Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

Non-linear Control of an Autonomous Ground Vehicle

In this paper, in order to select a speed controller for a specific non-linear autonomous ground vehicle, proportional-integral-derivative (PID), Fuzzy, and linear quadratic regulator (LQR) controllers were designed. Here, in order to carry out the tuning of the above controllers, a multicomputer genetic algorithm (MGA) was designed. Then, the results of the MGA were used to parameterize the PID, Fuzzy and LQR controllers and to test them under laboratory conditions. Finally, a comparative analysis of the performance of the three controllers was conducted.

A Vision Based Target Detection System for Docking of an Autonomous Underwater Vehicle

This paper describes the development and preliminary experimental evaluation of a visionbased docking system to allow an Autonomous Underwater Vehicle (AUV) to identify and attach itself to a set of uniquely identifiable targets. These targets, docking poles, are detected using Haar rectangular features and rotation of integral images. A non-holonomic controller allows the Starbug AUV to orient itself with respect to the target whilst maintaining visual contact during the manoeuvre. Experimental results show the proposed vision system is capable of robustly identifying a pair of docking poles simultaneously in a variety of orientations and lighting conditions. Experiments in an outdoor pool show that this vision system enables the AUV to dock autonomously from a distance of up to 4m with relatively low visibility.

Data transformations in custom digital workflows : property graphs as a data model for user-defined mappings

This paper describes the use of property graphs for mapping data between AEC software tools, which are not linked by common data formats and/or other interoperability measures. The intention of introducing this in practice, education and research is to facilitate the use of diverse, non-integrated design and analysis applications by a variety of users who need to create customised digital workflows, including those who are not expert programmers. Data model types are examined by way of supporting the choice of directed, attributed, multi-relational graphs for such data transformation tasks. A brief exemplar design scenario is also presented to illustrate the concepts and methods proposed, and conclusions are drawn regarding the feasibility of this approach and directions for further research.

Selection and monitoring of navigation modes for an autonomous rover

Considering the wide spectrum of situations that it may encounter, a robot navigating autonomously in outdoor environments needs to be endowed with several operating modes, for robustness and efficiency reasons. Indeed, the terrain it has to traverse may be composed of flat or rough areas, low cohesive soils such as sand dunes, concrete road etc. . .Traversing these various kinds of environment calls for different navigation and/or locomotion functionalities, especially if the robot is endowed with different locomotion abilities, such as the robots WorkPartner, Hylos [4], Nomad or the Marsokhod rovers. Numerous rover navigation techniques have been proposed, each of them being suited to a particular environment context (e.g. path following, obstacle avoidance in more or less cluttered environments, rough terrain traverses...). However, seldom contributions in the literature tackle the problem of selecting autonomously the most suited mode [3]. Most of the existing work is indeed devoted to the passive analysis of a single navigation mode, as in [2]. Fault detection is of course essential: one can imagine that a proper monitoring of the Mars Exploration Rover Opportunity could have avoided the rover to be stuck during several weeks in a dune, by detecting non-nominal behavior of some parameters. But the ability to recover the anticipated problem by switching to a better suited navigation mode would bring higher autonomy abilities, and therefore a better overall efficiency. We propose here a probabilistic framework to achieve this, which fuses environment related and robot related information in order to actively control the rover operations.

A near-to-far non-parametric learning approach for estimating traversability in deformable terrain

It is well recognized that many scientifically interesting sites on Mars are located in rough terrains. Therefore, to enable safe autonomous operation of a planetary rover during exploration, the ability to accurately estimate terrain traversability is critical. In particular, this estimate needs to account for terrain deformation, which significantly affects the vehicle attitude and configuration. This paper presents an approach to estimate vehicle configuration, as a measure of traversability, in deformable terrain by learning the correlation between exteroceptive and proprioceptive information in experiments. We first perform traversability estimation with rigid terrain assumptions, then correlate the output with experienced vehicle configuration and terrain deformation using a multi-task Gaussian Process (GP) framework. Experimental validation of the proposed approach was performed on a prototype planetary rover and the vehicle attitude and configuration estimate was compared with state-of-the-art techniques. We demonstrate the ability of the approach to accurately estimate traversability with uncertainty in deformable terrain.

Real-time image classification for adaptive mission planning using an Autonomous Underwater Vehicle

Real-time image analysis and classification onboard robotic marine vehicles, such as AUVs, is a key step in the realisation of adaptive mission planning for large-scale habitat mapping in previously unexplored environments. This paper describes a novel technique to train, process, and classify images collected onboard an AUV used in relatively shallow waters with poor visibility and non-uniform lighting. The approach utilises Förstner feature detectors and Laws texture energy masks for image characterisation, and a bag of words approach for feature recognition. To improve classification performance we propose a usefulness gain to learn the importance of each histogram component for each class. Experimental results illustrate the performance of the system in characterisation of a variety of marine habitats and its ability to operate onboard an AUV's main processor suitable for real-time mission planning.

From vision to actions: Towards adaptive and autonomous humanoid robots

Although robotics research has seen advances over the last decades robots are still not in widespread use outside industrial applications. Yet a range of proposed scenarios have robots working together, helping and coexisting with humans in daily life. In all these a clear need to deal with a more unstructured, changing environment arises. I herein present a system that aims to overcome the limitations of highly complex robotic systems, in terms of autonomy and adaptation. The main focus of research is to investigate the use of visual feedback for improving reaching and grasping capabilities of complex robots. To facilitate this a combined integration of computer vision and machine learning techniques is employed. From a robot vision point of view the combination of domain knowledge from both imaging processing and machine learning techniques, can expand the capabilities of robots. I present a novel framework called Cartesian Genetic Programming for Image Processing (CGP-IP). CGP-IP can be trained to detect objects in the incoming camera streams and successfully demonstrated on many different problem domains. The approach requires only a few training images (it was tested with 5 to 10 images per experiment) is fast, scalable and robust yet requires very small training sets. Additionally, it can generate human readable programs that can be further customized and tuned. While CGP-IP is a supervised-learning technique, I show an integration on the iCub, that allows for the autonomous learning of object detection and identification. Finally this dissertation includes two proof-of-concepts that integrate the motion and action sides. First, reactive reaching and grasping is shown. It allows the robot to avoid obstacles detected in the visual stream, while reaching for the intended target object. Furthermore the integration enables us to use the robot in non-static environments, i.e. the reaching is adapted on-the- fly from the visual feedback received, e.g. when an obstacle is moved into the trajectory. The second integration highlights the capabilities of these frameworks, by improving the visual detection by performing object manipulation actions.

On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

Improvement On Brooks Chromatic Bound For A Class Of Graphs

Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).

Autonomous UAVs wildlife detection using thermal imaging, predictive navigation and computer vision

There is an increased interest on the use of Unmanned Aerial Vehicles (UAVs) for wildlife and feral animal monitoring around the world. This paper describes a novel system which uses a predictive dynamic application that places the UAV ahead of a user, with a low cost thermal camera, a small onboard computer that identifies heat signatures of a target animal from a predetermined altitude and transmits that target’s GPS coordinates. A map is generated and various data sets and graphs are displayed using a GUI designed for easy use. The paper describes the hardware and software architecture and the probabilistic model for downward facing camera for the detection of an animal. Behavioral dynamics of target movement for the design of a Kalman filter and Markov model based prediction algorithm are used to place the UAV ahead of the user. Geometrical concepts and Haversine formula are applied to the maximum likelihood case in order to make a prediction regarding a future state of the user, thus delivering a new way point for autonomous navigation. Results show that the system is capable of autonomously locating animals from a predetermined height and generate a map showing the location of the animals ahead of the user.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

Acyclic edge coloring of subcubic graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and it is denoted by a′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors.