Consider the following communication problem, which leads to a new notion of edge colouring. The communication network is represented by a bipartite multigraph, where the nodes on one side are the transmitters and the nodes on the other side are the receivers. The edges correspond to messages, and every edge e is associated with an integer c(e), corresponding to the time it takes the message to reach its destination. A proper k-edge-colouring with delays is a function f from the edges to {0, 1, . . ., k − 1}, such that, for every two edges e1 and e2 with the same transmitter, f(e1) ≠ f(e2), and for every two edges e1 and e2 with the same receiver, f(e1) + c(e1) ≢ f(e2) + c(e2) (mod k). Ross, Bambos, Kumaran, Saniee and Widjaja [18] conjectured that there always exists a proper edge colouring with delays using k = Δ + o(Δ) colours, where Δ is the maximum degree of the graph. Haxell, Wilfong and Winkler [11] conjectured that a stronger result holds: k = Δ + 1 colours always suffice. We prove the weaker conjecture for simple bipartite graphs, using a probabilistic approach, and further show that the stronger conjectureholds for some multigraphs, applying algebraic tools.

This paper presents an approach to reduce the technical complexity of a service robotic system by means of systematic and well-balanced user-involvement. By taking advantage of the user's cognitive capabilities during task execution, a technically manageable robotic system, which is able to execute tasks on a high level of abstraction reliably and robustly, emerges. For the realisation of this approach, the control architecture MASSiVE has been implemented, which is used for the control of the rehabilitation robot FRIEND II. It supports task execution on the basis of a priori defined and formally verified task-knowledge. This task-knowledge contains all possible sequences of operations as well as the symbolic representation of objects required for the execution of a specific task. The seamless integration of user interactions into this task-knowledge, in combination with MASSiVE's user-adapted human–machine interface layer, enables the system to deliberately interact with the user during run-time.

We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3-colours a random 4-regular graph. The analysis includes use of the differential equation method, and exponential bounds on the tail of random variables associated with branching processes. A substantial part of the analysis applies to random d-regular graphs in general.

The proposed algorithm integrates in a single planner the global motion planning and local obstacle avoidance capabilities. It efficiently guides the robot in a dynamic environment. This eliminates some of the traditional problems of planned architectures (model-plan-act scheme) while obtaining many of the qualities of behavior-based architectures. The computational efficiency of the method allows the planner to operate at high-rate sensor frequencies. This avoids the need for using both a collision-avoidance algorithm and a global motion planner for navigation in a cluttered environment. The method combines map-based and sensor-based planning operations to provide a smooth and reliable motion plan. Operating on a simple grid-based world model, the method uses a fast marching technique to determine a motion plan on a Voronoi extended transform extracted from the environment model. In addition to this real-time response ability, the method produces smooth and safe robot trajectories.

We consider the task-oriented modeling of the differential kinematics of nonholonomic mobile manipulators (NMMs). A suitable NMM Jacobian is defined that relates the available input commands to the time derivative of the task variables, and can be used to formulate and solve kinematic control problems. When the NMM is redundant with respect to the given task, we provide an extension of two well-known redundancy resolution methods for fixed-base manipulators (Projected Gradient and Task Priority) and introduce a novel technique (Task Sequencing) aimed at improving performance, e.g., avoiding singularities. The proposed methods are applied then to the specific case of image-based visual servoing, where the NMM image Jacobian combines the interaction matrix and the kinematic model of the mobile manipulator. Comparative numerical results are presented for two case studies.

The idea underlying this Special Issue arises from previous successfully international events organized in this robotics context. Thus, during 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, hosted in Edmonton, Canada, a Workshop, with the same title was successfully organized by this guest editor. Moreover, this editor was involved in this research area, as co-Chair of the “Manipulation and Grasping Interest Group”, within the European Robotics Research Network (i.e. EURON), from 2001, organizing also a couple of International Summer Schools, supported by EURON, on these topics (Spain, 2001 and 2004). On the other hand, as time goes by, more and more robotics applications are oriented towards working in all kind of service domains, such as hospitals, museums, etc. Hence, the interest on those robotic systems, integrating manipulation and navigation capabilities, namely mobile manipulators, is drastically increasing around the entire world. Therefore, this special issue is trying to face this new scenario providing a comprehensive overview of some key topics, foundations and applications within the Mobile Manipulators context, including human-robot interaction aspects and critical issues related with navigation and manipulation performance, among others.

Building a probabilistic network for a real-life domain of application is a hard and time-consuming process, which is generally performed with the help of domain experts. As the scope and, hence, the size and complexity of networks are increasing, the need for proper management of the elicited domain knowledge becomes apparent. To study the usefulness of ontologies for this purpose, we constructed an ontology for the domain of oesophageal cancer, based on a real-life probabilistic network for the staging of cancer of the oesophagus and the knowledge elicited for its construction. In this paper, we describe the various components of our ontology and outline the benefits of using ontologies in engineering probabilistic networks.

Let A be a set of N matrices. Let g(A) ≔ |A + A| + |A · A|, where A + A = {a1 + a2 ∣ ai ∈ A} and A · A = {a1a2 ∣ ai ∈ A} are the sum set and product set. We prove that if the determinant of the difference of any two distinct matrices in A is nonzero, then g(A) cannot be bounded below by cN for any constant c. We also prove that if A is a set of d × d symmetric matrices, then there exists ϵ = ϵ(d)>0 such that g(A)>N1+ϵ. For the first result, we use the bound on the number of factorizations in a generalized progression. For the symmetric case, we use a technical proposition which provides an affine space V containing a large subset E of A, with the property that if an algebraic property holds for a large subset of E, then it holds for V. Then we show that the system a2 : a ∈ V is commutative, allowing us to decompose as eigenspaces simultaneously, so we can finish the proof with induction and a variant of the Erdős–Szemerédi argument.

We describe how non-crossing partitions arise in substitution method calculations. By using efficient algorithms for computing non-crossing partitions we are able to substantially reduce the computational effort, which enables us to compute improved bounds on the percolation thresholds for three percolation models. For the Kagomé bond model we improve bounds from 0.5182 ≤ pc ≤ 0.5335 to 0.522197 ≤ pc ≤ 0.526873, improving the range from 0.0153 to 0.004676. For the (3, 122) bond model we improve bounds from 0.7393 ≤ pc ≤ 0.7418 to 0.739773 ≤ pc ≤ 0.741125, improving the range from 0.0025 to 0.001352. We also improve the upper bound for the hexagonal site model, from 0.794717 to 0.743359.

We show that every regular tournament on n vertices has at least n!/(2 + o(1))n Hamiltonian cycles, thus answering a question of Thomassen [17] and providing a partial answer to a question of Friedgut and Kahn [7]. This compares to an upper bound of about O(n0.25n!/2n) for arbitrary tournaments due to Friedgut and Kahn (somewhat improving Alon's bound of O(n0.5n!/2n)). A key ingredient of the proof is a martingale analysis of self-avoiding walks on a regular tournament.

Mobile manipulation involves the most important key issue in robotics: integration. While hardware integration seems to be nearly solved due to the increasing dominance of PC-compatible systems, software integration is still a challenge, since a lot of issues arise with the variety of operating systems, device drivers, application libraries, and programming languages which need to be merged in any real-world robotic system. This paper presents a software architecture, which seamlessly integrates robot arms, mobile bases, vision systems and sensing devices, in a distributed, homogeneous agent framework. Based on the Java platform, the agent-based architecture allows great flexibility in the integration of components, and provides a simple yet extensible and powerful software layer to develop further mobile manipulating environments. Detailed software issues, as well as preliminary results are shown, which pave the way towards the development of network-ready applications involving mobile and manipulating artifacts.

We present an approach to enriching the type system of ML with a restricted form of dependent types, where type index terms are required to be drawn from a given type index language that is completely separate from run-time programs, leading to the DML() language schema. This enrichment allows for specification and inference of significantly more precise type information, facilitating program error detection and compiler optimization. The primary contribution of the paper lies in our language design, which can effectively support the use of dependent types in practical programming. In particular, this design makes it both natural and straightforward to accommodate dependent types in the presence of effects such as references and exceptions.

In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated — informal logic, argumentation theory, evidence law and legal reasoning — but also more recent work in applying and developing it in computer science and artificial intelligence (AI). Beginning with a simple example of an everyday argument, we present an analysis of it visualized as an argument diagram constructed using a software tool. In the context of a brief history of the development of diagramming, it is then shown how argument diagrams have been used to analyse and work with argumentation in law, philosophy and AI.

The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's theorem, the strong isometric dimension of the Hamming graphs K2 □ Kn is determined.

We study a dynamically evolving random graph which adds vertices and edges using preferential attachment and is ‘attacked by an adversary’. At time t, we add a new vertex xt and m random edges incident with xt, where m is constant. The neighbours of xt are chosen with probability proportional to degree. After adding the edges, the adversary is allowed to delete vertices. The only constraint on the adversarial deletions is that the total number of vertices deleted by time n must be no larger than δn, where δ is a constant. We show that if δ is sufficiently small and m is sufficiently large then with high probability at time n the generated graph has a component of size at least n/30.

This paper deals with sensor-based motion planning method for a robot arm manipulator operating among unknown obstacles of arbitrary shape. It can be applied to online collision avoidance with no prior knowledge of the obstacles. Infrared sensors are used to build a description of the robot's surroundings. This approach is based on the configuration space but the construction of the C-obstacle surface is avoided. The point automation is confined on some planes with square grids in the C-space. A path-searching algorithm based on square grids is used to guide the automation maneuvering around the C-obstacles on the selected planes. To avoid the construction of the C-obstacle surface, the robot geometry model is expanded, and the static collision detection method is used. Hence, the computation time is reduced and the algorithm can work in real time. The effectiveness of the proposed method is verified by a series of experiments.

The problem studied in this paper is a mobile robot that autonomously navigates in a domestic environment, builds a map as it moves along and localizes its position in it. In addition, the robot detects predefined objects, estimates their position in the environment and integrates this with the localization module to automatically put the objects in the generated map. Thus, we demonstrate one of the possible strategies for the integration of spatial and semantic knowledge in a service robot scenario where a simultaneous localization and mapping (SLAM) and object detection recognition system work in synergy to provide a richer representation of the environment than it would be possible with either of the methods alone. Most SLAM systems build maps that are only used for localizing the robot. Such maps are typically based on grids or different types of features such as point and lines. The novelty is the augmentation of this process with an object-recognition system that detects objects in the environment and puts them in the map generated by the SLAM system. The metric map is also split into topological entities corresponding to rooms. In this way, the user can command the robot to retrieve a certain object from a certain room. We present the results of map building and an extensive evaluation of the object detection algorithm performed in an indoor setting.

Let be a set of modules and parameterized modules including type sharing constraint specifications. We prove that determining the set of the effective modules described by is undecidable. As a consequence, type sharing constraints are proved to be not always avoidable by constructive transformations.