Circle Constraint Research Articles

List 2-distance coloring for planar graphs with short circle constraints

The [Formula: see text]-[Formula: see text]-distance coloring of the graph [Formula: see text] refers to that it satisfies the mapping: [Formula: see text], such that the vertex [Formula: see text] and [Formula: see text], whose distance is at most [Formula: see text], receive different colors, namely [Formula: see text]. Denote [Formula: see text]distancecoloring}, which is a list 2-distance chromatic number of the graph [Formula: see text]. This paper proves that [Formula: see text] for the graph [Formula: see text] without 3-cycles and intersecting 4-cycles and [Formula: see text].

Automated quantification of glenoid bone loss in CT scans for shoulder dislocation surgery planning.

Estimation of glenoid bone loss in CT scans following shoulder dislocation is required to determine the type of surgery needed to restore shoulder stability. This paper presents a novel automatic method for the computation of glenoid bone loss in CT scans. The model-based method is a pipeline that consists of four steps: (1) computation of an oblique plane in the CT scan that best matches the glenoid face orientation; (2) selection of the glenoid oblique CT slice; (3) computation of the circle that best fits the posteroinferior glenoid contour; (4) quantification of the glenoid bone loss. The best-fit circle is computed with newly defined Glenoid Clock Circle Constraints. The pipeline and each of its steps were evaluated on 51 shoulder CT scans (44 patients). Ground truth oblique slice, best-fit circle, and glenoid bone loss measurements were obtained manually from three clinicians. The full pipeline yielded a mean absolute error (%) for the bone loss deficiency of 2.3 ± 2.9mm (4.67 ± 3.32%). The mean oblique CT slice selection difference was 1.42 ± 1.32 slices, above the observer variability of 1.74 ± 1.82 slices. The glenoid bone loss deficiency measure (%) on the ground truth oblique glenoid CT slice has a mean average error of 0.54 ± 1.03mm (4.76 ± 3.00%), close to the observer variability of 0.93 ± 1.40mm (2.98 ± 4.97%). Our pipeline is the first fully automatic method for the quantitative analysis of glenoid bone loss in CT scans. The computed glenoid bone loss report may assist orthopedists in selecting and planning surgical shoulder dislocation procedures.

A Fast Circle Detection Algorithm Based on Circular Arc Feature Screening

Circle detection is a crucial problem in computer vision and pattern recognition. In this paper, we propose a fast circle detection algorithm based on circular arc feature screening. In order to solve the invalid sampling and time consumption of the traditional circle detection algorithms, we improve the fuzzy inference edge detection algorithm by adding main contour edge screening, edge refinement, and arc-like determination to enhance edge positioning accuracy and remove unnecessary contour edges. Then, we strengthen the arc features with step-wise sampling on two feature matrices and set auxiliary points for defective circles. Finally, we built a square verification support region to further find the true circle with the complete circle and defective circle constraints. Extensive experiments were conducted on complex images, including defective, blurred-edge, and interfering images from four diverse datasets (three publicly available and one we built). The experimental results show that our method can remove up to 89.03% of invalid edge points by arc feature filtering and is superior to RHT, RCD, Jiang, Wang, and CACD in terms of speed, accuracy, and robustness.

A Fourier Approach to Kinematic Acquisition of Geometric Constraints of Planar Motion for Practical Mechanism Design

Abstract This paper studies the problem of geometric constraint acquisition from a given planar motion task using Fourier descriptor. In the previous work, we established a computational geometric framework for simultaneous type and dimensional synthesis of planar dyads by extracting line or circle constraints from a sequence of task poses. In cases where six or more poses are specified as the desired movement, the resulting optimal constraint may be nowhere in the accuracy neighborhood to be viewed as an approximate line or circle. The approach herein enhances the framework by exploiting Fourier transform to capture the feasible constraint of a continuous motion with a large set of poses. Theoretically, any arbitrary point trajectory on the task motion can be transformed to an array of harmonics and used as a constraint; on a practical level, only those with low number of harmonics could allow accurate realization by simple planar mechanisms suitable for real applications, e.g., four- and six-bar linkages, cams, and coupled serial chains. Therefore, the practical goal is to find the simple Fourier constraint defined with the least number of harmonics. Two examples of designing assistive mechanisms for upper- and lower-limb rehabilitation are provided in the end to illustrate the effectiveness of our approach.

Towards longitudinal and lateral coupling control of autonomous vehicles using offset free MPC

Model predictive control (MPC) is widely used in the motion control of autonomous vehicles. However, the conventional MPC relies on an accurate model and cannot achieve offset-free tracking in steady-state when the autonomous vehicle encounters external disturbance and parameter perturbation. Based on our recently designed C++ offset-free MPC (OF-MPC) solver, this paper uses MPC to solve the longitudinal and lateral coupling control problem directly. In the modeling stage, the constraints of the tire friction circle are approximated by the polygon. And then the polygon constraints are mapped into the state and control space. Finally, the tire friction circle constraints are approximated as convex linear inequality constraints, which are used as the vehicle stability boundary condition. Meanwhile, a convex optimization method is used to solve the reference value problem of MPC, and a systematic method that can prevent the reference value from being outside the feasible region is proposed. The real-time simulation and actual vehicle results show that the algorithm can solve both lateral and longitudinal disturbances problems. The algorithm achieves better tracking accuracy and high-speed stability due to consideration of the longitudinal and lateral coupling constraints. Benefiting from the proposed efficient solver, the average time to complete all calculations, including logic processing and input–output processing, is only about 5ms when the horizon length is 50.

Census of bounded curvature paths

A bounded curvature path is a continuously differentiable piece-wise $$C^2$$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and engineering since the bound on curvature models the trajectory of the motion of robots under turning circle constraints. Analyzing global properties of spaces of bounded curvature paths is not a simple matter since the length variation between length minimizers of arbitrary close endpoints or directions is in many cases discontinuous. In this note, we develop a simple technology allowing us to partition the space of spaces of bounded curvature paths into one-parameter families. These families of spaces are classified in terms of the type of connected components their elements have (homotopy classes, isotopy classes, or isolated points) as we vary a parameter defined in the reals. Consequently, we answer a question raised by Dubins (Pac J Math 11(2):471–481, 1961).

Camera calibration with coplanar conics: a unified explanation and ambiguity analysis

In this paper, we propose a two-step method to give a unified explanation of camera calibration with two coplanar conics. Various kinds of conics-based patterns in which often two parameters are unknown have been studied in previous literatures. The key in such algorithms is to adopt different strategies to compute the world-to-image projective transformation (also called 2D homography). In the first step of our method, we show that two unknown parameters can always be computed in general cases by utilizing the underlying constraints on all parameters through the projective transformation (mathematically called projective invariants). The accompanied ambiguity problem is that the solutions of the unknown parameters are multiple. In the second step, the four intersection points (real or complex) of two totally known conics are utilized to compute the homography. The ambiguity in this step arises from the point correspondence problem. This results in multiple possibilities of correspondences followed by the ambiguous homographies. After analyzing the reasons of the two kinds of ambiguities, we apply the Centre Circle constraint to completely remove them. Finally, the experiments are shown to validate the proposed technique.

Applying the unit circle constraint to the diagonal loaded minimum variance distortionless response beamformer

Estimating the direction of arrival of a narrowband planewave using a uniform line array is a common array processing problem. Capon's minimum variance distortionless response (MVDR) adaptive beamformer (ABF) suppresses interferers by steering nulls in their directions while maintaining unity gain in the desired look direction. Practical ABFs replace the ensemble covariance matrix (ECM) with a sample covariance matrix (SCM) estimated from array observations, or snapshots. When the ABF cannot average enough snapshots, the SCM is a poor estimate of the ECM, and may be rank deficient. Applying diagonal loading (DL) to the SCM improves the ABF's performance by limiting the white noise power, but may also limit interferer suppression. Projecting the zeros of the beamformer's array polynomial onto the unit circle (UC) provides deeper nulls to suppress interferers but exhibits worse white noise behavior than DL. The UCDL MVDR beamformer combines the UC constraint with the DL MVDR weights to achieve better SINR than either the UC or DL MVDR alone. Even when the UCDL beamformer suffers mismatch on the DL level, the UCDL SINR rivals or betters the DL MVDR with the optimal DL level. [Research funded by ONR grant N00014-15-1-2238.]

Circle geometric constraint model for open-pit mine ore-matching and its applications

The circle geometric constraint model (CGCM) was put forward for resolving the open-pit mine ore-matching problems (OMOMP). By adopting the approaches of graph theory, block model of blasted piles was abstracted into a set of nodes and directed edges, which were connected together with other nodes in the range of circle constraints, to describe the mining sequence. Also, the constructing method of CGCM was introduced in detail. The algorithm of CGCM has been realized in the DIMINE system, and applied to a short-term (5 d) program calculation for ore-matching of a cement limestone mine in Hebei Province, China. The applications show that CGCM can well describe the mining sequence of ore blocks and its mining geometric constraints in the process of mining blasted piles. This model, which is applicable for resolving OMOMP under complicated geometric constraints with accurate results, provides effective ways to solve the problems of open-pit ore-matching.

Operational optimization of a simulated atmospheric distillation column using support vector regression models and information analysis

Like any other production processes, atmospheric distillation of crude oil is too complex to be accurately described with first principle models, and on-site experiments guided by some statistical optimization method are often necessary to achieve the optimum operating conditions. In this study, the design of experiment (DOE) optimization procedure proposed originally by Chen et al. (1998) and extended later by Chu et al. (2003) has been revised by using support vector regression (SVR) to build models for target processes. The location of future experiments is suggested through information analysis which is based on SVR models for the performance index and observed variables and reduces significantly the number of experiments needed. A simulated atmospheric distillation column (ADC) is built with Aspen Plus (version 11.1) for a real operating ADC. Kernel functions and parameters are investigated for SVR models to represent suitably the behavior of the simulated ADC. To verify the effectiveness of the revised DOE optimization procedure, three case studies are carried out: (1) The modified Himmelblau function is minimized under a circle constraint; (2) the net profit of the simulated ADC is maximized with all the 15 controlled variables free for adjusting in their operational ranges; (3) the net profit of the simulated ADC is maximized with fixed production rates for the three side-draws.

Decline design in underground mines using constrained path optimisation

This paper focuses on the problem of optimising the design of an underground mine decline, so as to minimise the costs associated with infrastructure development and haulage over the lifetime of the mine. A key design consideration is that the decline must be navigable by trucks and mining equipment, hence must satisfy both gradient and turning circle constraints. The decline is modelled as a mathematical network that captures the operational constraints and costs of a real mine, and is optimised using geometric techniques for constrained path optimisation. A deep understanding of the geometric properties of gradient and turning circle constrained paths has led to a very efficient procedure for designing optimal declines. This procedure has been automated in a new version of a software tool, decline optimisation tool. A case study is described indicating the substantial improvements of the new version of the decline optimisation tool over the earlier one.

Network modelling of underground mine layout: two case studies

AbstractThe dominant working structure of an underground mine is a set of interconnected tunnels which provides access to ore zones and haulage of ore from the designated ore zones to the mill. This set of interconnected tunnels forms a network. We describe a mathematical network model and the modelling features of our two software tools for designing underground mine layouts that minimise associated costs. The application of these techniques is illustrated in two industry case studies. In the first, we apply the underground network optimisation tool to design an extension to an Australian gold mine where 15 new distinct orebodies are located in a 3 km long region, several hundred metres underground. In a second case study, we design a single decline for accessing a large orebody where a turning circle constraint is a significant factor. An efficient decline is found using the decline optimisation tool.

Constrained optimization of combustion in a simulated coal-fired boiler using artificial neural network model and information analysis ☆

Combustion in a boiler is too complex to be analytically described with mathematical models. To meet the needs of operation optimization, on-site experiments guided by the statistical optimization methods are often necessary to achieve the optimum operating conditions. This study proposes a new constrained optimization procedure using artificial neural networks as models for target processes. Information analysis based on random search, fuzzy c-mean clustering, and minimization of information free energy is performed iteratively in the procedure to suggest the location of future experiments, which can greatly reduce the number of experiments needed. The effectiveness of the proposed procedure in searching optima is demonstrated by three case studies: (1) a bench-mark problem, namely minimization of the modified Himmelblau function under a circle constraint; (2) both minimization of NO x and CO emissions and maximization of thermal efficiency for a simulated combustion process of a boiler; (3) maximization of thermal efficiency within NO x and CO emission limits for the same combustion process. The simulated combustion process is based on a commercial software package CHEMKIN, where 78 chemical species and 467 chemical reactions related to the combustion mechanism are incorporated and a plug-flow model and a load-correlated temperature distribution for the combustion tunnel of a boiler are used.

Simultaneous Optimization of Dynamic Reactions of a Four-Bar Linkage With Prescribed Maximum Shaking Force

A three-counterweight technique for simultaneously minimizing the maximum values of such dynamic reactions as the bearing force, the input moment, and the shaking moment of a constant input speed four-bar linkage, while additionally obtaining a prescribed maximum value of the shaking force, is introduced. The chosen optimization formulation is new to the field of mechanism design; a certain minimization parameter is made the objective function. The maximum values of the individual dynamic reactions are then minimized by inequality constraints which force the differences between these reactions (due to the presence of counterweights) and the maximum value of the same reactions in the unbalanced mechanism to be smaller than the minimization parameter at as many mechanism positions as required. The prescribed maximum shaking force is attained by an equality constraint which has been called the general equipollent circle constraint equation. The method, which employs an augmented Lagrangian penalty function code, produced good results in the optimization of the dynamic reactions of partially and fully force balanced example mechanisms.

A Novel Method for Prescribing the Maximum Shaking Force of a Four-Bar Linkage with Flexibility in Counterweight Design

A new partial force balancing method for four-bar linkages, which allows the prescribing of the maximum shaking force, is presented. This two-counterweight method is based on the controlled reduction of the size of the shaking force hodograph of the unbalanced mechanism. The introduction of what has been called the equipollent circle constraint equation makes it possible to attain the identical reduction in maximum shaking force for a wide theoretical range of counterweight radii and angles. A sample problem, dealing with a 50 percent reduction in the maximum shaking force, shows that the increases in bearing forces, shaking moments, and input moment are minimal over a considerable portion of this design range.