The Wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. We obtain expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed point equations. Covariances, asymptotic correlations, and bivariate limit laws for the Wiener index and the internal path length are given.

We show that recognizing the K3-freeness and K4-freeness of graphs is hard, respectively, for two-player nondeterministic communication protocols using exponentially many partitions and for nondeterministic syntactic read-r times branching programs.

The key ingredient is a generalization of a colouring lemma, due to Papadimitriou and Sipser, which says that for every balanced red—blue colouring of the edges of the complete n-vertex graph there is a set of εn2 triangles, none of which is monochromatic, such that no triangle can be formed by picking edges from different triangles. We extend this lemma to exponentially many colourings and to partial colourings.

15th TRIENNIAL WORLD CONGRESS OF THE INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL (IFAC), BARCELONA, SPAIN, 21st–26th JULY, 2002

The World Congress under the Spanish presidency (Prof. P. Albertos) brought together about 2000 researchers and practitioners of control theory, technology and applications. The famous Gran Teatro del Liceo of Barcelona was the right location for the opening ceremony, whereas the congress sessions were held at the campus of the Universidad Politecnica de Catalunia.

INTERKAMA AUTOMATION FAIR

Düsseldorf (Germany); February 16–20, 2003.

Enquiries to:

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Postfach 101006

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40474 DÜSSELDORF

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E-mail: info@messe-duesseldorf.de

In this paper we consider thc problem of optimal control design for off-line programming in educational assembly robotics. After introducing some key features for mechanical, electrical design systems and computer-control and programming of a prototype robot, we discuss the control system and the off-line programming for a case study of educational robotics. We propose a new Dynamic Optimal Time-Energy Trajectography (DOTET) controller based on the complete dynamic model of the robot and which takes into account intrinsic and extrinsic constraints, robot singularities and requirements of the task and the environment. Numerical results are given to demonstrate the efficiency of our design.

This paper extends the model developed previously by the authors,1 for studying dynamic stability of mobile manipulators. The extended model not only takes into account the dynamics of the base that can potentially rock back-and-forth, but also accounts for the flexibility of the contact between the base and the ground. A novel method of virtual links is used to reformulate the problem of modeling the non-fixed base manipulator in terms of a fixed-base manipulator with one degree of freedom joints. The resulting model is then used to simulate planar movements of a Caterpillar excavator-based log-loader. The results clearly demonstrate the relationship between movement of the implement and the stability of the machine. The flexible contact between the base and the ground is also shown to influence the stability. The results are also compared with those obtained by the previous model, which assumed rigid contact between the base and the ground. It is demonstrated that the assumption of rigid contact tends to overestimate the stability. Consequently, flexibility in the contact bet- ween the base and the ground must be considered to more accurately predict the stability of mobile manipulators.

I. AUTOMATION REPORTS

I.1. UK Manufacturers Buy Largest Number of Robots Since Records Began in 1978

Latest research figures from the University of Warwick (UK) show that UK manufacturers installed a record breaking 1,941 robots in 2001 – the largest number of new robots ever installed in the UK in any one year since records began in 1978.

A top to random shuffle of a deck of cards is performed by taking the top card off of the deck and replacing it in a randomly chosen position of the deck. We find approximations of the relative entropy of a deck of n cards after m successive top to random shuffles. Initially the relative entropy decays linearly and for larger m it decays geometrically at a rate that alters abruptly at m = n log n. It converges to an explicitly given expression when m = [n log n+cn] for a constant c.

We answer a question of Sós by showing that, if a graph G of order n and density p has no complete minor larger than would be found in a random graph G(n, p), then G is quasi-random, provided either p > 0.45631 … or κ(G) [ges ] n(log log log n)/(log log n), where 0.45631 … is an explicit constant.

The results proved can also be used to fill the gaps in an argument of Thomason, describing the extremal graphs having no Kt minor for given t.

Robots are expected to be pervasive in the society in a not too distant future where they will work extensively as assistants of humans in various activities. With this in view, a novel affect-sensitive architecture for human-robot cooperation is presented in this paper where the robot is expected to recognize human psychological states. As a demonstration, an online heart rate variability analysis to infer the mental stress of a human engaged in a task is presented. This technique involves real-time heart rate monitoring, signal processing using both Fourier Transforrn and Wavelet Transform, and inferring the stress condition based on the level of activation of the sympathetic and parasympathetic nervous systems using fuzzy logic. Results from human subject trials are presented to validate the presented methodology. This stress detection technique is expected to be useful in the future human-robot cooperation activities, where the robot will recognize human stress and respond appropriately.

This paper presents an attractive position-based visual servoing approach for camera-in-hand robotic systerns. The major contribution of this work is in devising an elegant and pragmatic approach for 3D visual tracking, which yielded good target tracking performance. It differs from the other known techniques, in its approach for image interpretation and the introduction of a Smith-like predictor control structure to overcome the inherent multi-rate time delayed nature of the visual servoing system. A complete description is made of the proposed MSP-DH visual servoing system. Experiments on the target tracking performance on XY planar motion using an AdeptOne robotic system are presented to illustrate the controller performance. In addition, experimental results have clearly shown the capability of the MSP-DH visual servoing system in performing 3D-dynamic visual servoing.

The use of Clifford or geometric algebra for dealing with three dimensional geometry is discussed. One issue is the representation of the rigid body motions of rotations and translations as elements within the algebra. The approach used is to work with projective geometry and choose the square of an additional basis element to be large (infinite). This allows Euclidean points to be represented as vectors in the algebra and transforms on these to be handled using bivectors. This paper looks at the use of Clifford algebra for handling the types of transforms required in robotic applications. A number of example applications are given.

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.

A multifunctional 4 legged walking machine that is being developed in the Robotics Research Centre (NTU) is described. The major factors influencing the design requirements include minimisation of the weight of the machine and maximisation of workspace of the legs. The designed walking machine can adopt a variety of configurations, such as insect, mammalian, reptile or human. The device is invertable (i.e. can turn over). It can use its legs as manipulators, hence it can perform basic pick-and-place functions. A control system was built using the QNX real-time operating system platform. The software was designed using the client-server approach.

In this paper we study distances in random subgraphs of a generalized n-cube [Qscr]ns over a finite alphabet S of size s. [Qscr]ns is the direct product of complete graphs over s vertices, its vertices being the n-tuples (x1, …, xn), with xi ∈ S, i = 1, … n, and two vertices being adjacent if they differ in exactly one coordinate. A random (induced) subgraph γ of [Qscr]ns is obtained by selecting [Qscr]ns-vertices with independent probability pn and then inducing the corresponding edges from [Qscr]ns. Our main result is that dγ(P,Q) [les ] [2k+3]d[Qscr]ns(P,Q) almost surely for P,Q ∈ γ, pn = n−a and 0 [les ] a < ½, where k = [1+3a/1−2a] and dγ and d[Qscr]ns denote the distances in γ and [Qscr]ns, respectively.

This paper focuses on using a singularly perturbed approach to derive a vibration damping control law in which a pole assignment feedback method is utilized. The composite control system is characterized by two components which can be computed separately. The one is Cartesian-based PI control which drives the end-effector of a flexible manipulator to track the desired time-based trajectory. The other is pole assignment feedback control which damps out vibrations during and at the end of trajectory tracking. An advantage of this composite control method in real implementation is that it does not require a derivative of the end-effector's position, and the derivatives of signals from the strain gauges. From the characteristics and implementation points of view, it appears to be simple to use. Laboratory experiments were conducted to evaluate the performance of the proposed control method.

The hexagonal lattice site percolation critical probability is shown to be at most 0.79472, improving the best previous mathematically rigorous upper bound. The bound is derived by using the substitution method to compare the site model with the bond model, the latter of which is exactly solved. Shortcuts which eliminate a substantial amount of computation make the derivation of the bound possible.