Coordination on Lie groups

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left-or rightinvariance with respect to the absolute position on the group lead to two different characterizations of relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2). © 2008 IEEE.

Re-mobilization of pile shaft friction after an earthquake

During strong earthquakes, significant excess pore pressures can develop in saturated soils. After shaking ceases, the dissipation of these pressures can cause significant soil settlement, creating downward-acting frictional loads on piled foundations. Additionally, if the piles do not support the full axial load at the end of shaking, then the proportion of the superstructure's vertical loading carried by the piles may change as a result of the soil settlement, further altering the axial load distribution on piles as the soil consolidates. In this paper, the effect of hydraulic conductivity and initial post-shaking pile head loading is investigated in terms of the changing axial load distribution and settlement responses. The investigation is carried out by considering the results from four dynamic centrifuge experiments in which a 2 × 2 pile group was embedded in a two-layer profile and subjected to strong shaking. It is found that large contrasts in hydraulic conductivity between the two layers of the soil model affected both the pile group settlements and axial load distribution. Both these results stem from the differences in excess pore pressure dissipation, part of which took place very rapidly when the underlying soil layer had a large hydraulic conductivity.

Water supply to a geotechnical centrifuge for pile jetting in sand

The supply of water is often required during a centrifuge experiment. For the case of pile jetting, significant flow volumes and pressures are required from the water supply. This paper aims to detail the successful provision of water at high pressures and large flow rates to a centrifuge, using a novel water supply system. An impeller pump was used to pressurise the water in advance of the slip rings, with further pressure provided by the fluid accelerating along the centrifuge beam arm. A maximum pressure of 2 MPa and continuous flow rate of 6 litres per minute were achieved. The calculation of water pressure away from the measurement location is presented, offering a repeatable solution for the pressure at any point in the pipe work. © 2010 Taylor & Francis Group, London.

Optimal data fitting on lie groups: A coset approach

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in n to data which can be solved using principal component analysis. We show how the fitting problem can be reduced for biinvariant distances to a generalized mean calculation on an homogeneous space. For biinvariant Riemannian distances we provide an algorithm based on the Karcher mean gradient algorithm. We illustrate our approach by some examples on SO(n). © 2010 Springer -Verlag Berlin Heidelberg.

A role of monitoring to reduce the uncertainty in the performance of pile foundations

In typical conventional foundation design, the inherent variability of soil properties, model uncertainty and construction variability are not modeled explicitly. A main drawback of this is that the effect of each variability on the probability of an unfavorable event cannot be evaluated quantitatively. In this paper, a method to evaluate the uncertainty-reduction effect on the performance of a vertically-loaded pile foundation by monitoring the pile performance (such as pile load testing or placing sensors in piles) is proposed. The effectiveness of the proposed method is examined based on the investigation of a 120-pile foundation placed on three different ground profiles. The computed results show the capability of evaluating the uncertainty-reduction effect on the performance of a pile foundation by monitoring. © 2014 Taylor & Francis Group, London.