notion of order is available, thereby providing a graded parameterization. An important feature is that each graded space is diffeomorphic to a Euclidean space. In view of this fact we hope that many of the local results in identification (valid only if the parameter space is Euclidean) an actually be generalized globally. Moreover we show that the topology induced on the space of all plants by this space is finer than the graph topology.     

Neutralizing human monoclonal antibodies binding multiple serotypes of botulinum neurotoxin

Botulism, a disease of humans characterized by prolonged paralysis, is caused by botulinum neurotoxins (BoNTs), the most poisonous substances known. There are seven serotypes of BoNT (A-G) which differ from each other by 34-64% at the amino acid level. Each serotype is uniquely recognized by polyclonal antibodies, which originally were used to classify serotypes. To determine if there existed monoclonal antibodies (mAbs) capable of binding two or more serotypes, we evaluated the ability of 35 yeast-displayed single-chain variable fragment antibodies generated from vaccinated humans or mice for their ability to bind multiple BoNT serotypes. Two such clonally related human mAbs (1B18 and 4E17) were identified that bound BoNT serotype A (BoNT/A) and B or BoNT/A, B, E and F, respectively, with high affinity. Using molecular evolution techniques, it proved possible to both increase affinity and maintain cross-serotype reactivity for the 4E17 mAb. Both 1B18 and 4E17 bound to a relatively conserved epitope at the tip of the BoNT translocation domain. Immunoglobulin G constructed from affinity matured variants of 1B18 and 4E17 were evaluated for their ability to neutralize BoNT/B and E, respectively, in vivo. Both antibodies potently neutralized BoNT in vivo demonstrating that this epitope is functionally important in the intoxication pathway. Such cross-serotype binding and neutralizing mAbs should simplify the development of antibody-based BoNT diagnostics and therapeutics.