This paper describes a hybrid approach to a fast and accurate localization method for legged robots based on Fuzzy-Markov (FM) and Extended Kalman Filters (EKF). Both FM and EKF techniques have been used in robot localization and exhibit different characteristics in terms of processing time, convergence, and accuracy. We propose a Fuzzy-Markov–Kalman (FM–EKF) localization method as a combined solution for a poor predictable platform such as Sony Aibo walking robots. The experimental results show the performance of EKF, FM, and FM-EKF in a localization task with simple movements, combined behaviors, and kidnapped situations. An overhead tracking system was adopted to provide a ground truth to verify the performance of the proposed method.

A set of integers is called a B2[g] set if every integer m has at most g representations of the form m = a + a′, with a ≤ a′ and a, a′ ∈ . We obtain a new lower bound for F(g, n), the largest cardinality of a B2[g] set in {1,. . .,n}. More precisely, we prove that infn→∞ where ϵg → 0 when g → ∞. We show a connection between this problem and another one discussed by Schinzel and Schmidt, which can be considered its continuous version.

We study the asymptotic distribution of the displacements in hashing with coalesced chains, for both late-insertion and early-insertion. Asymptotic formulas for means and variances follow. The method uses Poissonization and some stochastic calculus.

Gerards and Seymour (see [10], p. 115) conjectured that if a graph has no odd complete minor of order l, then it is (l − 1)-colourable. This is an analogue of the well-known conjecture of Hadwiger, and in fact, this would immediately imply Hadwiger's conjecture. The current best-known bound for the chromatic number of graphs with no odd complete minor of order l is by the recent result by Geelen, Gerards, Reed, Seymour and Vetta [8], and by Kawarabayashi [12] later, independently. But it seems very hard to improve this bound since this would also improve the current best-known bound for the chromatic number of graphs with no complete minor of order l.

Motivated by this problem, in this note we show that there exists an absolute constant f(k) such that any graph G with no odd complete minor of order k admits a vertex partition V1, . . ., V496k such that each component in the subgraph induced on Vi (i ≥ 1) has at most f(k) vertices. When f(k) = 1, this is a colouring of G. Hence this is a relaxation of colouring in a sense, and this is the first result in this direction for the odd Hadwiger's conjecture.

Our proof is based on a recent decomposition theorem due to Geelen, Gerards, Reed, Seymour and Vetta [8], together with a connectivity result that forces a huge complete bipartite minor in large graphs by Böhme, Kawarabayashi, Maharry and Mohar [3].

Requirements about the quality of clinical guidelines can be represented byschemata borrowed from the theory of abductive diagnosis, using temporal logicto model the time-oriented aspects expressed in a guideline. Previously, we haveshown that these requirements can be verified using interactive theorem provingtechniques. In this paper, we investigate how this approach can be mapped to thefacilities of a resolution-based theorem prover, otter and acomplementary program that searches for finite models of first-order statements,mace-2. It is shown that the reasoning required for checking thequality of a guideline can be mapped to such a fully automated theorem-provingfacilities. The medical quality of an actual guideline concerning diabetesmellitus 2 is investigated in this way.

Sokal in 2001 proved that the complex zeros of the chromatic polynomial PG(q) of any graph G lie in the disc |q| < 7.963907Δ, where Δ is the maximum degree of G. This result answered a question posed by Brenti, Royle and Wagner in 1994 and hence proved a conjecture proposed by Biggs, Damerell and Sands in 1972. Borgs gave a short proof of Sokal's result. Fernández and Procacci recently improved Sokal's result to |q| < 6.91Δ. In this paper, we shall show that all real zeros of PG(q) are in the interval [0,5.664Δ). For the special case that Δ = 3, all real zeros of PG(q) are in the interval [0,4.765Δ).

This paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

This work considers the problem of force/position regulation for a robotic finger in compliant contact with an unknown curved surface resulting in uncertain force and position control subspaces. The proposed controller is an adaptive control scheme of a simple structure that achieves the desired target by the on-line tuning of the position and force control actions to their corresponding actual subspaces at the desired point using motion state feedback. The local asymptotic stability of the system equilibrium point is proved and an estimate of the region of attraction is given. The controller performance is illustrated by a simulation example.

In this paper, a Gaifman–Shapiro-style module architecture is tailoredto the case of smodels programs under the stable model semantics. Thecomposition of smodels program modules is suitably limited by moduleconditions which ensure the compatibility of the module system with stablemodels. Hence the semantics of an entire smodels program dependsdirectly on stable models assigned to its modules. This result is formalized asa module theorem which truly strengthens V. Lifschitz and H.Turner's splitting-set theorem (June 1994, Splitting a logic program. InLogic Programming: Proceedings of the Eleventh InternationalConference on Logic Programming, Santa Margherita Ligure, Italy, P.V. Hentenryck, Ed. MIT Press, 23–37) for the class of smodelsprograms. To streamline generalizations in the future, the module theorem isfirst proved for normal programs and then extended to cover smodelsprograms using a translation from the latter class of programs to the formerclass. Moreover, the respective notion of module-level equivalence, namelymodular equivalence, is shown to be a proper congruencerelation: it is preserved under substitutions of modules that are modularlyequivalent. Principles for program decomposition are also addressed. Thestrongly connected components of the respective dependency graph can beexploited in order to extract a module structure when there is no explicita priori knowledge about the modules of a program. Thepaper includes a practical demonstration of tools that have been developed forautomated (de)composition of smodels programs.

A graph construction game is a Maker–Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graph KN. Maker's aim is to claim a copy of a given target graph G while Breaker's aim is to prevent Maker from doing so. In this paper we show that if G is a d-degenerate graph on n vertices and N > d1122d+9n, then Maker can claim a copy of G in at most d1122d+7n rounds. We also discuss a lower bound on the number of rounds Maker needs to win, and the gap between these bounds.

Let ai,bi, i = 0, 1, 2, . . . be drawn uniformly and independently from the unit interval, and let t be a fixed real number. Let a site (i, j) ∈ be open if ai + bj ≤ t, and closed otherwise. We obtain a simple, exact expression for the probability Θ(t) that there is an infinite path (oriented or not) of open sites, containing the origin. Θ(t) is continuous and has continuous first derivative except at the critical point (t=1), near which it has critical exponent (3 − )/2.

The paper is concerned with the relationship between the equation of elastic line motion, the “Euler-Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

A two-channel bilateral controller is proposed for teleoperation systems. The controller takes into account both the free space motion and the constrained motion. Specifically, the force-position (F-P) architecture is applied during the constrained motion, while the position-position (P-P) architecture is applied during the free space motion. Theoretically, perfect transparency can be achieved. In addition, it does not need to switch the control modes of the master and the slave controllers during the transition between the free space motion and the constrained motion. Experiments are conducted to validate the analysis, and to demonstrate the effectiveness of the proposed bilateral controller. The limitations of the proposed controller are also discussed.

Knowledge of the physical properties of terrain surrounding a planetary exploration rover can be used to allow a rover system to fully exploit its mobility capabilities. Terrain classification methods provide semantic descriptions of the physical nature of a given terrain region. These descriptions can be associated with nominal numerical physical parameters, and/or nominal traversability estimates, to improve mobility prediction accuracy. Here we study the performance of multisensor classification methods in the context of Mars surface exploration. The performance of two classification algorithms for color, texture, and range features are presented based on maximum likelihood estimation and support vector machines. In addition, a classification method based on vibration features derived from rover wheel–terrain interaction is briefly described. Two techniques for merging the results of these “low-level” classifiers are presented that rely on Bayesian fusion and meta-classifier fusion. The performance of these algorithms is studied using images from NASA's Mars Exploration Rover mission and through experiments on a four-wheeled test-bed rover operating in Mars-analog terrain. Also a novel approach to terrain sensing based on fused tactile and visual features is presented. It is shown that accurate terrain classification can be achieved via classifier fusion from visual and tactile features.

Let G denote a finite abelian group of order n and Davenport constant D, and put m = n + D − 1. Let x = (x1,. . .,xm) ∈ Gm. Gao's theorem states that there is a reordering (xj1, . . ., xjm) of x such that

Let w = (x1, . . ., wm) ∈ ℤm. As a corollary of the main result, we show that there are reorderings (xj1, . . ., xjm) of x and (wk1, . . ., wkm) of w, such thatwhere xj1 is the most repeated value in x. For w = (1, . . ., 1), this result reduces to Gao's theorem.

Disjunctive logic programming (DLP) is a very expressive formalism. It allows forexpressing every property of finite structures that is decidable in thecomplexity class ΣP2(=NPNP). Despite this high expressiveness, thereare some simple properties, often arising in real-world applications, whichcannot be encoded in a simple and natural manner. Especially properties thatrequire the use of arithmetic operators (like sum, times, or count) on a set ormultiset of elements, which satisfy some conditions, cannot be naturallyexpressed in classic DLP. To overcome this deficiency, we extend DLP byaggregate functions in a conservative way. In particular, we avoid theintroduction of constructs with disputed semantics, by requiring aggregates tobe stratified. We formally define the semantics of the extended language (called ), and illustrate how it can be profitably used for representingknowledge. Furthermore, we analyze the computational complexity of , showing that the addition of aggregates does not bring a highercost in that respect. Finally, we provide an implementation of in DLV—a state-of-the-art DLP system—andreport on experiments which confirm the usefulness of the proposed extensionalso for the efficiency of computation.

This part of the paper investigates the wrench capabilities of redundantly actuated planar parallel manipulators (PPMs). The wrench capabilities of PPMs are determined by mapping a hypercube from the torque space into a polytope in the wrench space. For redundant PPMs, one actuator output capability constrains the wrench space with a smaller polytope that is contained inside the overall polytope. Performance indices are derived from six study cases. These indices are employed to analyze the wrench workspace for constant orientation of the mobile platform of the non-redundant 3-RRR PPM, and actuation redundant 4-RRR and 3-RRR PPMs, where the underline indicates the actuated joints. A comparison of the results shows that both of the redundantly-actuated PPMs give better wrench capabilities than the non-redundant PPM. However, it is shown that scaled for the operational cost (wrench capabilities divided by total actuation output) the non-redundant 3-RRR PPM provides the highest maximum reachable force, the 3-RRR PPM produces the highest isotropic force, and the 4-RRR yields the highest reachable moment.

Operational space control of industrial robots is addressed in this document. We analyze a two-loop hierarchical control with the resolved motion rate controller (RMRC) as outer loop and the joint velocity PI controller as inner loop; the latter is the typical velocity controller used in industrial robots. We prove, by the first time, that these simple controllers make the solutions of the closed-loop system uniformly ultimately bounded. Additionally, we give some simple guidelines for the selection of the control gains so as to ensure an explicit bound of the tracking error.

We consider Glauber dynamics on finite spin systems. The mixing time of Glauber dynamics can be bounded in terms of the influences of sites on each other. We consider three parameters bounding these influences: α, the total influence on a site, as studied by Dobrushin; α′, the total influence of a site, as studied by Dobrushin and Shlosman; and α″, the total influence of a site in any given context, which is related to the path-coupling method of Bubley and Dyer. It is known that if any of these parameters is less than 1 then random-update Glauber dynamics (in which a randomly chosen site is updated at each step) is rapidly mixing. It is also known that the Dobrushin condition α < 1 implies that systematic-scan Glauber dynamics (in which sites are updated in a deterministic order) is rapidly mixing. This paper studies two related issues, primarily in the context of systematic scan: (1) the relationship between the parameters α, α′ and α″, and (2) the relationship between proofs of rapid mixing using Dobrushin uniqueness (which typically use analysis techniques) and proofs of rapid mixing using path coupling. We use matrix balancing to show that the Dobrushin–Shlosman condition α′ < 1 implies rapid mixing of systematic scan. An interesting question is whether the rapid mixing results for scan can be extended to the α = 1 or α′ = 1 case. We give positive results for the rapid mixing of systematic scan for certain α = 1 cases. As an application, we show rapid mixing of systematic scan (for any scan order) for heat-bath Glauber dynamics for proper q-colourings of a degree-Δ graph G when q ≥ 2Δ.