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.

KNOWLEDGE IN ACTION: LOGICAL FOUNDATIONS FOR SPECIFYING AND IMPLEMENTING DYNAMICAL SYSTEMS, by Raymond Reiter, MIT Press, Cambridge, Mass., 2001, xx + 424 pp., ISBN 0-262-18218-l (Hardback, £34.50)

This paper describes a new approach to path planning of robot manipulators with many degrees of freedom. It is designed for on-line motion in dynamic and unpredictable environments. The robots react to moving obstacles using a local and reactive algorithm restricted to a subset of its configuration space. The lack of a long-term view of local algorithms (local minima problems) is solved using an off-line pre-planning stage that chooses the subset of the configuration space that minimises the probability of not finding collision free paths. The approach is implemented and tested on a system of three Scorbot-er IX five link robots.

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

In this paper, a new method – named lumped kinetostatic modeling – to analyze the effect of the link flexibility on the mechanism's stiffness is provided. A new type of mechanism whose degree of freedom (dof) is dependent on a passive constraining leg connecting the base and the platform is introduced and analyzed. With the proposed kinetostatic model, a significant effect of the link flexibility on the mechanism's precision has been demonstrated. The influence of the change in structure parameters, including material properties, on the system behavior is discussed. In the paper, the geometric model of this kind of mechanism is first introduced. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances; some results and design guidelines are obtained. Finally, the optimization of the precision is addressed using a genetic algorithm.