In elementary robotics, it is very well known that the rotation of an object by the angles respectively Ψ (x), Θ (y), Φ (z) wrt** a fixed coordinate system (RPY) results in the same angular position for the object as the position achieved by the rotation of that object by the angles respectively Φ (z), Θ (y), Ψ (x) wrt a moving (with the object) coordinate system (euler angles). The proofs given up to now for such consequences are not general and for any such problem usually involve the calculation of the transformation matrix for both cases and observing the equivalence of the two matrices [1, 2, 3]. In this paper a fundamental and at the same time general proof is given for such results. It is shown that this equivalence in reverse order can be extended to the general class of transformations which keep the local relations constant (i.e., each transformation should keep the local relations constant). For example, rotation, translation and scaling are 3 types of transformations which can be located in this general class.
The paper presents an application of fuzzy logic modeling techniques for design and development of a classification system for car driver's vigilance level detection. Especially, the micro-sleeps detection is of our primary interest. Detection is based on a pattern analysis of EEG signal spectrograms, which are acquired by monitoring the driver during a driving process. The system is based on the concept of radial implicative fuzzy system, which can be treated as a logical system accommodating acquired knowledge in a structured form.
Data mining nowadays belongs to the most prominent Information
technologies, experiencing a boom of interest from users and software producers. Traditionally, extracting knowledge from data has been a domain of statisticians, and the largest variety of rnethods encountered in commercial data mining systems are actually methods for statistical data analysis tasks. One of the most important ones among them is testing hypotheses about the probability distribution underlying the data. Basically, it consists in checking the null hypothesis that the probability distribution, a priori cissumed to belong to a broad set of distributions, actually belongs to one of its narrow subsets, which must be precisely delimited in advance. However, in a situation in which the data mining is performed, there are seldom enough clues for such a precise delimitation. That is why the generalizations of statistical hypotheses testing to vague hypotheses háve been investigated for more than a decade, so far following the most straightforward way - to replace the set defining the null hypothesis by a fuzzy set. In this páper, a principally different generalization is proposed, based on the observational-logic approach to data mining, and in particular to hypotheses testing. Its key idea is to view statistical testing of a fuzzy hypothesis cis an application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data. The theoretical principles of the approach are elaborated for both crisp and fuzzy significance levels, and illustrated on the quantifier lower critical implication, well known from the data mining system Guha. Finally, the implementation of the approach is briefly sketched.
Over the years, one of the challenges of a rule based expert system is the possibility of evolving a compact and consistent knowledge-base with a fewer numbers of rules that are relevant to the application domain, in order to enhance the comprehensibility of the expert system. In this paper, the hybrid of fuzzy rule mining interestingness measures and fuzzy expert system is exploited as a means of solving the problem of unwieldiness and maintenance complication in the rule based expert system. This negatively increases the knowledge-base space complexity and reduces rule access rate which impedes system response time. To validate this concept, the Coronary Heart Disease risk ratio determination is used as the case study. Results of fuzzy expert system with a fewer numbers of rules and fuzzy expert system with a large numbers of rules are presented for comparison. Moreover, the effect of fuzzy linguistic variable risk ratio is investigated. This makes the expert system recommendation close to human perception.
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set S and inequality relations on Xs = S × R. Moreover, we also investigate a relationship between the functions of S and Xs.
A class of functional equations with nonlinear iterates is discussed on the unit circle ${\mathbb{T}}^1$. By lifting maps on ${\mathbb{T}}^1$ and maps on the torus ${\mathbb{T}}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
A general model of the Dolichopoda cave cricket life cycle was produced using RAMAS/stage simulations based on the Beverton & Holt recruitment function. The model indicates the main population parameters responsible for life cycle adjustments to ecologically different cave habitats. The lack of a uniform rate of oviposition throughout adult life, combined with egg and nymphal diapause, results in regular population growth characterized by adults emerging every two years and cohorts overlapping every other year. This pattern is common in populations living in artificial caves where the scarcity of food is likely to favour individuals that synchronise their activity with the seasonal variations in the epigean habitat. In contrast, a uniform rate of oviposition throughout adult life and no egg or nymphal diapause results in a continuous reproductive activity, and the occurrence of adults all the year round. In this case, it was not possible to distinguish between cohorts. This pattern is well represented in populations inhabiting natural caves with stable food resources. The availability of data for a population that resulted from an experimental colonization allowed us to test this model.
A general synchronization method is proposed for a class of nonlinear chaotic systems involving uncertain parameters and nonlinear transmitted signals. Under some mild conditions, it shows that the class of nonlinear chaotic systems can be treated as linear time-varying systems driven by the additive white noise contaminated at the receiver, or the observed output. Synchronization can be achieved by using Kalman filtering technology. We present some sufficient conditions under which the states of the driven system are able to track the states of the drive system asymptotically, and good tracking performance can be obtained in the presence of the additive white noise involved in the observed output.
We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.
In this paper, a family of hybrid control algorithms is presented; where it is merged a free camera-calibration image-based control scheme and a direct force controller, both with the same priority level. The aim of this generalised hybrid controller is to regulate the robot-environment interaction into a two-dimensional task-space. The design of the proposed control structure takes into account most of the dynamic effects present in robot manipulators whose inputs are torque signals. As examples of this generalised structure of hybrid force/vision controllers, a linear proportional-derivative structure and a nonlinear proportional-derivative one (based on the hyperbolic tangent function) are presented. The corresponding stability analysis, using Lyapunov's direct method and invariance theory, is performed to proof the asymptotic stability of the equilibrium vector of the closed-loop system. Experimental tests of the control scheme are presented and a suitable performance is observed in all the cases. Unlike most of the previously presented hybrid schemes, the control structure proposed herein achieves soft contact forces without overshoots, fast convergence of force and position error signals, robustness of the controller in the face of some uncertainties (such as camera rotation), and safe operation of the robot actuators when saturating functions (non-linear case) are used in the mathematical structure. This is one of the first works to propose a generalized structure of hybrid force/vision control that includes a closed loop stability analysis for torque-driven robot manipulators.