Path Generation Problem Research Articles

Path Generation for a Given Performance Evaluation Value Interval by Modifying Bat Algorithm with Heuristic

Path generation means generating a path or a set of paths so that the generated path meets specified properties or constraints. To our knowledge, generating a path with the performance evaluation value of the path within a given value interval has received scant attention. This paper subtly formulates the path generation problem as an optimization problem by designing a reasonable fitness function, adapts the Markov decision process with reward model into a weighted digraph by eliminating multiple edges and non-goal dead nodes, constructs the path by using a priority-based indirect coding scheme, and finally modifies the bat algorithm with heuristic to solve the optimization problem. Simulation experiments were carried out for different objective functions, population size, number of nodes, and interval ranges. Experimental results demonstrate the effectiveness and superiority of the proposed algorithm.

A general automatic method for mechanism optimization based on kinematic constraints and analytical Jacobian matrix

This paper proposes a general formulation intended for dimensional synthesis of kinematic chains based on the derivation of kinematic constraint equations in their matrix form and their subsequent assembly in a system of linear equations. In this way, the proposed formulation allows to calculate in a simple way the partial derivatives of the nodal coordinates of a mechanism with respect to the dimensional or input parameters. Here, a complete mathematical development of the equations is presented, obtaining a formulation suitable for its implementation in computer programs. The main utility of this type of calculation is its application to gradient calculation within optimal dimensional synthesis, being valid for different types of objectives (function, path, and motion generation), and for any planar mechanism composed of any number of elements connected by joints of revolution (R), prismatic (P) or the combination R + P. The developments described in this paper have been implemented in general-purpose GUI software to solve path generation problems.

AUTOMATIC TOOL PATH GENERATION IN CONTOUR MILLING USING GENETIC ALGORITHM

The purpose of this paper is to present new approach in automatic tool path generation in contour milling based on genetic algorithm and bitmap representation of work piece and additional resources. It deals with the problem of tool path generation and optimization in contour milling which is the most common case in metalworking industry. The starting point is assumption that the geometry of initial working piece, machined part and clamping fixtures is represented as bitmaps, then the mathematical model is presented and genetic algorithm is used to generate and optimize tool path. Proposed approach greatly reduced the costs of part production through improved machining efficiency, realized through independent software solution implemented in object-oriented language Delphi and can be used as starting point for fully autonomous NC code generation.

Learning Path Optimization Based on Multi-Attribute Matching and Variable Length Continuous Representation

Personalized learning path considers matching symmetrical attributes from both learner and learning material. The evolutionary algorithm approach usually forms the learning path generation problem into a problem that optimizes the matching degree of the learner and the generated learning path. The proposed work considers the matching of the following symmetrical attributes of learner/material: ability level/difficulty level, learning objective/covered concept, learning style/supported learning styles, and expected learning time/required learning time. The prerequisites of material are considered constraints. A variable-length representation of the learning path is adopted based on floating numbers, which significantly reduces the encoding length and simplifies the learning path generating process. An improved differential evolution algorithm is applied to optimize the matching degree of learning path and learner. The quantitative experiments on different problem scales show that the proposed system outperforms the binary-based representation approaches in scaling ability and outperforms the comparative algorithms in efficiency.

Collision-free and smooth path generation method of five-axis ball-end milling considering effective tool diameter change

Ball-end cutters are widely used in five-axis sculptured surface machining. It is desired to avoid drastic changes of rotary axis movements for improving the kinematics performance of machine tools while ensuring collision-free during five-axis machining. It cannot acquire the optimum solution when cutter orientations are first generated and then adjusted to avoid collisions. The cutter orientations should be generated and optimized in their feasible regions wholly while the computation load is usually large. Different relative postures between a ball-end cutter and workpiece during the machining process will produce different effective tool diameters of the ball-end cutter, resulting in different cutting speeds. Using a variable cutting speed along a tool path can unfavorably affect the process' technological effects (e. g. surface quality, tool life). It is desired to keep the effective tool diameter constant or at a very slightly varying value during five-axis ball-end machining. Moreover, it is also desired to make the cutting point in a high position of the ball-end cutter tool edge, increasing the effective tool diameter. A smooth and collision-free tool path generation method of five-axis ball-end machining while minimizing the effective tool diameter variation and increasing the effective tool diameter of the ball-end cutter along a tool path is proposed. Tool orientations along a tool path are generated and optimized within their feasible regions and the proposed method solves the smoothness tool path generation problem by applying sequentially for the rough and fine search spaces to reduce the computing time. The numerical examples and the machining experiment illustrate the effectiveness of the proposed method.

Exploration of Laser Marking Path and Algorithm Based on Intelligent Computing and Internet of Things.

Nowadays, laser processing technology is being used more and more in various fields, and the requirements for laser control procedures are getting higher and higher. This paper aims to study the path generation problem of laser marking technology in order to improve the efficiency of laser marking as well as the protection of the marking material. Therefore, we creatively propose two-path generation methods, namely, sawtooth parallel and contour parallel, and design the boundary curve offset algorithm and domain partition intersection algorithm for the computer simulation of the two marking paths, respectively. Through the simulation, we discussed the efficiency and marking quality of the two path generation methods and gave the conclusion that the efficiency of the sawtooth parallel path generation method is greater than that of the contour parallel path generation method under specific parameters.

Koopman Operator-Based Knowledge-Guided Reinforcement Learning for Safe Human-Robot Interaction.

We developed a novel framework for deep reinforcement learning (DRL) algorithms in task constrained path generation problems of robotic manipulators leveraging human demonstrated trajectories. The main contribution of this article is to design a reward function that can be used with generic reinforcement learning algorithms by utilizing the Koopman operator theory to build a human intent model from the human demonstrated trajectories. In order to ensure that the developed reward function produces the correct reward, the demonstrated trajectories are further used to create a trust domain within which the Koopman operator–based human intent prediction is considered. Otherwise, the proposed algorithm asks for human feedback to receive rewards. The designed reward function is incorporated inside the deep Q-learning (DQN) framework, which results in a modified DQN algorithm. The effectiveness of the proposed learning algorithm is demonstrated using a simulated robotic arm to learn the paths for constrained end-effector motion and considering the safety of the human in the surroundings of the robot.

Uniform Coverage Tool Path Generation for Robotic Surface Finishing of Curved Surfaces

We provide a novel solution to the problem of robot tool path generation to uniformly cover the surface area of a curved surface with varying curvatures by using a circular, flat finishing tool. We first develop a local contact shape descriptor using tools from differential geometry to estimate the contact shape and its area between the finishing tool and the workpiece surface under an applied normal force. Based on this varying contact area as the tool moves on the surface, we describe a tool path planning strategy that provides full and uniform coverage of a free-form or curved surface with the least amount of overlap. As opposed to fixed spacing paths with point contact in most existing approaches, we provide a novel path generation method where the interval spacing between neighboring path segments is determined by the contact area, which is position-dependent and varies along the surface in accordance with its principal curvatures. An efficient bisection method is employed in the proposed off-line path planning strategy. Numerical studies were conducted for ruled and general curved surfaces to compare the contact areas and coverage of the resulting path with paths generated using two other approaches from the literature. Real-time surface finishing experiments with a six degree-of-freedom robot equipped with a surface finishing tool were also conducted for both these surfaces to validate the proposed approach. Results from the numerical studies and experiments are presented and discussed.

Design of four-bar mechanism for vibratory tillage cultivator using five precision position method for path generation problem

Design of four-bar mechanism for vibratory tillage cultivator using five precision position method for path generation problem

Design of four-bar mechanism for vibratory tillage cultivator using five precision position method for path generation problem

Design of four-bar mechanism for vibratory tillage cultivator using five precision position method for path generation problem

Geometrical Similarity Error Function-Innovative Adaptive Algorithm methodology in path generation synthesis of the four-bar mechanism using metaheuristic algorithms

This paper presents a novel methodology for path generation synthesis of the four-bar mechanism. A new objective function for the path generation synthesis problem, namely, the Geometrical Similarity Error Function (GSEF), is introduced. Indeed, GSEF assesses the similarity between generated and desired paths, and its number of design variables is less than those in the other synthesis methods. Then, using an Innovative Adaptive Algorithm (IAA), some operators are utilized for matching two similar paths. GSEF-IAA methodology has some significant advantages over the reported synthesis methods. The method is fast, takes much less CPU time, and saves a large amount of computer memory. Four path generation problems are solved using GSEF-IAA, and the results are compared with those of previous methods using some well-known optimization algorithms to demonstrate the efficiency of GSEF-IAA methodology.

The Synthesis of Planar Four-Bar Linkage for Mixed Motion and Function Generation.

The synthesis of four-bar linkage has been extensively researched, but for a long time, the problem of motion generation, path generation, and function generation have been studied separately, and their integration has not drawn much attention. This paper presents a numerical synthesis procedure for four-bar linkage that combines motion generation and function generation. The procedure is divided into two categories which are named as dependent combination and independent combination. Five feasible cases for dependent combination and two feasible cases for independent combination are analyzed. For each of feasible combinations, fully constrained vector loop equations of four-bar linkage are formulated in a complex plane. We present numerical examples to illustrate the synthesis procedure and determine the defect-free four-bar linkages.

Robust and efficient tool path generation for machining low-quality triangular mesh surfaces

This paper presents a new method to generate iso-scallop tool paths for triangular mesh surfaces. With the popularity of 3D scanning techniques, scanning-derived mesh surfaces have seen a significant increase in their application to machining. Quite often, such mesh surfaces exhibit defects such as noises, which differentiate them from the good-quality mesh surfaces previous research work focuses on. To generate tool paths for such low-quality mesh surfaces, the primary challenge lies in robustness against the defects. In this work, a robust tool path generation method is proposed for low-quality mesh surfaces. In addition to robustness, the method is quite efficient, providing the benefit of faster iterations and improved integration between scanning and machining. The fundamental principle of the method is to convert the tool path generation problem to the heat diffusion problem that has robust and efficient algorithms available. The effectiveness of the method will be demonstrated by a series of case studies and comparisons.

Constraint handling technique for four-bar linkage path generation using self-adaptive teaching–learning-based optimization with a diversity archive

This article proposes an alternative constraint handling technique for the four-bar linkage path generation problem. The constraint handling technique that is traditionally applied uses an exterior penalty function, and has been found to be inefficient, particularly when dealing with constraints on the input angles. The new technique deals with both input crank rotation and Grashof's criterion. Four classical path generation problems are used to test the performance of the proposed technique. A new adaptive teaching–learning-based optimization (TLBO) scheme is used to solve several optimization problems. This technique is referred to here as teaching–learning-based optimization with a diversity archive (ATLBO-DA), and was specifically developed for this design problem. The results show that this new design concept gives better results than those of previous work, and that ATLBO-DA is superior to the original version and other metaheuristic algorithms.

Research on tool path generation for integrated off-axis four-mirror group in single point diamond turning

Multi-free-surface mirror integrated system is the development trend of optical system, but its ultra-precision machining is very difficult, this paper mainly studies the tool path generation problem of multi-free-surface reflector integrated system. In this paper, two tool path generation methods for the off-axis four-mirror group machining with SPDT are presented, one tool path generation method is separate machining and the other is integrated machining. Both methods are based on cylindrical spiral and generate tool path by projecting points onto surfaces. For the tool path generation method of integrated machining, the linear transition is used to realize the smooth transition of the mirror surfaces. By comparing the simulation machining of two kinds of tool path generating methods, it is found that the integrated tool path generating method is more suitable for off-axis four-mirror group machining and has higher machining efficiency.

A novel analytical method for four-bar path generation synthesis based on Fourier series

This paper presents a novel analytical approach for synthesizing a path-generation mechanism without any limitation on the number of precision points. Compared with classical analytical methods, the novelty of the proposed method is that the synthesis equations were established based on the relationship between the design variables and the Fourier coefficients of the path instead of the displacement matrix. Based on the presented synthesis equations, the path generation problem of planar four-bar linkages was reduced to solving two polynomial equations of low complexity. Moreover, a general formula was derived from the analytical solutions of the new synthesis equations, whereby the design variables could be directly calculated with the Fourier coefficients of the prescribed path. Five examples are provided to evaluate the efficiency and accuracy of the proposed method. The findings indicate that the proposed method is simple, efficient, and readily programmed.

Synthesis of a Spatial RRSS Mechanism for Path Generation Using the Numerical Atlas Method

Abstract An open path synthesis method for a spatial revolute-revolute-spherical-spherical (RRSS) mechanism is presented in this paper. The mathematical model for the trajectory curve is established. The characteristics of an RRSS mechanism in a standard installation position are revealed: the projection points of the coupler curve on the Oxy plane rotate by the corresponding input angles around the z-axis, and the generated points lie on an ellipse. Based on this finding, a 17-dimensional path generation problem can be translated into two lower-dimensional matching recognition problems and one actual size and installation position calculation problem. The path generation can be achieved by three steps. First, a database of four dimensional rotation angle parameters is established. By comparing the similarities between the mechanism feature curve of the prescribed open curve and its corresponding mechanism feature ellipse (MFE), the angles of installation, the initial angle of the input link, and the elliptic feature parameters of the desired RRSS mechanism can be approximately determined. Then, a 13-dimensional dynamic self-adapting numerical atlas database is established, which contains six basic dimensional types (BDTs) and seven wavelet feature parameters, and the BDTs of the desired RRSS mechanism are obtained. Finally, based on the relationship between the MFE of the prescribed curve and the BDTs of the desired RRSS mechanism, the calculation models for the actual link lengths and installation positions of the desired RRSS mechanism were established. Three examples are presented in this paper.

Optimization of planar mechanisms by using a minimum distance function

The paper examines the application of a general minimum distance error function to the dimensional kinematic synthesis of bidimensional mechanisms. The minimum distance approach makes it possible to solve the problem maintaining the same generality as that of the minimum deformation energy method while solving the problems that occasionally appear in the former method involving low stiffness mechanisms. It is a general method that can deal both with unprescribed and prescribed timing problems, and is applicable for path generation problems, function generation, solid guidance, and any combination of the aforementioned requirements as introduced in the usual precision point scheme. The method exhibits good convergence and computational efficiency. The minimum distance error function is solved with a sequential quadratic programming (SQP) approach. In the study, the synthesis problem is also optimized by using SQP, and the function can be easily adapted to other methods such as genetic algorithms.In the study, the minimum distance approach is initially presented. Subsequently, an efficient SQP method is developed by using analytic derivatives for solving. The next point addresses the application of the concept for the synthesis of mechanisms by using an SQP approach with approximate derivatives. This delivers a situation where the optimization is performed on an error function that itself consists of an inner optimization function. A few examples are presented and are also compared with the minimum deformation energy method. Finally, a few conclusions and future studies are discussed.

Alternative Constraint Handling Technique for Four-Bar Linkage Motion Generation

This paper proposes an extension of a new concept for four-bar path generation and a new penalty constraint handling technique from our previous work to a motion generation problem. The proposed technique could neglect the timing constraint for problems without prescribed timing, which is found to be an efficient technique for a four-bar path generation problem. Later, the remaining constraints are solved with a new constraint handling technique that also gives high performance. The technique is one kind of penalty function techniques. The present work proposes to combine the previous two methods for solving the four-bar motion generation problems. The comparative study, optimisation of motion generation problems with a new and a traditional penalty techniqueare solved by using self-adaptive population size teaching-learning based optimization (SAP-TLBO), is presented. In this study, three new motion generation test problems are used to test the proposed technique. The results show that the new technique gives acceptable results and can be applied with the motion generation problems without prescribed timing.

Hybrid Lagrange interpolation differential evolution algorithm for path synthesis

A hybrid Lagrange interpolation differential evolution algorithm (HLIDE) is proposed in this study for path synthesis of four-bar mechanisms. HLIDE combines two algorithms of differential evolution (DE) with Lagrange interpolation local search (LILS). LILS performs a local search in the neighborhood of the best individual to enhance the local exploitation capability of DE. In addition, an adaptive local search strategy is presented to further improve the efficiency of LILS. This technique can adaptively apply LILS based on the performance of LILS and DE in previous generations. To evaluate the efficiency and accuracy of HLIDE, five cases of path synthesis involving four-bar mechanisms were tested. Moreover, three well-known evolutionary algorithms, i.e., particle swarm optimization, teaching-learning-based optimization, and differential evolution, were implemented and compared in the five cases. Previous solutions for the same path generation problems by different evolutionary algorithms are summarized and compared in this study. Experimental results showed that HLIDE has significantly better performance in solving the synthesis problems of mechanisms when compared to other algorithms.