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Panoramic video multimedia technology has made significant advancements in recent years, providing users with an immersive experience by displaying the entire 360° spherical scene centered around their virtual location. However, due to its larger data volume compared to traditional video formats, transmitting high-quality videos requires more bandwidth. It is important to note that users do not see the whole 360° content simultaneously, but only a portion that is within their viewport. To save bandwidth, viewport-based adaptive streaming has become a significant technology that transmits only the viewports of interest to the user in high quality. Therefore, the accuracy of viewport prediction plays a crucial role. However, the performance of viewport prediction is affected by the size of the prediction window, which decreases significantly as the window size increases. In order to address this issue, we propose an effective self-attention viewport prediction model based on distance constraint in this paper. Firstly, by analyzing the existing viewport trajectory dataset, we find the randomness and continuity of the viewport trajectory. Secondly, to solve the randomness problem, we design a viewport prediction model based on a self-attention mechanism to provide more trajectory information for long inputs. Thirdly, in order to ensure the continuity of the predicted viewport trajectory, the loss function is modified with the distance constraint to reduce the change in the continuity of prediction results. Finally, the experimental results based on the real viewport trajectory datasets show that the algorithm we propose has higher prediction accuracy and stability compared with the advanced models. [ABSTRACT FROM AUTHOR]

This paper investigates the fault-tolerant control problem for vehicular platoons with time-varying actuator fault directions and distance constraints. A bias constraint function is introduced to convert the asymmetric constraints into symmetric ones, based on which a unified barrier Lyapunov function (BLF) method is proposed to ensure distance constraints. Further, an adaptive fixed-time fault-tolerant controller in the context of a sliding mode control technique is proposed, wherein a new Nussbaum function is adopted to address the effects of unknown time-varying actuator fault directions. It is proved that both individual vehicle stability and string stability can all be guaranteed, and the effectiveness of the proposed algorithm is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

The lanes merging control is discussed in this paper for the vehicle platoon while the distance as well as bearing angle constraints among the adjacent vehicles are considered. Differing from the existing strategies, some practical concerns are discussed and dealt with in the controller design. First, to lower the dependence on an accurate system model, an ultra‐local model‐based system description is given. Moreover, an adaptive sliding mode disturbance observer is hence constructed so as to offset the lumped disturbance in the newly transformed system. Second, we divide the multi‐lane fusion target into two parts, namely the distance keeping and bearing angle tracking. Specifically, the distance keeping rules are ensured by utilizing the interval expression‐based prescribed performance control and the newly designed time‐varying integral barrier Lyapunov function. As for the bearing angle tracking, the constraints on the bearing angle and the vehicle's angular velocity are guaranteed by the integral barrier Lyapunov function. In addition to these, the event‐triggered control scheme is also considered during the distance keeping and bearing angle tracking so as to reduce the communication burden. Finally, simulation results are provided to show the effectiveness of the given control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the fault-tolerant control problem for vehicular platoons with time-varying actuator fault directions and distance constraints. A bias constraint function is introduced to convert the asymmetric constraints into symmetric ones, based on which a unified barrier Lyapunov function (BLF) method is proposed to ensure distance constraints. Further, an adaptive fixed-time fault-tolerant controller in the context of a sliding mode control technique is proposed, wherein a new Nussbaum function is adopted to address the effects of unknown time-varying actuator fault directions. It is proved that both individual vehicle stability and string stability can all be guaranteed, and the effectiveness of the proposed algorithm is verified through numerical simulations.

• For calibration of 6-DOF industrial robot, a two-step method is proposed based on distance constraints. • The coupling of MD-H parameters in the calibration is reduced by the grouping strategy. • The grouping strategy of MD-H parameters is optimized by simulations. • The feasibility of two-step calibration is verified by the experiment. The positioning accuracy of industrial robots is critical for their applications, which can be improved through calibration. This paper proposes a two-step calibration method for six-degree-of-freedom (6-DOF) industrial robots to reduce couplings of their modified Denavit-Hartenberg (MD-H) model parameters during optimization processes of kinematic calibration. In this method, a distance error model is established based on the distance constraints, and the MD-H model parameters of the industrial robots are identified group by group using the Levenberg-Marquardt (LM) algorithm. To determine the optimal MD-H model parameter grouping, the different grouping strategies are simulated and analyzed. In the proposed method, the coordinate system transformation between the measurement frame and the robot base frame can be avoided based on the distance error model, thereby reducing the errors introduced by the coordinate system transformation during the calibration process. Finally, the proposed two-step calibration method is verified through an experiment. The experimental result shows that the distance/positioning accuracy on the robot end-effector is improved from 0.602 mm/2.7317 mm to 0.151 mm/0.717 mm after calibration. The presented study may be beneficial for improving performance of industrial robots. [ABSTRACT FROM AUTHOR]

We consider a geometric optimization problem of distributed multi-input multi-output (MIMO) radar systems with widely separated radar nodes in this article. The aim is to maximize the radar surveillance performance in a given area of interest by adjusting the node positions, while satisfying practical spatial distance constraints among radar nodes. Typical constraints can be, for example, the maximum distance constraints between nodes and fusion centers (FCs) due to limited communication and the minimum distance constraints to ensure a better system spatial diversity. To achieve this goal, we first derive an analytical expression for a weighted coverage ratio (WCR) metric to evaluate the system surveillance performance. Then, using the WCR metric as the objective function, we formulate a spatial constrained geometric optimization problem for three typical MIMO radar system architectures, each of which has a unique expression of distance constraints. However, the formulated optimization problem is computationally intractable for practical scenarios due to its high dimensionality, non-convexity and especially the complex spatial constraints. To solve this problem, we propose an enhanced particle swarm optimization (PSO) algorithm, and different from the standard PSO, the particles of the proposed enhanced PSO can properly consider the distance constraints within themselves during swarm optimization process. Finally, various numerical studies show that the proposed method can effectively maximize the surveillance performance while satisfying the complex distance constraints.

This paper focuses on the better performance between the garment simulation result and the simulation speed. For simplicity and clarity, a notation “PART” is defined to indicate the areas between the garment and the human body satisfying some constraints. The discrete mechanical model can be achieved by the two-stage process. In the first stage, the garment can be divided into several PARTs constrained by the distance. In the second stage, the mechanical model of each PART is formulated with a mathematical expression. Thus, the mechanical model of the garment can be obtained. Through changing the constrained distance, the simulation result and the simulation speed can be observed. From the variable distance, a desired value can be chosen for an optimal value. The results of simulations and experiments demonstrate that the better performance can be achieved at a higher speed by saving runtime with the acceptable simulation results and the efficiency of the proposed scheme can be verified as well.

Indoor objects' accessible area generation considering distance constraints is of important realistic significance for spatial analysis. To the best of our knowledge, few studies have been conducted on indoor accessible area generation considering distance constraints. And because of different spatial characteristics between indoor and outdoor environment, the commonly used approach in outdoor space is not suitable for indoor space. In this paper, based on the hybrid spatial data model of geometric and symbolic model, an accessible area generation approach considering distance constraints for indoor environment is proposed by improving traditional spatial buffer zone generation technique. The buffer zone generation with a predefined distance around indoor objects within their located subspace is executed first; then, based on the indoor spatial connectivity, buffer generation around exit points is successively executed in its next connected subspaces until the distance decreases to zero. The merge of these generated buffer zones is the result of accessible area generation with a predefined distance constraint. During the process, two kinds of spatial search strategies, depth-first search and breadth-first search, are presented. Two sets of experiments are conducted to validate the correctness and efficiency of the proposed approach. Results show that the approach can be effectively used to solve the problem of indoor objects' accessible area generation with distance constraints. Moreover, the potential use, as well as the limitation of the proposed approach is discussed in this paper. [ABSTRACT FROM AUTHOR]

In the open location‐routing problem (OLRP), one has a set of candidate depots to be installed and the vehicles start from the depot, visit all customers, and are not required to return to the depot after completing their service. Thus, the OLRP involves the problems of facility location and open vehicle routing. In this paper, a new mixed integer programming formulation for the OLRP is presented by proposing a set of constraints to obtain valid solutions formed by a graph consisting of a spanning tree in each connected component of the graph. This approach results in an alternative way of avoiding generating subtours, which significantly simplifies the set of constraints associated with the connectivity of the solution and the vehicle capacity requirements. The computational results show that the proposed formulation is competitive against state of‐the‐art methods for this type of problems. [ABSTRACT FROM AUTHOR]

Multiple Traveling Repairman Problem with Distance Constraints (MTRPD) is an extension of the NP-hard Multiple Traveling Repairman Problem. In MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers with the following constraints. First, each vehicle's travel distance is limited by a threshold. Second, each customer must be visited exactly once. Our goal is to find the visiting order that minimizes the sum of waiting times. To solve MTRPD we propose to combine the Insertion Heuristic (IH), Variable Neighborhood Search (VNS), and Tabu Search (TS) algorithms into an effective two-phase metaheuristic that includes a construction phase and an improvement phase. In the former phase, IH is used to create an initial solution. In the latter phase, we use VNS to generate various neighborhoods, while TS is employed to mainly prohibit from getting trapped into cycles. By doing so, our algorithm can support the search to escape local optima. In addition, we introduce a novel neighborhoods' structure and a constant time operation which are efficient for calculating the cost of each neighboring solution. To show the efficiency of our proposed metaheuristic algorithm, we extensively experiment on benchmark instances. The results show that our algorithm can find the optimal solutions for all instances with up to 50 vertices in a fraction of seconds. Moreover, for instances from 60 to 80 vertices, almost all found solutions fall into the range of 0.9%--1.1% of the optimal solutions' lower bounds in a reasonable duration. For instances with a larger number of vertices, the algorithm reaches good-quality solutions fast. Moreover, in a comparison to the state-of-the-art metaheuristics, our proposed algorithm can find better solutions. [ABSTRACT FROM AUTHOR]

The Close-Enough Arc Routing Problem, also called Generalized Directed Rural Postman Problem, is an arc routing problem with interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets within a certain distance of a meter, the receiver is able to record the gas, water, or electricity consumption. Therefore, the vehicle does not need to traverse every street, but only a few, in order to be close enough to each meter. In this paper we deal with an extension of this problem, the Distance-Constrained Generalized Directed Rural Postman Problem or Distance-Constrained Close Enough Arc Routing Problem, in which a fleet of vehicles is available. The vehicles have to leave from and return to a common vertex, the depot, and the length of their routes must not exceed a maximum distance (or time). For solving this problem we propose a matheuristic that incorporates an effective exact procedure to optimize the routes obtained. Extensive computational experiments have been performed on a set of benchmark instances and the results are compared with those obtained with an exact procedure proposed in the literature. [ABSTRACT FROM AUTHOR]

This paper focuses on the better performance between the garment simulation result and the simulation speed. For simplicity and clarity, a notation "PART" is defined to indicate the areas between the garment and the human body satisfying some constraints. The discrete mechanical model can be achieved by the two-stage process. In the first stage, the garment can be divided into several PARTs constrained by the distance. In the second stage, the mechanical model of each PART is formulated with a mathematical expression. Thus, the mechanical model of the garment can be obtained. Through changing the constrained distance, the simulation result and the simulation speed can be observed. From the variable distance, a desired value can be chosen for an optimal value. The results of simulations and experiments demonstrate that the better performance can be achieved at a higher speed by saving runtime with the acceptable simulation results and the efficiency of the proposed scheme can be verified as well. [ABSTRACT FROM AUTHOR]

The paper presents a Bézier triangle based isogeometric shape optimization method. Bézier triangles are used to represent both the geometry and physical fields. For a given physical domain defined by B-spline boundary, a coarse Bézier triangular parameterization is automatically generated. This coarse mesh is used to maintain parameterization quality and move mesh by solving a pseudo linear elasticity problem. Then a fine mesh for isogeometric analysis is generated from the coarse mesh through degree elevation and refinement. As the fine mesh retains the same geometric map as the coarse mesh, we can guarantee mesh validity with the coarse mesh only. This bi-level mesh allows us to achieve high numerical accuracy of isogeometric analysis and lower computational cost on mesh validity control and mesh movement. Due to the use of B-spline boundary, the optimized shape can be compactly represented with a relatively small number of optimization variables. Due to the use Bézier triangles, this shape optimization method is applicable to structures of complex topology and allows for local refinement for analysis. By representing the squared distance between two Bézier curves as a Bézier form, a distance check scheme is also introduced to prevent intersections of design boundaries and control the thickness of structural connections. Numerical examples on minimal compliance design and design of negative Poisson ratios are presented to demonstrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

We present a novel analytical method to calculate conformational entropy of ideal cross-linking polymers from the configuration integral by employing a Mayer series expansion. Mayer-functions describing chemical bonds within the chain and for cross-links are sharply peaked over the temperature range of interest, and, are well approximated as statistically weighted Dirac delta-functions that enforce distance constraints. All geometrical deformations consistent with a set of distance constraints are integrated over. Exact results for a contiguous series of connected loops are employed to substantiate the validity of a previous phenomenological distance constraint model that describes protein thermodynamics successfully based on network rigidity.

The sensor localization problem can be formalized using distance and orientation constraints, typically in 3D. Local methods can be used to refine an initial location estimation, but in many cases such estimation is not available and a method able to determine all the feasible solutions from scratch is necessary. Unfortunately, existing methods able to find all the solutions in distance space can not take into account orientations, or they can only deal with one- or two-dimensional problems and their extension to 3D is troublesome. This paper presents a method that addresses these issues. The proposed approach iteratively projects the problem to decrease its dimension, then reduces the ranges of the variable distances, and back-projects the result to the original dimension, to obtain a tighter approximation of the feasible sensor locations. This paper extends previous works introducing accurate range reduction procedures which effectively integrate the orientation constraints. The mutual localization of a fleet of robots carrying sensors and the position analysis of a sensor moved by a parallel manipulator are used to validate the approach. [ABSTRACT FROM AUTHOR]

The multiview variety from computer vision is generalized to images by cameras of points linked by a distance constraint. The resulting five-dimensional variety lives in a product of projective planes. We determine defining polynomial equations, and we explore generalizations of this variety to scenarios of interest in applications. [ABSTRACT FROM AUTHOR]

We further develop our phi-function technique for solving Cutting and Packing problems. Here we introduce quasi-phi-functions for an analytical description of non-overlapping and containment constraints for 2D- and 3D-objects which can be continuously rotated and translated. These new functions can work well for various types of objects, such as ellipses, for which ordinary phi-functions are too complicated or have not been constructed yet. We also define normalized quasi-phi-functions and pseudonormalized quasi-phi-functions for modeling distance constraints. To show the advantages of our new quasi-phi-functions we apply them to the problem of placing a given collection of ellipses into a rectangular container of minimal area. We use radical free quasi-phi-functions to reduce it to a nonlinear programming problem and develop an efficient solution algorithm. We present computational results that compare favourably with those published elsewhere recently. [ABSTRACT FROM AUTHOR]

Many remarkably robust, rapid and spontaneous self-assembly phenomena occurring in nature can be modeled geometrically, starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical, as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates that correspond to various types of macrostates can significantly increase efficiency and accuracy, i.e., reduce the notorious complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency, as well as accuracy vs. efficiency trade-offs in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres, with the following goals. (1) We give new, formal definitions of various concepts relevant to the sphere-based assembly setting that occur in previous work and, in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously-developed concepts include, for example: (i) assembly configuration spaces; (ii) stratification of assembly configuration space into configurational regions defined by active constraint graphs; (iii) paths through the configurational regions; and (iv) coarse assembly pathways. (2) We then demonstrate the new symmetry concepts to compute the sizes and numbers of orbits in two example settings appearing in previous work. (3) Finally, we give formal statements of a variety of open problems and challenges using the new conceptual definitions. [ABSTRACT FROM AUTHOR]

This paper describes a kinematic calibration method developed to improve the accuracy of a six-axis serial industrial robot in a specific target workspace, using distance and sphere constraints. A simulation study demonstrates the ability of the calibration approach to identify the kinematic parameters, regardless of measurement noise. Experimental validation shows that the robot's accuracy inside the target workspace is significantly improved by reducing the mean and maximum distance errors from 0.698 to 0.086 mm and from 1.321 to 0.127 mm, respectively. The experimental data are collected using a Renishaw precision touch probe mounted on the flange of a FANUC LR Mate 200iC and a special triangular plate with three datum 2-in spheres 300 mm apart. The calibration method uses an optimization model based on fitting several probed positions on spheres and minimizing the residual of the spheres' center-to-center distances. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of finding optimal vehicle routes to minimize the overall travel time, with constraints on the minimum and maximum amount of time spent on each route. The problem extends previous work on the distance-constrained vehicle routing problem by introducing lower bounds on route durations to ensure that the resulting routes are balanced. The article also explicitly addresses the situation where a solution is artificially balanced as a result of inoptimal orders of visits. The article describes alternative ways in which the restrictions on route connectivity, duration, and artificial balancing can be formulated, and introduces an exact algorithm based on cutting planes and mixed-integer linear programming. To the best of our knowledge, this is the first exact algorithm proposed for such a problem that explicitly addresses artificially balanced routes. Computational results are presented for three versions of the exact algorithm using TSPLIB instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(2), 166-179 2015 [ABSTRACT FROM AUTHOR]

The sensor localization problem can be formalized using distance and orientation constraints, typically in 3D. Local methods can be used to refine an initial location estimation, but in many cases such estimation is not available and a method able to determine all the feasible solutions from scratch is necessary. Unfortunately, existing methods able to find all the solutions in distance space can not take into account orientations, or they can only deal with one- or two-dimensional problems and their extension to 3D is troublesome. This paper presents a method that addresses these issues. The proposed approach iteratively projects the problem to decrease its dimension, then reduces the ranges of the variable distances, and back-projects the result to the original dimension, to obtain a tighter approximation of the feasible sensor locations. This paper extends previous works introducing accurate range reduction procedures which effectively integrate the orientation constraints. The mutual localization of a fleet of robots carrying sensors and the position analysis of a sensor moved by a parallel manipulator are used to validate the approach.

Many remarkably robust, rapid and spontaneous self-assembly phenomena occurring in nature can be modeled geometrically, starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical, as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates that correspond to various types of macrostates can significantly increase efficiency and accuracy, i.e., reduce the notorious complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency, as well as accuracy vs. efficiency trade-offs in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres, with the following goals. (1) We give new, formal definitions of various concepts relevant to the sphere-based assembly setting that occur in previous work and, in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously-developed concepts include, for example: (i) assembly configuration spaces; (ii) stratification of assembly configuration space into configurational regions defined by active constraint graphs; (iii) paths through the configurational regions; and (iv) coarse assembly pathways. (2) We then demonstrate the new symmetry concepts to compute the sizes and numbers of orbits in two example settings appearing in previous work. (3) Finally, we give formal statements of a variety of open problems and challenges using the new conceptual definitions.

Highlights: [•] We incorporate fuzzy logic to create fuzzy contact maps for helix pairs. [•] Similar distance map regions to a query are retrieved based on fuzzy contact map similarity. [•] Retrieved distance map regions are used to predict a distance map using bound smoothing. [•] The EMBED algorithm is used on the predicted distance map to obtain 3D structure. [•] We obtain good structures at various levels of noise. [Copyright &y& Elsevier]