Gallai-colorings are edge-colored complete graphs in which there are no rainbow triangles. Within such colored complete graphs, we consider Ramsey-type questions, looking for specified monochromatic graphs. In this work, we consider monochromatic bipartite graphs since the numbers are known to grow more slowly than for non-bipartite graphs. The main result shows that it suffices to consider only 3colorings which have a special partition of the vertices. Using this tool, we find several sharp numbers and conjecture the sharp value for all bipartite graphs. In particular, we determine the Gallai-Ramsey numbers for all bipartite graphs with two vertices in one part and initiate the study of linear forests.
Purpose
To achieve stable gait planning and enhance the motion performance of quadruped robot, this paper aims to propose a motion control strategy based on central pattern generator (CPG) and back-propagation neural network (BPNN).
Design/methodology/approach
First, the Kuramoto phase oscillator is used to construct the CPG network model, and a piecewise continuous phase difference matrix is designed to optimize the duty cycle of walk gait, so as to realize the gait planning and smooth switching. Second, the mapper between CPG output and joint drive is established based on BP neural network, so that the quadruped robot based on CPG control has better foot trajectory to enhance the motion performance. Finally, to obtain better mapping effect, an evaluation function is resigned to evaluate the proximity between the actual foot trajectory and the ideal foot trajectory. Genetic algorithm and particle swarm optimization are used to optimize the initial weights and thresholds of BPNN to obtain more accurate foot trajectory.
Findings
The method provides a solution for the smooth gait switching and foot trajectory of the robot. The quintic polynomial trajectory is selected to testify the validity and practicability of the method through simulation and prototype experiment.
Originality/value
The paper solved the incorrect duty cycle under the walk gait of CPG network constructed by Kuramoto phase oscillator, and made the robot have a better foot trajectory by mapper to enhance its motion performance.
There are kinds of defects that may appear in the process of Liquid Crystal Display (LCD) manufacturing, which cannot be effectively detected, owing to the uneven illumination, low contrast, and miscellaneous patterns of defects. To improve the efficiency of defect detection and ensure the quality of LCD, three visual real‐time detection methods are adopted for detecting six different defects in multiple backgrounds, where image preprocessing methods are used to highlight the defects and facilitate the segmentation and detection. Specifically, the interclass variance (OTSU) method is used to segment and mark Liquid Crystal Display (LCD) Mura and scratch defects in six kinds of solid color backgrounds; the method and the connectivity‐4 judgment criteria are adopted to label edge defects in grid display background; the gray mean and standard deviation of the segmented subregions are calculated to recognize the color gradation defect in the 32‐level gradation display background. Experimental results show that LCD Mura defects and scratches can be segmented more completely by the proposed method compared with the benchmark methods, and the edge defects can be identified accurately by the OTSU‐based method and particle‐based morphological processing with grids as the detection background, and the color gradation can also be recognized with the 32‐level gray gradation as the background.
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