A new approach to the design of a fuzzy continuous gain scheduled H∞ controller based on Taylor series fitting for n-joint rigid robotic manipulators, which guarantees satisfactory dynamic characteristics in the whole movement range, is presented. This scheme combines the gain scheduled H∞ theory with the Linear Matrix Inequalities (LMI) approach to design a continuous gain scheduled H∞ controller, which is applicable to systems with fast state variations so that the deficiency of the coventional gain scheduled controllers is overcome, with the use of Taylor series fitting. Fuzzy control is then incorporated so that the design controller possesses the characteristics of a fast response for large errors and a well-damped response for small errors. The system thus always has a good dynamic performance along with the variations of the system states. Simulations and experiments demonstrate the effectiveness of the designed controller.

This paper presents an adaptation of Lowe's numerical model-based camera localisation algorithm to the domain of indoor mobile robotics. While the original method is straightforward and even elegant, it nonetheless exhibits certain weaknesses. First, due to an affine approximation, the method is not consistent with perspective projection especially when the dimensions of objects seen are large in comparison with their distances to the camera. Next, the non-linearity of equations makes convergence properties sensitive both to the initial solution estimate and to noise. By taking the specificity and exigency of the mobile robotics domain into account, a new formulation of this method is proposed in order to improve efficiency, accuracy and robustness in the presence of noisy data and variable initial conditions. According to this formulation, line correspondences are used rather than points, the number of degrees of freedom is reduced, the affine approximation is removed and rotation is uncoupled from translation. Test results with both synthetic and real images illustrate the improvements expected from theoretical modifications.

In order to handle a material with either a delicate surface or an air permeable structure, a novel nozzle was designed and developed. This nozzle utilises the phenomena of the radial air outflow. It is envisaged that this new nozzle will handle materials by eliminating surface marking and air permeable structure problems.

This special issue of Mathematical Structures in Computer Science is devoted to the theory and applications of graph transformations. This research area dates back to the early seventies and is based on mathematical techniques from graph theory, algebra, logic and category theory. The theory of graph transformations has become attractive as a modelling and programming paradigm for complex graphical structures in a large variety of areas in computer science and for applications to other fields. During the Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems (GRATRA 2000) – a satellite of ETAPS 2000 in Berlin – 35 lectures were presented by participants from all over the world. The authors of presentations that stressed the theoretical point of view were invited to submit a full version of their presentation to Mathematical Structures in Computer Science. After a careful refereeing process nine papers have been accepted, seven of which are included in this special issue.

The paper by Ehrenfeucht, Petre, Prescott and Rozenberg connects the important new area of DNA computing in vivo to our area of graph transformation. An application of hypergraph constructions to the static analysis of concurrent systems is presented by König, and normal forms for context-free node rewriting hypergraph grammars by Klempien-Hinrichs. The construction of pushout complements for ‘partly total algebras’ generalising attributed graphs is presented by Burmeister, Llabrés and Roselló. Finally, Courcelle and Makowsky present operations on relational structures (generalising different kinds of graphs and hypergraphs) that are compatible with monadic second order logic. Four other accepted papers could not be included in this special issue because of space limitations.

They will appear in regular issues of MSCS:

— R. Heckel, M. Llabrés, H. Ehrig and F. Orejas: Concurrency and loose semantics of open graph transformation systems.

— L. Helouet, C. Jard and B. Caillaud: An event structure based semantics for high-level message sequence charts.

— J. Larossa and G. Valiente: Constraint satisfaction algorithms for graph pattern matching.

— N. Verlinden and D. Janssens: Algebraic properties for Local Action Systems.

We are most grateful to all the referees of these papers, to Olga Runge and Claudia Ermel for technical support, and to Giuseppe Longo and Cambridge University Press for fruitful cooperation in editing this special issue.

We investigate well-structured graph-driven parity-FBDDs, which strictly generalizethe two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Booleanfunctions represented by well-structured graph-driven parity-FBDDs in terms ofinvariants of the function represented and the graph-ordering used.As a consequence, we derive a lower bound criterion and prove an exponentiallower bound for certain linear code functions.The second main result of this paper is a polynomial time algorithm thatminimizes the number of nodes in a graph-driven parity-FBDD.

We show that, for any stochastic event p of period n, there exists ameasure-once one-way quantum finite automaton (1qfa) with at most $2\sqrt{6n}+25$ states inducing the event ap+b, for constants a>0, b ≥ 0, satisfying a+b ≥ 1. This fact is proved by designing analgorithm which constructs the desired 1qfa in polynomial time. As a consequence, we get that any periodic language of period n can beaccepted with isolated cut point by a 1qfa with no more than $2\sqrt{6n}+26$ states. Our results give added evidence of the strength of measure-once1qfa's with respect to classical automata.

It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem of finding the set of winning positions in a parity game. The algorithm can be seen as a reduction of a parity to a safety game and computation of the set of winning positions in the resulting game.

Given an ordered alphabet anda permutation, according to the lexicographic order,on the set of suffixes of a word w,we present in this article a linear time and space method to determine whether a word w' has the same permutation on its suffixes.Using this method, we are then also able to build the class of all thewords having the same permutation on their suffixes, first of all the smallest one.Finally, we note that this work can lead to a method for generating a Lyndon word randomly in linear time or for computingthe set of Lyndon words of length n.

Two linear numeration systems, withcharacteristic polynomial equal to theminimal polynomial of two Pisot numbers β and γ respectively,such thatβ and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other oneis computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodicpoints of a sofic dynamical system associated with some Parry number.

We investigate the density of critical factorizations of infinite sequences of words. The density of critical factorizationsof a word is the ratio between the number of positions that permit a critical factorization, and the number of all positions of a word. We give a short proof of the Critical Factorization Theorem and show that the maximal number of noncritical positions of a word between two critical ones is less than the period of that word. Therefore, we consider only words of index one, that is words where the shortest period is larger than one half of their total length, in this paper. On one hand, we consider words with the lowest possible number of critical points and show, as an example, that every Fibonacci word longer than five has exactly one critical factorization and every palindrome has at least two critical factorizations. On the other hand, sequences of words with a high density of critical points are considered. We show how to construct an infinite sequence of words in four letters where every point in every word is critical. We construct an infinite sequence of words in three letters with densities of critical points approaching one, using square-free words, and an infinite sequence of words in two letters with densities of critical points approaching one half, using Thue–Morse words. It is shown that these bounds are optimal.

In this paper, two different control methods are developed for an operator-assisted mobile robotic system for high load applications. For high load applications of mobile robots, an accurate tire model that considers wheel slip needs to be studied to achieve robustness of the system response. First, a simple operator-manipulator coordination system is developed based on explicit force control. Then, a position controller for the platform is designed to minimize the effect of wheel slip on control performance and integrated with the force controller for the operator-manipulator subsystem based on a motion coordination scheme. Then, a new type of human-robot coordination control method is developed, in which robust force control of the manipulator and impedance control of the mobile platform are integrated to achieve robust response and smooth interaction between the operator, the manipulator and the mobile platform. In simulation, the developed methods are compared for control performance on following the operator's motion intention.

This paper proposes a method for transversal passing through singularities of corank 1, both for nonredundant and redundant robotic manipulators. The method modifies the Jacobian matrix of manipulator's forward kinematics to retrieve its full rank at singularities. Natural candidates for the Jacobian matrix modification are derivatives of determinants of full size sub-matrices of the Jacobian matrix. The method is illustrated with examples, including a PUMA manipulator and 2-link and 3-link planar manipulators. Some restrictions on the applicability of the method for nonredundant manipulators are also discussed.

This paper presents a general methodology for the off-line planning of optimal trajectory of robot manipulators by taking into account the grasping forces in the manipulator gripper. The mechanical energy of the actuators has been considered for the formulation of the objective function. The optimization problem has been formulated as subject to physical constraints, input torque/force constraints and payload constraints. The mathematical model takes into account the coupled nonlinear equations of manipulator motion. A numerical example shows the efficiency of the proposed procedure.