Morse-Bott functions on orthogonal groups

We make a detailed study of various (quadratic and linear) Morse-Bott trace functions on the orthogonal groups $O(n)$. We describe the critical loci of the quadratic trace function Tr$(AXBX^T)$ and determine their indices via perfect fillings of tables associated with the multiplicities of the eigenvalues of $A$ and $B$. We give a simplified treatment of T. Frankel's analysis of the linear trace function on $SO(n)$, as well as a combinatorial explanation of the relationship between the mod $2$ Betti numbers of $SO(n)$ and those of the Grassmannians $\mathbb{G}(2k,n)$ obtained from this analysis. We review the basic notions of Morse-Bott cohomology in a simple case where the set of critical points has two connected components. We then use these results to give a new Morse-theoretic computation of the mod $2$ Betti numbers of $SO(n)$.Comment: 28 page

Assembly as a noncooperative game of its pieces: analysis of 1D sphere assemblies

We propose an event-driven algorithm for the control of simple robot assembly problems based on noncooperative game theory. We examine rigorously the simplest setting — three bodies with one degree of freedom and offer extensive simulations for the 2 DOF extension. The initial analysis and the accompanying simulations suggest that this approach may indeed, offer an attractive means of building robust event driven assembly systems

Investigating Validation of Armey Curve Hypothesis for G7 Countries using ARDL Model

The effect of the government size on economic growth still keeps its unclear status despite the works in this field. According to the Armey Hypothesis (1995), which one of the studies developed for the volume of government size in economy, the increase in the public volume in economy will increase economic growth up to a certain level, and when the maximum level is reached, the increase in public volume will cause decreases in economic growth. In this study, the issues of whether the Armey Hypothesis is valid or not for G7 countries has been investigated, and the optimum public volume has been determined for G7 countries. In testing Armey Curve hypothesis, we use ARDL cointegration procedure. The results of empirical findings argue that the Armey Hypothesis is valid for US, and Canada, and France when it is invalid for other G7 countries

Investigating Validation of Armey Curve Hypothesis for G7 Countries using ARDL Model

The effect of the government size on economic growth still keeps its unclear status despite the works in this field. According to the Armey Hypothesis (1995), which one of the studies developed for the volume of government size in economy, the increase in the public volume in economy will increase economic growth up to a certain level, and when the maximum level is reached, the increase in public volume will cause decreases in economic growth. In this study, the issues of whether the Armey Hypothesis is valid or not for G7 countries has been investigated, and the optimum public volume has been determined for G7 countries. In testing Armey Curve hypothesis, we use ARDL cointegration procedure. The results of empirical findings argue that the Armey Hypothesis is valid for US, and Canada, and France when it is invalid for other G7 countries

Assembly as a noncooperative game of its pieces: the case of endogeneous disk assemblies

We propose an event-driven approach to planning and control of robot assembly problems using ideas from non-cooperative game theory. We report on the results of an extensive simulation study for a very simple two degree of freedom case - the arrangement of disks on a plane by a disk shaped robot

Plant layout and pick-and-place strategies for improving performances in secondary packaging plants of food products

The aim of secondary packaging plants is to pick food products from a conveyor belt and to place them into boxes. The typical configuration of these packaging plants consists of a set of sequential robot stations, performing pick and place cycles from one conveyor to another parallel one, which transport the products and the boxes to be filled. Depending on the relative movement of the two conveyors, the plant operates in co-current or counter-current flow configuration. Undesired perturbations in the product flow rate from its nominal value can lead to critical events, i.e. unpicked product at the end of the first conveyor or not-completely filled boxes. Even if the structures of co-current flow and of counter-current flow plants, are very similar, their behaviour in non-nominal or perturbed conditions can be significantly different. The aim of this paper is to deeply investigate the behaviour of these two kinds of secondary packaging lines, evaluating their performances in the case of different pick and place strategies, using discrete events simulation techniques. Results show to which extent the different proposed control strategies can improve the performances of both co-current and counter-currents plants and, in particular, how co-current plant layouts can achieve performances which are equivalent to, or perhaps even better than, those that can be obtained with a counter-current plant layout, that cannot be freely used since it has been patented. The simulation tool, control algorithms and results presented can help packaging plant designers for choosing the most appropriate solutions and for properly sizing the plant. Copyright © 2012 John Wiley & Sons, Lt

Event Driven Parts Moving in 2D Endogenuous Environments

This paper is concerned with the parts’ moving problem based on an event-driven planning and control. We are interested in developing feedback based approaches to the automatic generation of actuator commands that cause the robot to move a set of parts from an arbitrary initial disassembled configuration to a specif ed final configuration. In the Phase I of this project, a composite algorithm that reactively switches between different feedback controllers has been shown to induce a noncooperative game being played among the parts being manipulated. This paper describes experimental results with EDAR - Event-Driven Assembler Robot - developed for moving parts based on feedback techniques. For more information: Kod*La

Feedback-Based Event-Driven Parts Moving

A collection of unactuated disk-shaped parts must be brought by an actuated manipulator robot into a specified configuration from arbitrary initial conditions. The task is cast as a noncooperative game played among the parts—which in turn yields a feedback-based event-driven approach to plan generation and execution. The correctness of this approach, an open question, has been demonstrated in simpler settings and is further suggested by the extensive experiments reported here using an actual working implementation with EDAR—a mobile robot operating in a purely feedback-based event-driven manner. These results verify the reliability of this approach against uncertainties in sensory information and unanticipated changes in workspace configuration

On the Coordinated Navigation of Multiple Independent Disk-Shaped Robots

This paper addresses the coordinated navigation of multiple independently actuated disk-shaped robots - all placed within the same disk-shaped workspace. Assuming perfect sensing, shared centralized communications and computation, as well as perfect actuation, we encode complete information about the goal, obstacles and workspace boundary using an artificial potential function over the cross product space of the robots’ simultaneous configurations. The closed-loop dynamics governing the motion of each robot take the form of the appropriate projection of the gradient of this function. We show, with some reasonable restrictions on the allowable goal positions, that this function is an essential navigation function - a special type of artificial potential function that is ensured of connecting the kinematic planning with the dynamic execution in a manner that guarantees collision-free navigation of each robot to its destination from almost all initial free placements. We summarize the results of an extensive simulation study investigating such practical issues as average resulting trajectory length and robustness against simulated sensor noise