AbstractsMathematics

Traditionally images are digitized, processed and displayed in a rectangular grid. But rectangular grid has many inherent ambiguities such as continuity, inter-pixel distance, etc. These ambiguities restrict rectangular grid to obtain better results in low resolution image processing. This study considers a particular topic of mathematical morphology image processing based on binary, grayscale and fuzzy discipline for hexagonally sampled low resolution images and multi-legged robot walking strategies. The proposed research presents a methodology for hexagonally sampled images that consist of processing, and display of processed images on hexagonal grid. Image processing includes binary, grayscale and fuzzy morphological operations with different sizes, shapes and directional fuzzy structuring elements with an application of noise removal and edge detection. Edge detection method for low resolution images are very significant for multi-legged robot walking strategy with low computation power in real time applications. Edge detection method can aid multi-legged robot to avoid standing zone edges, gaps/obstacles etc. Moreover, if a leg is damaged, then robot needs some alternative strategies to complete its mission. Thus, this study proposes a removable leg and sliding leg approach to solve this problem. A fault leg can be detaches and other legs can be slide to better position by the command of operator to get better alternative gait configuration. Based on leg sequence, stride length, longitudinal stability and efficiency, alternative gaits are evaluated. This study recommends tables for different gait sequence with progressive efficiency. These tables can provide options for alternative gait and information about certain damaged leg. Moreover, a procedure for a multiâlegged robot to complete its mission after serious leg failure is included. By taking the recommended tables and procedure, the multi-legged robot can overcome any fault event and maintain stability and efficiency. In addition, performance evaluation conducted to demonstrate that hexagonal grid structure coupled with binary, grayscale and fuzzy morphological image processing is more robust than the rectangular counterpart in many applications including edge detection for low resolution images, multi-legged robot walking strategy etc.