Two well-known orders that have been introduced and studied in reliability theory are defined via stochastic comparison of inactivity time: the reversed hazard rate order and the mean inactivity time order. In this article, some characterization results of those orders are given. We prove that, under suitable conditions, the reversed hazard rate order is equivalent to the mean inactivity time order. We also provide new characterizations of the decreasing reversed hazard rate (increasing mean inactivity time) classes based on variability orderings of the inactivity time of k-out-of-n system given that the time of the (n − k + 1)st failure occurs at or sometimes before time t ≥ 0. Similar conclusions based on the inactivity time of the component that fails first are presented as well. Finally, some useful inequalities and relations for weighted distributions related to reversed hazard rate (mean inactivity time) functions are obtained.

It is known that Cournot game theory has been one of the theoretical approaches used more often to model electricity market behavior. Nevertheless, this approach is highly influenced by the residual demand curves of the market agents, which are usually not precisely known. This imperfect information has normally been studied with probability theory, but possibility theory might sometimes be more helpful in modeling not only uncertainty but also imprecision and vagueness. In this paper, two dual approaches are proposed to compute a robust Cournot equilibrium, when the residual demand uncertainty is modeled with possibility distributions. Additionally, it is shown that these two approaches can be combined into a bicriteria programming model, which can be solved with an iterative algorithm. Some interesting results for a real-size electricity system show the robustness of the proposed methodology.

We compare and test statistical estimates of failure propagation in data from versions of a probabilistic model of loading-dependent cascading failure and a power system blackout model of cascading transmission line overloads. The comparisons suggest mechanisms affecting failure propagation and are an initial step toward monitoring failure propagation from practical system data. Approximations to the probabilistic model describe the forms of probability distribution of cascade sizes.

It is widely accepted that medium-term generation planning can be advantageously modeled through market equilibrium representation. There exist several methods to define and solve this kind of equilibrium in a deterministic way. Medium-term planning is strongly affected by uncertainty in market and system conditions; thus, extensions of these models are commonly required. The main variables that should be considered as subject to uncertainty include hydro conditions, demand, generating units' failures, and fuel prices. This paper presents a model to represent a medium-term operation of the electrical market that introduces this uncertainty in the formulation in a natural and practical way. Utilities are explicitly considered to be maximizing their expected profits, and biddings are represented by means of a conjectural variation. Market equilibrium conditions are introduced by means of the optimality conditions of a problem, which has a structure that strongly resembles classical optimization of hydrothermal coordination. A tree-based representation to include stochastic variables and a model based on it are introduced. This approach to market representation provides three main advantages: Robust decisions are obtained; technical constraints are included in the problem in a natural way, additionally obtaining dual information; and large-size problems representing real systems in detail can be addressed.

This paper addresses computer simulation of cascading failures in electric power systems. The paper analyzes the convergence rates of estimator variance in importance sampling and in random search strategies. A uniform search strategy based on the Metropolis algorithm is proposed.

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of two upper orthant dispersive ordered random vectors are also dispersive ordered. Examples and applications are given.

The distribution of the linear combination αX + βY is derived when X and Y are independent Laplace random variables. Extensive tabulations of the associated percentage points are also given. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing, and other areas of informational sciences.

We propose the use of the cluster distribution, derived from a negative binomial probability model, to estimate the probability of high-order events in terms of number of lines outaged within a short time, useful in long-term planning and also in short-term operational defense to such events. We use this model to fit statistical data gathered for a 30-year period for North America. The model is compared to the commonly used Poisson model and the power-law model. Results indicate that the Poisson model underestimates the probability of higher-order events, whereas the power-law model overestimates it. We use the strict chi-square fitness test to compare the fitness of these three models and find that the cluster model is superior to the other two models for the data used in the study.

This paper describes a simulation model for a multi-legged locomotion system with joints at the legs having viscous friction, flexibility and backlash. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. Moreover, the robot body is divided into several segments in order to emulate the behaviour of an animal spine. The foot-ground interaction is modelled through a non-linear spring-dashpot system whose parameters are extracted from the studies on soil mechanics. To conclude, the performance of the developed simulation model is evaluated through a set of experiments while the robot leg joints are controlled using fractional order algorithms.

Underwater Modular Self-Reconfigurable (UMSR) robots, made up of many identical modules, can adjust their configurations to multiple underwater environments or tasks. They can be used in many complex underwater occasions where the ROVs/AUVs can't work well. However, their reconfiguration is difficult because this has to involve many connection adding and removing operations which are difficult to be executed in the underwater environment. To reduce the times of these operations, we propose the theory of Topological Transformation (TT), which includes some definitions in TT, the basic approach to TT, and the Genetic Algorithm (GA) based solution for the optimal TT.

Parallel kinematic machines (PKMs) and, in particular linapods, are being increasingly used in the industrial workplace. The complex control required for various linapod kinematics, each having different numbers and types of Degrees-of-Freedom (DOF), require corresponding transformations to be generated. This paper introduces a general form of transformation that can be adapted to a wide range of linapods. The approach is illustrated by an example and the concept of a five-DOF linapod for the milling process is proposed. Furthermore, the advantages from the two types of three-DOF Linapods are discussed, and it is shown how the position accuracy can be increased.

Cooperative robots are usually required in flexible manufacturing systems or complex working environments. In particular, when an object under processing is too big or too heavy, a single robot may not be enough to handle it. Two or more manipulators are to be used in such a case. This paper presents the study of the dynamic equations for two industrial robots holding a rigid object. To this end, holonomic constraints are combined with the manipulators and object equations of motion to obtain the dynamic model of the whole system, which can be used for simulation purposes. Experimental results are presented to validate the theoretical results.

An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial kinematic chains or its modification for closed-loop kinematic chains. The method developed is based upon analytical criteria for determining singular behavior of the mechanism. Singularities of manipulators with non-unilateral constraints have never been reported. The complete mathematical formulation is presented and illustrated using 4 & 5 DOF spatial manipulators. Four types of singularities are classified: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint are reaching its apex; Type III sets are domain boundary singularities, which are associated with the time initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II and Type III singularities.

A planar underactuated bipedal robot with an impulsive foot model is considered. The analysis extends previous work on a model with unactuated point feet of Westervelt et al. to include the actuator model of Kuo. The impulsive actuator at each leg end is active only during the double support phase, which results in the model being identical to the model with unactuated point feet for the single support phase. However, the impulsive foot actuation results in a different model for the double support map. Conditions for the existence of a hybrid zero dynamics for the robot with foot actuation are studied. A feedback design method is proposed that integrates actuation in the single and double support phases. A stability analysis is performed using a Poincaré return map. As in Kuo's model, a more efficient gait is demonstrated with an impulsive foot action.

This paper describes external camera-based shape estimation for continuum robots. Continuum robots have a continuous backbone made of sections which bend to produce changes of configuration. A major difficulty with continuum robots is the determination of the robot's shape, as there are no discrete joints. This paper presents a method for shape determination based on machine vision. Using an engineered environment and image processing from a high speed camera, shape determination of a continuum robot is achieved. Experimental results showing the effectiveness of the technique on our Elephant's Trunk Manipulator are presented.

In this work, the elementary task of controlling the contact of a one degree-of-freedom (dof) robot with a compliant surface is modeled as a switched system. A position controller is used for the free motion and a force controller for the contact task and the goal is to stabilize the robot in contact with the spring-like environment while exerting a desired force. As the robot makes or breaks contact, the control law switches accordingly and the aim is to examine the system's stability using ideas from hybrid stability theory. By considering typical candidate Lyapunov functions for each of the two discrete system states, conditions on feedback gains are derived that guarantee Lyapunov stability of the hybrid task. It is shown that conditions can be decoupled with respect to the discrete state only when the more general hybrid stability theorems are used.

An adaptive fuzzy sliding control scheme is proposed to control a passive robotic manipulator. The motivation for the design of the adaptive fuzzy sliding controller is to eliminate the chattering and the requirement of pre-knowledge on bounds of error associated with the conventional sliding control. The stability and convergence of the adaptive fuzzy sliding controller is proven both theoretically and practically by simulations. A three-link passive manipulator model with two unactuated joints is derived to be used in the simulations. Simulation results demonstrate that the proposed system is robust against structured and unstructured uncertainties.

An auto-bonding robot (ABR) that consists of the mechanism of adhesive dispensing and auto-bonding, a pneumatic system and a control system, is presented in this paper. It is designed for the bonding operation of cover-glasses and space solar cells using adhesives. An adhesive dispensing method is proposed to control the thickness and position of the adhesive layer on solar cells and to provide a satisfactory bonding accuracy. The bubble-free bonding process is realized by the leaning mechanism of a pneumatic sucker. Experimental comparison of the manual and automatic bonding methods showed that there are no fragment and air bubbles between the cover-glass and the space solar cell, and no outflow adhesive on the surface by the automatic bonding process in a non-vacuum condition. The novel automatic bonding robot greatly improved the lightweight space solar cells bonding quality and production rate.

For many biological creatures sensory whiskers are an effective means of detecting and recognising nearby objects. The project described in this paper has the aim of demonstrating that whisker sensors can be used as a similarly effective form of robot sensing. Many mobile robots have used whiskers as simple switches to warn of an imminent collision. However, these devices cannot provide the detailed surface profile information required to recognise and accurately locate objects. Several research groups have built advanced whisker sensors that can determine the position of a contact along the length of the whisker. Although these whisker sensors are usually little more than a length of flexible spring material they do require complex sensing and actuation mechanisms at the whisker root. In this project an array of eight whisker sensors is scanned over external objects by the motion of the robot. The resulting deflection of the whiskers is monitored by a potentiometer at each whisker root. By recording the deflection of the whiskers as they slide over external objects sequences of surface points can be determined. Object recognition algorithms have been developed that allow the robot to recognise, grasp and retrieve a range of objects using the whisker data. In this paper the robot, WhiskerBOT, is described together with the object recognition and localisation algorithms. Results of practical experiments are also presented.