Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Modelling and predictive control: Enabling technologies for reconfiguration

An approach to reconfiguring control systems in the event of major failures is advocated. The approach relies on the convergence of several technologies which are currently emerging: Constrained predictive control, High-fidelity modelling of complex systems, Fault detection and identification, and Model approximation and simplification. Much work is needed, both theoretical and algorithmic, to make this approach practical, but we believe that there is enough evidence, especially from existing industrial practice, for the scheme to be considered realistic. After outlining the problem and proposed solution, the paper briefly reviews constrained predictive control and object-oriented modelling, which are the essential ingredients for practical implementation. The prospects for automatic model simplification are also reviewed briefly. The paper emphasizes some emerging trends in industrial practice, especially as regards modelling and control of complex systems. Examples from process control and flight control are used to illustrate some of the ideas.

Towards the development of an integrated design framework using the Blackboard model

Current research into the process of engineering design is extending the use of computers towards the acquisition, representation and application of design process knowledge in addition to the existing storage and manipulation of product-based models of design objects. This is a difficult task because the design of mechanical systems is a complex, often unpredictable process involving ill-structured problem solving skills and large amounts of knowledge, some which may be of an incomplete and subjective nature. Design problems require the integration of a variety of modes of working such as numerical, graphical, algorithmic or heuristic and demand products through synthesis, analysis and evaluation activities.

This report presents the results of a feasibility study into the blackboard approach and discusses the development of an initial prototype system that will enable an alphanumeric design dialogue between a designer and an expert to be analysed in a formal way, thus providing real-life protocol data on which to base the blackboard message structures.

Forecasting high-frequency futures returns using online langevin dynamics

Forecasting the returns of assets at high frequency is the key challenge for high-frequency algorithmic trading strategies. In this paper, we propose a jump-diffusion model for asset price movements that models price and its trend and allows a momentum strategy to be developed. Conditional on jump times, we derive closed-form transition densities for this model. We show how this allows us to extract a trend from high-frequency finance data by using a Rao-Blackwellized variable rate particle filter to filter incoming price data. Our results show that even in the presence of transaction costs our algorithm can achieve a Sharpe ratio above 1 when applied across a portfolio of 75 futures contracts at high frequency. © 2011 IEEE.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Real-time marker prediction and CoR estimation in optical motion capture

Optical motion capture systems suffer from marker occlusions resulting in loss of useful information. This paper addresses the problem of real-time joint localisation of legged skeletons in the presence of such missing data. The data is assumed to be labelled 3d marker positions from a motion capture system. An integrated framework is presented which predicts the occluded marker positions using a Variable Turn Model within an Unscented Kalman filter. Inferred information from neighbouring markers is used as observation states; these constraints are efficient, simple, and real-time implementable. This work also takes advantage of the common case that missing markers are still visible to a single camera, by combining predictions with under-determined positions, resulting in more accurate predictions. An Inverse Kinematics technique is then applied ensuring that the bone lengths remain constant over time; the system can thereby maintain a continuous data-flow. The marker and Centre of Rotation (CoR) positions can be calculated with high accuracy even in cases where markers are occluded for a long period of time. Our methodology is tested against some of the most popular methods for marker prediction and the results confirm that our approach outperforms these methods in estimating both marker and CoR positions. © 2012 Springer-Verlag.

A novel process for transforming sheet metal blanks: Ridged die forming

Up to 20% of all sheet metal produced is scrapped as blanking skeletons. A novel process is therefore designed and examined, aiming to transform tessellating 'pre-blanks' in-plane into the real blanks required for stamping. Prior to blanking, the sheet is formed with a set of ridged dies, from which pre-blanks are cut and then flattened into true blanks. Several different approaches to designing ridged dies are evaluated by simulation and experiment, and the best results demonstrate a potential reduction in blanking yield losses for can-making from 9.3% to 6.9%. © 2013 CIRP.

Learning legged locomotion

Legged locomotion of biological systems can be viewed as a self-organizing process of highly complex system-environment interactions. Walking behavior is, for example, generated from the interactions between many mechanical components (e.g., physical interactions between feet and ground, skeletons and muscle-tendon systems), and distributed informational processes (e.g., sensory information processing, sensory-motor control in central nervous system, and reflexes) [21]. An interesting aspect of legged locomotion study lies in the fact that there are multiple levels of self-organization processes (at the levels of mechanical dynamics, sensory-motor control, and learning). Previously, the self-organization of mechanical dynamics was nicely demonstrated by the so-called Passive Dynamic Walkers (PDWs; [18]). The PDW is a purely mechanical structure consisting of body, thigh, and shank limbs that are connected by passive joints. When placed on a shallow slope, it exhibits natural bipedal walking dynamics by converting potential to kinetic energy without any actuation. An important contribution of these case studies is that, if designed properly, mechanical dynamics can generate a relatively complex locomotion dynamics, on the one hand, and the mechanical dynamics induces self-stability against small disturbances without any explicit control of motors, on the other. The basic principle of the mechanical self-stability appears to be fairly general that there are several different physics models that exhibit similar characteristics in different kinds of behaviors (e.g., hopping, running, and swimming; [2, 4, 9, 16, 19]), and a number of robotic platforms have been developed based on them [1, 8, 13, 22]. © 2009 Springer London.