Video Puzzle Game Application of Polyomino Re-tiling

Jho, Cheung-Woon; Lee, Won-hyung

doi:10.1007/978-94-007-5076-0_43

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…Although robots that were developed under the polyomino principle demonstrated exceptional area coverage performance, they are explicitly designed for impartial spaces. The polyomino robots consist of square blocks wherein the system can perform better in an impartial area [12]- [14]. However, performance degradation can occur if it is deployed in a non-parallelogram structured space.…”

Section: Introductionmentioning

confidence: 99%

Application of Tiling Theory for Path Planning Strategy in a Polyiamond Inspired Reconfigurable Robot

et al. 2019

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Commercial floor cleaning robots face significant challenges in accessing convex and narrow corners due to their fixed and regular morphologies. To overcome this, we develop a new class of selfreconfigurable floor cleaning robot, hTetrakis, which is composed of tetriamonds (four equilateral triangles aligned along the edges) that adopt three distinct forms (''I'', ''A'', and ''U'' shapes). When on a flat and rigid platform, these forms have convex corners that help to cover narrow regions. This paper addresses the mechanical structural design, reconfiguration of the robot platform through the hinge mechanism, and the electronics and navigation module of hTetrakis. Based on finite element studies, we estimate the system's natural frequency, stress, and deformation patterns developed in the structural components of the robot, and validate the proposed design to overcome structural failure and system resonance. In order to achieve maximum area coverage using the tetriamond forms, we formulate tiling theorems and apply them for pathplanning techniques during the floor cleaning process. By using a robot prototype, we conduct experiments to validate the proposed tiling theorem based on the percentage of area coverage, and demonstrate that this platform is able to cover the floor area efficiently. INDEX TERMSCoverage area, path planning strategy, polyiamond tiling theory, reconfigurable floor cleaning robots.

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Section: Introductionmentioning

confidence: 99%

Application of Tiling Theory for Path Planning Strategy in a Polyiamond Inspired Reconfigurable Robot

et al. 2019

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“…In this paper, we investigate the crucial requirements of autonomous complete area coverage by understanding the generation of the tileset according to tiling theory [32], its applications in gaming [33], and computer graphics [34]. Then, the proposed complete path planning framework is derived from the analytical tiling methodology through the logical process into systems that are demonstrable on the real Tetris-mimicked reconfigurable floor cleaning robot.…”

Section: Introductionmentioning

confidence: 99%

Complete Path Planning for a Tetris-Inspired Self-Reconfigurable Robot by the Genetic Algorithm of the Traveling Salesman Problem

Manimuthu

Veerajagadheswar

et al. 2018

Electronics

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The efficiency of autonomous systems that tackle tasks such as home cleaning, agriculture harvesting, and mineral mining depends heavily on the adopted area coverage strategy. Extensive navigation strategies have been studied and developed, but few focus on scenarios with reconfigurable robot agents. This paper proposes a navigation strategy that accomplishes complete path planning for a Tetris-inspired hinge-based self-reconfigurable robot (hTetro), which consists of two main phases. In the first phase, polyomino form-based tilesets are generated to cover the predefined area based on the tiling theory, which generates a series of unsequenced waypoints that guarantee complete coverage of the entire workspace. Each waypoint specifies the position of the robot and the robot morphology on the map. In the second phase, an energy consumption evaluation model is constructed in order to determine a valid strategy to generate the sequence of the waypoints. The cost value between waypoints is formulated under the consideration of the hTetro robot platform’s kinematic design, where we calculate the minimum sum of displacement of the four blocks in the hTetro robot. With the cost function determined, the waypoint sequencing problem is then formulated as a travelling salesman problem (TSP). In this paper, a genetic algorithm (GA) is proposed as a strong candidate to solve the TSP. The GA produces a viable navigation sequence for the hTetro robot to follow and to accomplish complete coverage tasks. We performed an analysis across several complete coverage algorithms including zigzag, spiral, and greedy search to demonstrate that TSP with GA is a valid and considerably consistent waypoint sequencing strategy that can be implemented in real-world hTetro robot navigations. The scalability of the proposed framework allows the algorithm to produce reliable results while navigating within larger workspaces in the real world, and the flexibility of the framework ensures easy implementation of the algorithm on other polynomial-based shape shifting robots.

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“…Polyomino tiling theory has been extensively studied in combinatorial mathematics as a distinct branch of mathematics with Golomb as the pioneering inventor in this field. The applications of this theory span a wide variety of fields including medicine [15], graphics, and gaming [16]. However, polyomino tiling theory has rarely been applied to the field of robotics and, therefore, presents a scope for tremendous research.…”

Section: Introductionmentioning

confidence: 99%

Multi-Criteria Decision Making for Efficient Tiling Path Planning in a Tetris-Inspired Self-Reconfigurable Cleaning Robot

et al. 2018

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In this study, we aim to optimize and improve the efficiency of a Tetris-inspired reconfigurable cleaning robot. Multi-criteria decision making (MCDM) is utilized as a powerful tool to target this aim by introducing the best solution among others in terms of lower energy consumption and greater area coverage. Regarding the Tetris-inspired structure, polyomino tiling theory is utilized to generate tiling path-planning maps which are evaluated via MCDM to seek a solution that can deliver the best balance between the two mentioned key issues; energy and area coverage. In order to obtain a tiling area that better meets the requirements of polyomino tiling theorems, first, the whole area is decomposed into five smaller sub-areas based on furniture layout. Afterward, four tetromino tiling theorems are applied to each sub-area to give the tiling sets that govern the robot navigation strategy in terms of shape-shifting tiles. Then, the area coverage and energy consumption are calculated and eventually, these key values are considered as the decision criteria in a MCDM process to select the best tiling set in each sub-area, and following the aggregation of best tiling path-plannings, the robot navigation is oriented towards efficiency and improved optimality. Also, for each sub-area, a preference order for the tiling sets is put forward. Based on simulation results, the tiling theorem that can best serve all sub-areas turns out to be the same. Moreover, a comparison between a fixed-morphology mechanism with the current approach further advocates the proposed technique.

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Video Puzzle Game Application of Polyomino Re-tiling

Cited by 6 publications

References 3 publications

Application of Tiling Theory for Path Planning Strategy in a Polyiamond Inspired Reconfigurable Robot

Application of Tiling Theory for Path Planning Strategy in a Polyiamond Inspired Reconfigurable Robot

Complete Path Planning for a Tetris-Inspired Self-Reconfigurable Robot by the Genetic Algorithm of the Traveling Salesman Problem

Multi-Criteria Decision Making for Efficient Tiling Path Planning in a Tetris-Inspired Self-Reconfigurable Cleaning Robot

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