An approach to the path planning of tube–sphere intersection welds with the robot dedicated to J-groove joints

In actual manufacturing process, many weldments have large dimensions and complex shapes, and they are usually assembled through a multi-pass welding process. The joints of the tube–sphere intersection (J-groove joints) are complex. This paper presents a complete solution in determining the welding paths based on a developed J-groove joint robot. Generating complex welding paths in terms of cubic B-spline curves is made easy using path control modules such as interpolation module and local modification module. The point inversion module using particle swarm optimization is introduced to address the partition of path, which is required of the welding process. Experimental results show that higher efficiency as well as better weld quality can be achieved, indicating a promising and practical use of the robot for welding applications, which is rarely available at present.     

A stable Gaussian radial basis function method for solving nonlinear unsteady convection–diffusion–reaction equations

We investigate a novel method for the numerical solution of two-dimensional time-dependent convection–diffusion–reaction equations with nonhomogeneous boundary conditions. We first approximate the equation in space by a stable Gaussian radial basis function (RBF) method and obtain a matrix system of ODEs. The advantage of our method is that, by avoiding Kronecker products, this system can be solved using one of the standard methods for ODEs. For the linear case, we show that the matrix system of ODEs becomes a Sylvester-type equation, and for the nonlinear case we solve it using predictor–corrector schemes such as Adams–Bashforth and implicit–explicit (IMEX) methods. This work is based on the idea proposed in our previous paper (2016), in which we enhanced the expansion approach based on Hermite polynomials for evaluating Gaussian radial basis function interpolants. In the present paper the eigenfunction expansions are rebuilt based on Chebyshev polynomials which are more suitable in numerical computations. The accuracy, robustness and computational efficiency of the method are presented by numerically solving several problems.     

A geometric approach to H∞ control of nonlinear Markovian jump systems

This paper first discusses the H_∞ control problem for a class of general nonlinear Markovian jump systems from the viewpoint of geometric control theory. Following with the updating of the Markovian jump mode, the appropriate diffeomorphism can be adopted to transform the system into special structures, which establishes the basis for the geometric control of nonlinear Markovian jump systems. Through discussing the strongly minimum-phase property or the strongly γ-dissipativity of the zero-output dynamics, the H_∞ control can be designed directly without solving the traditional coupled Hamilton–Jacobi inequalities. A numerical example is presented to illustrate the effectiveness of our results.     

Development of the quadruped walking robot,TITAN-IX — mechanical design concept and application for the humanitarian de-mining robot

This paper proposes a quadruped walking robot that has high performance as a working machine. This robot is needed for various tasks controlled by tele-operation, especially for humanitarian mine detection and removal. Since there are numerous personnel landmines that are still in place from many wars, it is desirable to provide a safe and inexpensive tool that civilians can use to remove those mines. The authors have been working on the concept of the humanitarian demining robot systems for 4 years and have performed basic experiments with the first prototype VK-I using the modified quadruped walking robot, TITAN-VIII. After those experiments, it was possible to refine some concepts and now the new robot has a tool (end-effector) changing system on its back, so that by utilizing the legs as manipulation arms and connecting various tools to the foot, it can perform mine detection and removal tasks. Toaccomplish these tasks, we developed various end-effectors that can be attached to the working leg. In this paper we will discuss the mechanical design of the new walking robot called TITAN-IX to be applied to the new system VK-II.     

A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi–Sugeno fuzzy systems

This paper deals with stability analysis and control design problems for continuous-time Takagi–Sugeno (T–S) fuzzy systems. The first aim is to present less conservative linear matrix inequality (LMI) conditions to design controllers and assess the stability. The second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction (DA) via LMIs. The results are based on the fuzzy Lyapunov functions (FLFs) and non-parallel distributed compensation (non-PDC) approaches. Finally, examples illustrate the effectiveness and merits of the proposed methods.     

A stress–based approach to the optimal design of structures with unilateral behavior of material or supports

The paper presents a stress-based approach that copes with the optimal design of truss-like elastic structures in case of unilateral behavior of material or ground supports. The conventional volume-constrained minimization of compliance is coupled with a set of local stress constraints that are enforced, all over the domain or along prescribed boundaries, to control the arising of members with tension-only or compression-only strength. A Drucker–Prager failure criterion is formulated to provide a smooth approximation of the no-tension or no-compression conditions governing the stress field. A selection strategy is implemented to handle efficiently the multi-constrained formulation that is solved through mathematical programming. Benchmark examples are investigated to discuss the features of the achieved optimal designs, as compared with problems involving material and ground supports with equal behavior in tension and compression. Numerical simulations show that a limited set of constraints is needed in the first iterations to steer the solution of the energy-driven optimization towards designs accounting for the prescribed assumption of unilateral strength.     

A virtual pegging approach to the max–min optimization of the bi-criteria knapsack problem

We are concerned with a variation of the knapsack problem, the bi-objective max–min knapsack problem (BKP), where the values of items differ under two possible scenarios. We have given a heuristic algorithm and an exact algorithm to solve this problem. In particular, we introduce a surrogate relaxation to derive upper and lower bounds very quickly, and apply the pegging test to reduce the size of BKP. We also exploit this relaxation to obtain an upper bound in the branch-and-bound algorithm to solve the reduced problem. To further reduce the problem size, we propose a ‘virtual pegging’ algorithm and solve BKP to optimality. As a result, for problems with up to 16,000 items, we obtain a very accurate approximate solution in less than a few seconds. Except for some instances, exact solutions can also be obtained in less than a few minutes on ordinary computers. However, the proposed algorithm is less effective for strongly correlated instances.     

A timeline for hand function following exposure to 2 °C water

In some regions of the North Atlantic Ocean water temperatures are close to 0 °C for half of the year. Individuals who work in this extremely cold water environment will experience hand temperatures that are associated with reduced hand function (e.g. < 8 °C). Despite this reality there is a paucity of research that indicates how long individuals can work in extremely cold waters before their hand temperature drops below the critical thresholds for hand function. The purpose of this study was to investigate the timeline for hand function following exposure to 2 °C water. Participants immersed their hands in 2 °C water and then fine manual dexterity and tactile sensitivity were assessed every 30 s until the index finger temperature dropped below the critical temperature threshold. The results showed that the initial impairment in tactile sensitivity and fine manual dexterity occurred very quickly (90 s of exposure) and the critical temperature threshold was passed at approximately 120 s. These findings demonstrate that hand function will start to deteriorate in less than 2 min during exposure to extremely cold water and therefore the time window for safe and effective use of the hands in cold water is extremely short. Knowledge concerning the timeline for hand function following cold water exposure is relevant to industry because it can inform occupational time management practices, be used as a criterion for assessing occupational manual performance during training, and be used as a guide to modify behaviours and task requirements for cold water work.     

Human–robot communication for collaborative decision making — A probabilistic approach

Humans and robots need to exchange information if the objective is to achieve a task collaboratively. Two questions are considered in this paper: what and when to communicate. To answer these questions, we developed a human–robot communication framework which makes use of common probabilistic robotics representations. The data stored in the representation determines what to communicate, and probabilistic inference mechanisms determine when to communicate. One application domain of the framework is collaborative human–robot decision making: robots use decision theory to select actions based on perceptual information gathered from their sensors and human operators. In this paper, operators are regarded as remotely located, valuable information sources which need to be managed carefully. Robots decide when to query operators using Value-Of-Information theory, i.e. humans are only queried if the expected benefit of their observation exceeds the cost of obtaining it. This can be seen as a mechanism for adjustable autonomy whereby adjustments are triggered at run-time based on the uncertainty in the robots’ beliefs related to their task. This semi-autonomous system is demonstrated using a navigation task and evaluated by a user study. Participants navigated a robot in simulation using the proposed system and via classical teleoperation. Results show that our system has a number of advantages over teleoperation with respect to performance, operator workload, usability, and the users’ perception of the robot. We also show that despite these advantages, teleoperation may still be a preferable driving mode depending on the mission priorities.     

A method for solving systems of linear interval equations applied to the Leontief input–output model of economics

A new approach to solving systems of linear interval equations based on the generalized procedure of interval extension is proposed. This procedure is based on the treatment of interval zero as an interval centered around zero, and for this reason it is called the “interval extended zero” method. Since the “interval extended zero” method provides a fuzzy solution to interval equations, its interval representations are proposed. It is shown that they may be naturally treated as modified operations of interval division. These operations are used for the modified interval extensions of known numerical methods for solving systems of linear equations and finally for solving systems of linear interval equations. Using a well known example, it is shown that the solution obtained by the proposed method can be treated as an inner interval approximation of the united solution and an outer interval approximation of the tolerable solution, and lies within the range of possible AE-solutions between the extreme tolerable and united solutions. Generally, we can say that the proposed method provides the results which can be treated as approximate formal solutions sometimes referred to as algebraic solutions. Seven known examples are used to illustrate the method’s efficacy and advantages in comparison with known methods providing formal (algebraic) solutions to systems of linear interval equations. It is shown that a new method provides results which are close to the so-called maximal inner solutions (the corresponding method was developed by Kupriyanova, Zyuzin and Markov) and the algebraic solutions obtained by the subdifferential Newton method proposed by Shary. It is important that the proposed method makes it possible to avoid inverted interval solutions. The influence of the system’s size and number of zero entries on the results is analyzed by applying the proposed method to the Leontief input–output model of economics.     

A mini–max spanning forest approach to the political districting problem

We formulate the problem of political districting as a mini–max spanning forest problem, and present some local search-based heuristics to solve the problem approximately. Through numerical experiments, we evaluate the performance of the developed algorithms. We also give a case study of a prefecture in Japan for the election of the Lower House Members of the National Diet. We observe that ‘hyperopic’ algorithm usually gives satisfactory solutions, with the resulting districts all connected and usually balanced in size.     

A two-phase approach to solve the synchronized bin–forklift scheduling problem

In this paper, we propose a two-phase approach to solve a combined routing and scheduling problem that occurs in the textile industry: fabrics are dyed by dye-jets and transported by forklifts. The objective is to minimize the cost of the unproductive activities, i.e., the dye-jet setup times and the forklift waiting time. The first phase solves an integer linear program to assign jobs (fabrics) to dye-jets while minimizing the setup cost; we compare an arc-based and a path-based formulation. The second phase uses a mixed-integer linear program for the dye-jet scheduling and both the routing and scheduling of forklifts. Experiments are performed on real data provided by a major multinational company, and larger test problems are randomly generated to assess the algorithm. The tests were conducted using Cplex 12.6.0 and a column generation solver. The numerical results show that our approach is efficient in terms of both solution quality and computational time.     

A receding–horizon approach to the nonlinear H∞ control problem

The receding–horizon (RH) methodology is extended to the design of a robust controller of H_∞ type for nonlinear systems. Using the nonlinear analogue of the Fake H_∞ algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input–output map of the closed-loop system obtained with the RH control law has a bounded L₂-gain. Robustness properties of the nonlinear H_∞ control law in face of dynamic input uncertainty are considered.     

A shared workspace to support man–machine reasoning: application to cooperative distant diagnosis

This paper focuses on man–machine cooperation problems. In particular, it deals with those problems that occur when both human and machine have to achieve a shared reasoning activity. It puts forward a man–machine approach that is dedicated to technical diagnosis problem solving. Coordination of human and automated reasoning is key to solving this problem, since efficiency depends on both sharing and interpreting exchanged data. A shared workspace is proposed to support both machines and their human operators. This workspace is kept as close as possible to human representations in order to reduce cooperation costs. The paper describes those coordination mechanisms that are able to support such a cooperative activity using a shared workspace. In order to assess the costs and benefits of such cooperation, these mechanisms are applied to a complex industrial problem: diagnosis and troubleshooting in a phone network. The results show the full impact of cooperation on human–machine reasoning.     

Progress and prospects of the human–robot collaboration

Recent technological advances in hardware design of the robotic platforms enabled the implementation of various control modalities for improved interactions with humans and unstructured environments. An important application area for the integration of robots with such advanced interaction capabilities is human–robot collaboration. This aspect represents high socio-economic impacts and maintains the sense of purpose of the involved people, as the robots do not completely replace the humans from the work process. The research community’s recent surge of interest in this area has been devoted to the implementation of various methodologies to achieve intuitive and seamless human–robot-environment interactions by incorporating the collaborative partners’ superior capabilities, e.g. human’s cognitive and robot’s physical power generation capacity. In fact, the main purpose of this paper is to review the state-of-the-art on intermediate human–robot interfaces (bi-directional), robot control modalities, system stability, benchmarking and relevant use cases, and to extend views on the required future developments in the realm of human–robot collaboration.     

Fractional calculus — A new approach to the analysis of generalized fourth-order diffusion–wave equations

The homotopy perturbation method is applied to the generalized fourth-order fractional diffusion–wave equations. The problem is formulated in the Caputo sense. Moreover, a reliable scheme for calculating nonlinear operators is proposed. The results reveal that the present method is very effective and convenient.     

A Bessel polynomial approach for solving general linear Fredholm integro-differential–difference equations

In this paper, to find an approximate solution of general linear Fredholm integro-differential–difference equations (FIDDEs) under the initial-boundary conditions in terms of the Bessel polynomials, a practical matrix method is presented. The idea behind the method is that it converts FIDDEs to a matrix equation which corresponds to a system of linear algebraic equations and is based on the matrix forms of the Bessel polynomials and their derivatives by means of collocation points. The solutions are obtained as the truncated Bessel series in terms of the Bessel polynomials J _n (x) of the first kind defined in the interval [0, ∞). The error analysis and the numerical examples are included to demonstrate the validity and applicability of the technique.     

A meshless method for solving the time fractional advection–diffusion equation with variable coefficients

In this paper, an efficient and accurate meshless method is proposed for solving the time fractional advection–diffusion equation with variable coefficients which is based on the moving least square (MLS) approximation. In the proposed method, firstly the time fractional derivative is approximated by a finite difference scheme of order $O\left({\left(\delta t\right)}^{2?\alpha }\right),0<\alpha \le 1$ and then the MLS approach is employed to approximate the spatial derivative where time fractional derivative is expressed in the Caputo sense. Also, the validity of the proposed method is investigated in error analysis discussion. The main aim is to show that the meshless method based on the MLS shape functions is highly appropriate for solving fractional partial differential equations (FPDEs) with variable coefficients. The efficiency and accuracy of the proposed method are verified by solving several examples.