Minimal distance calculation between the industrial robot and its workspace based on circle/polygon-slices representation

The real-time and reliable collision detection is the vital basis for the robotic motion control in real applications. In this work, the minimal distance calculation between the industrial robot and its workspace is presented. This method first uses circular/polygonal slices to represent robotic sub-structures with curved edges more accurately, and uses polygonal planes to construct its workspace. Being the basis of the distance calculation, the shortest distance between the spatial circle/polygon and the polygonal plane, as well as that between the circular/polygonal plane and the polygonal plane are first modelled through spatial relation analysis. The simulation validation indicates that the proposed algorithm is more efficient and reliable than both the point-clouds-based and bounding-volume-hierarchies-based algorithms. And the influence of the refinement size on the performance of the proposed model is revealed. Finally, the application example shows that this work is a significant contribution for the collision-free motion control of the industrial robot. The proposed algorithm can also be applied to the distance calculation of other complex objects because of the generality of the proposed slices representation way.     

Using Estimated Missing Spatial Data with the 2-Median Model

Spatial operations research problems seek best locations, often points of minimum aggregate weighted distance, requiring georeferenced data as input. Frequently maps of such data are incomplete, with holes in their geographic distributions. Spatial statistical procedures are available to complete these data sets with best estimates of the missing values. Impacts such imputations have on 2-median facility location–allocation solutions are explored. The sampling distribution of the spatial mean and standard distance of these medians are studied. Population density is used as the weight attribute in determining location-allocation solutions because it can be accurately described with a relatively simple spatial statistical model.     

Aspects Regarding the Conception,Modeling and Implementation of an Articulated Robot in Space with Noises and Vibrations

The authors want to conceive and to model a structure of a 6R serial modular industrial robot with six freedom degrees. Some specific points are followed: the direct geometric modelling of the robot using the matrix of rotation method, the given in 3D modelling of the robot, the presentation of its components having some possible applications in the processes of production in the spaces with noises and vibrations. The direct geometrical modelling will be determinate the relative orientation matrices, which express the position of each system T_i, (i=1-6), according to the system T_i–1, also expressing the vectors of relative position of origin O_i of the systems T_i. They will be expressed the orientation of each system T_i in account to the fixed system T_o attached to the robot base, the set of independent parameters of orientation then are obtained the final equation of the column vector of the generalized coordinates, which express the position and the orientation of the clamping device. The paper presents the two possible applications of the studied robot implementation in a flexible manufacturing cel for the manipulation operations of parts. The robot will be used on the other side for the execution of weld in a points applied to the car carcases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Accurate Distance Algorithm for Octree‐Encoded Objects

Distance algorithms are most frequently used in robotics to determine the distance between two obstacles in the environment of a robot or between a sensor point and an object. Bounding volumes are a common technique; this technique relies on a hierarchical model representation of the two surfaces using axis‐aligned bounding boxes. Formoving objects it is interesting to use unaligned octrees to avoid the wrapping effect that occurs when performing octree decomposition in a common coordinate system after several rotations. We discuss the algorithm for computing accurate enclosures for the distance between objects represented by axis‐aligned or unaligned octrees. This algorithm is based on a new, recently published distance algorithm between two objects represented by axis‐aligned octrees. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Burgers and Black–Merton–Scholes equations with real time variable and complex spatial variable

The purpose of this article is to study the Burgers and Black–Merton–Scholes equations with real time variable and complex spatial variable. The complexification of the spatial variable in these equations is made by two different methods which produce different equations: first, one complexifies the spatial variable in the corresponding (real) solution by replacing the usual sum of variables (translation) by an exponential product (rotation) and secondly, one complexifies the spatial variable in the corresponding evolution equation and then one searches for analytic and non-analytic solutions. By both methods, new kinds of evolution equations (or systems of equations) in two dimensional spatial variables are generated and their solutions are constructed.     

FOREST ROTATIONS AND STAND INTERDEPENDENCY: OWNERSHIP STRUCTURE AND TIMING OF DECISIONS

ABSTRACT. This paper extends the Hartman model to study the optimal rotation age of two interdependent stands at the steady state, when the rotation ages of the two stands are equal and the stream of amenities produced from the two stands may be complements or substitutes, both in space and over time. In the presence of stand interdependence both the ownership structure and the sequence of decision making matters. Rotation age choices are examined and compared under a variety of equilibria, including Nash, Stackelberg and sole owner cases. We show that the sole owner's rotation age is longer than the rotation age under both Nash and Stackelberg assumptions if the stands are spatial complements but shorter if they are spatial substitutes. The precise relationship between the Nash and Stackelberg rotation ages and the qualitative properties of rotation ages in terms of timber prices, regeneration costs and interest rates also depend on how spatial substitutability and complementarity between stands evolves through time.     

The contributions regarding the conception,designing, modelling and the implementation in a flexible cell of fabrication of a modular serial robot

The authors of the presented paper are propose to relief the calculus, modelling and construction of the translation module of an industrial robot which possess in his cinematic chain five degrees of freedom, type TTRTR. It is propose a choosing variant of the direct current driving engine of the translation module, knowing the output momentum and calculating the input momentum. This is realized by equalize of an equation which results from dynamic modeling of the robot with a designing equation which keep in view the component elements of the structure of the module. The robot is composed by: module of translation on horizontal to the base of the robot (MTB-Sil), module of translation on vertical (MTV-Sil), module of rotation round the vertical axis from the robot's arm, module of translation from the structure of the robot's arm (MT-Sil) and module of orientation assembled with clamping device. In the paper, also is presented an economic study regarding the implementation of the analyzed robot in a manufactural cell concerning the manufacturing and assembling of some types of car radiators. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scheduling for an arc-welding robot considering heat-caused distortion

This paper focuses on an arc-welding robot scheduling problem, which is the problem of determining the sequence of welding operations while avoiding heat-caused distortion for the objective of minimizing the time required to complete a given set of welding operations. Each welding operation is specified by a weld line with two end points, each of which can be a possible starting point of the welding operation for that weld line. Because of the heat-caused distortion, there must be a certain period of time (delay) between welding operations associated with weld lines near each other. We develop several heuristic algorithms, in which heuristics for the travelling salesman problem are modified to cope with characteristics of the problem considered here. To show the performance of the heuristics suggested in this paper, computational experiments are performed on a number of randomly generated test problems and results are reported.     

Trajectory Modeling of Robot Manipulators in the Presence of Obstacles

This paper presents two different strategies for the problem of the optimal trajectory planning of robot manipulators in the presence of fixed obstacles. The first strategy is related to the situation where the trajectory must pass through a given number of points. The second strategy corresponds to the case where only the initial and final points are given. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. The trajectories are defined using spline functions and are obtained through offline computation for online operation. Sequential unconstrained minimization techniques (SUMT) have been used for the optimization. The obstacles are considered as three-dimensional objects sharing the same workspace performed by the robot. The obstacle avoidance is expressed in terms of the distances between potentially colliding parts. Simulation results are presented and show the efficiency of the general methodology used in this paper.     

A random forest application to contact‐state classification for robot programming by human demonstration

This paper addresses the non‐parametric estimation of the stochastic process related to the classification problem that arises in robot programming by demonstration of compliant motion tasks. Robot programming by demonstration is a robot programming paradigm in which a human operator demonstrates the task to be performed by the robot. In such demonstration, several observable variables, such as velocities and forces can be modeled, non‐parametrically, in order to classify the current state of a contact between an object manipulated by the robot and the environment in which it operates. Essential actions in compliant motion tasks are the contacts that take place, and therefore, it is important to understand the sequence of contact states made during a demonstration, called contact classification. We propose a contact classification algorithm based on the random forest algorithm. The main advantage of this approach is that it does not depend on the geometric model of the objects involved in the demonstration. Moreover, it does not rely on the kinestatic model of the contact interactions. The comparison with state‐of‐the‐art contact classifiers shows that random forest classifier is more accurate. Copyright © 2015 John Wiley & Sons, Ltd.     

Cyclic scheduling of a 2-machine robotic cell with tooling constraints

In this study, we deal with the robotic cell scheduling problem with two machines and identical parts. In an ideal FMS, CNC machines are capable of performing all the required operations as long as the required tools are stored in their tool magazines. However, this assumption may be unrealistic at times since the tool magazines have limited capacity and in many practical instances the required number of tools exceeds this capacity. In this respect, our study assumes that some operations can only be processed on the first machine while some others can only be processed on the second machine due to tooling constraints. Remaining operations can be processed on either machine. The problem is to find the allocation of the remaining operations to the machines and the optimal robot move cycle that jointly minimize the cycle time. We prove that the optimal solution is either a 1-unit or a 2-unit robot move cycle and we present the regions of optimality. Finally, a sensitivity analysis on the results is conducted.     

Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.     

Scheduling in robotic cells: Complexity and steady state analysis

This paper considers the scheduling of operations in a manufacturing cell that repetitively produces a family of similar parts on several machines served by a robot. The decisions to be made include finding the robot move cycle and the part sequence that jointly minimize the production cycle time, or equivalently maximize the throughput rate. We focus on complexity issues and steady state performance. In a three machine cell producing multiple part-types, we prove that in two out of the six potentially optimal robot move cycles for producing one unit, the recognition version of the part sequencing problem is unary NP-complete. The other four cycles have earlier been shown to define efficiently solvable part 'sequencing problems. The general part sequencing problem not restricted to any robot move cycle in a three machine cell is shown to be unary NP-complete. Finally, we discuss the ways in which a robotic cell converges to a steady state.     

On the Application of Accurate Distance Algorithms to Multibody Simulations

Distance algorithms are most frequently used in robotics to determine the distance between two obstacles in the environment of a robot or between a sensor point and an object. We extend the multibody simulation package MOBILE for an application of accurate algorithms for distance computation between objects represented by convex or non-convex polyhedra. These objects are represented by their vertices and oriented facets. As an application example, a multibody system is discussed where a sensor point moves close to a non-convex obstacle. The computed results show that the algorithms developed are suitable for accurate real-time multibody simulations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model Based Control of a Parallel Robot – A Comparison of Control Algorithms

In this contribution the control behavior of a special construction of a parallel robot, called multi-axes test facility, is investigated. After a brief discussion of the different tasks of the robot the construction of the robot is briefly presented. To solve the tasks, different control algorithms are derived based on model equations of different complexity of the robot. Depending on the task to be performed by the robot, the controllers compensate the kinematic and/or kinetic coupling of the degrees of freedom of the robot, stabilize the system and achieve the desired spatial motion of each degree of freedom as well as sufficient robustness with respect to parameter uncertainties and load variations. A few results obtained in computer simulations and laboratory experiments are presented and judged with respect to the quality of control, the closeness to reality of the computer simulations, and the amount of costs and work needed to realize the different solutions.     

Models of stochastic geometry — A survey

This paper discusses some models of stochastic geometry which are of potential interest for operations research. These are the Boolean model, a certain model for random compact sets and marked point processes. The Boolean model is a generalization of the well-known queueing systemM/G/. The random compact set model may be useful for modelling spatial spreading processes such as fires, cancers or holes in the Earth's surface. Marked point processes are used here as models of forests and used for a statistical study of the spatial distribution of damaged trees.Extended version of an Invited Lecture on the 16th Symposium for OR in Hamburg 1992.     

Galois theory for sets of operations closed under permutation,cylindrification, and composition

A set of operations on A is shown to be the set of linear term operations of some algebra on A if and only if it is closed under permutation of variables, addition of inessential variables, and composition, and if it contains all projections. A Galois framework is introduced to describe the sets of operations that are closed under the operations mentioned above, not necessarily containing all projections. The dual objects of this Galois connection are systems of pointed multisets, and the Galois closed sets of dual objects are described accordingly. Moreover, the closure systems associated with this Galois connection are shown to be uncountable (even if the closed sets of operations are assumed to contain all projections).     

COILS FOR VECTORSPACE CATEGORIES

Coils as components of Auslander–Reiten quivers of algebras and coil algebras are introduced by Assem and Skowroński. This concept is applied in the present paper to vectorspace categories. The four admissible operations on an Auslander–Reiten component of a vectorspace category, and the notions of v-coils and of vcoil vectorspace categories are introduced. A detailed study on the indecomposable objects of factorspace category of a vcoil vectorspace category is carried out.     

Dynamic Modeling and Force Control of a Redundant Robot for Polishing Applications

For many robotic applications with tasks such as cutting, assembly or polishing, it is necessary to get in contact with the surrounding. In this paper a redundant robot with seven degrees of freedom in a metal polishing task is considered. For simulation as well as for the controller design a dynamic model of the robot and a contact model are required. The equations of motion of the robot are calculated with the Projection Equation in subsystem representation and the contact model contains linear tool elasticities and work piece elasticities. In the case of a polishing task, a constant contact force during the process is required even if the robot moves along a trajectory. Thus some degrees of freedom of the robot tool center point have to be position controlled while the other ones have to be force controlled. The redundant robot offers the possibility to avoid singular positions or to maximize the available end-effector forces within the inverse kinematics and is therefore best suited for polishing large objects. The actual process forces are measured with a six axis force-torque-sensor mounted at the tool center point. These forces are used in a parallel force/position control law to achieve the desired behavior. Results from measurements of a test arrangement are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)