GUARDIANS final report part 1 (draft): a robot swarm assisting a human fire fighter

Emergencies in industrial warehouses are a major concern for fire fighters. The large dimensions together with the development of dense smoke that drastically reduces visibility, represent major challenges. The Guardians robot swarm is designed to assist re ghters in searching a large warehouse. In this paper we discuss the technology developed for a swarm of robots assisting re ghters. We explain the swarming algorithms which provide the functionality by which the robots react to and follow humans while no communication is required. Next we discuss the wireless communication system, which is a so-called mobile ad-hoc network. The communication network provides also the means to locate the robots and humans. Thus the robot swarm is able to provide guidance information to the humans. Together with the fire fighters we explored how the robot swarm should feed information back to the human fire fighter. We have designed and experimented with interfaces for presenting swarm based information to human beings

Optimising triangulated polyhedral surfaces with self-intersections

We discuss an optimisation procedure for triangulated polyhedral surfaces (referred to as (2 - 3) D triangulations) which allows us to process self-intersecting surfaces. As an optimality criterion we use minimisation of total absolute extrinsic curvature (MTAEC) and as a local transformation - a diagonal flip, defined in a proper way for (2 - 3) D triangulations. This diagonal flip is a natural generalisation of the diagonal flip operation in 2D, known as Lawson's procedure. The difference is that the diagonal flip operation in (2 - 3)D triangulations may produce self-intersections. We analyze the optimisation procedure for (2 - 3) D closed triangulations, taking into account possible self-intersections. This analysis provides a general insight on the structure of triangulations, allows to characterise the types of self-intersections, as well as the conditions for global convergence of the algorithm. It provides also a new view on the concept of optimisation on the whole and is useful in the analysis of global and local convergence for other optimisation algorithms. At the end we present an efficient implementation of the optimality procedure for (2 - 3)D triangulations of the data, situated in the convex position, and conjecture possible results of this procedure for non-convex data

Decimation and smoothing of triangular meshes based on curvature from the polyhedral Gauss map

This paper presents an improvement on methods to simplify, de-noise and identify feature regions of a triangular mesh, based on curvature estimations. Computations of curvature are obtained from the polyhedral Gauss Maps of the individual vertices. This allows identification of positive and negative curvature components, thus determining the Total Absolute Curvature (TAC) of a vertex. Using this new measure the curvature computed is more reliable and provides more information on the features of the polyhedral surface. The TAC of a region is obtained by summing the TAC's of the vertices in the region, which also provides identification of regions of similar curvature on a mesh model. In order to use this information for mesh simplification we introduce the weighted total absolute curvature measure, abbreviated as WTAC, which takes into consideration not only the curvature but also the area of the region, normalised in a specific way. We apply then the triangle decimation of a mesh, by removing vertices with the smallest WTAC. The decimation algorithm automatically performs also a smoothing (de-noising) operation by deleting outliers. By setting thresholds on the WTAC one can. obtain various degrees of decimation (smoothness). All operations are linear with respect to the number of vertices in the mesh

Producing animations from 3D face scans

In this paper we take our existing research into 3D surface scanning using uncoded structured light, optimized for human faces, and develop a method to record a sequence of face movements and visualise these as an animation in real time; we call this method the 3D Animation Processor (3DAP). The applications for this work include 2D and 3D face recognition, broadcast and feature film animation, and computer games production. It should be stressed that the 3D recording of facial movements in real time is a difficult problem that is attracting considerable research attention; but accurate and appealing results have so far proved elusive. We record the faces of a number of speaking subjects, process the data representing their shape and colour as it changes over time, and visualise the animated face models. We identify a particular problem in franze continuity, whereby unacceptable jumps and jitters occur in both the shape of the face and its colour mapping, and begin to solve this problem using hole-filling and interframe interpolation. We also investigate methods of feature tagging, so that the model can be placed in a fixed coordinate system and thereby incorporated into computer generated animations

Enhancing game physics using Gauss map computation

The present paper presents an algorithm to make fast and simple computations of the surface curvature of polyhedral objects in 3D, using a method called the Polyhedral Gauss Map. The computations are simple and can be done either in advance for static objects that are not modified during the game, or in real time, for dynamically changing entities. The curvature information can be applied for the computations of the physical properties and behaviour of objects in a game, for example, estimating the 'roughness' of terrain or measuring the curvature of a race track in order to find the optimal path or identify objects of different curvature when sliding down a sloped surface

Mixed human-robot team navigation in the GUARDIANS project

A theoretical framework for generating navigation behaviour patterns in mixed human-robot groups in complex environments is proposed. This framework represents an essential part in the development of a multiple robot-human system for assisting firefighters in search and rescue operations in the GUARDIANS project. In order to produce the desired behaviours an artificial potential field method has been developed. We distinguish a three classes of agents: robots, humans and obstacles, and apply different potential functions to them. Depending on the situation, we switch from one function to another; this allows to generate desired behaviour patterns as well as to avoid certain local minima. Typical behaviour patterns are singled out and their stability is discussed. Stability analysis is based on geometric considerations, that permits to avoid bulky computations and provide graphic demonstrations of convergence. The proposed framework can be used in other robotic applications where a group of heterogenous agents is deployed

On the determination of the potential function from given orbits

The paper deals with the problem of finding the field of force that generates a given (N - 1)-parametric family of orbits for a mechanical system with N degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov's problem. We apply the obtained results to generalize the theorem enunciated by Joukovski in 1890, solve the inverse Stackel problem and solve the problem of constructing the potential-energy function U that is capable of generating a bi-parametric family of orbits for a particle in space. We determine the equations for the sought-for function U and show that on the basis of these equations we can define a system of two linear partial differential equations with respect to U which contains as a particular case the Szebehely equation. We solve completely a special case of the inverse dynamics problem of constructing U that generates a given family of conics known as Bertrand's problem. At the end we establish the relation between Bertrand's problem and the solutions to the Heun differential equation. We illustrate our results by several examples

Modeling the flow of dense suspensions of deformable particles in three dimensions

We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common-yet numerically expensive-approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells-a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a 50 mu mx40 mu mx40 mu m simulation domain and only hours for 200 DPs in 80 mu mx30 mu mx30 mu m. Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models

A scale invariant surface curvature estimator

Abstract. In this paper we introduce a new scale invariant curvature measure, similarity curvature. We define a similarity curvature space which consists of the set of all possible similarity curvature values. An estimator for the similarity curvature of digital surface points is developed. Experiments and results applying similarity curvature to synthetic data are also presented.