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

Abstract

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.

System Level Modeling and Control Design of hTetrakis–A Polyiamond Inspired Self-Reconfigurable Floor Tiling Robot

“…The hTetrakis platform is suitable for accessing narrow and constrained spaces and has showed a superior area coverage performance in parallelogram based region as verified in the previous work [20]. In this section, we carried out simualtion experiments to check the mobility and positioning of the platform in test bed environment.…”

“…1. All these configurations have convex boundary corners; as a result, the platform can reach sharp and narrow spaces of the environment, as described in our previous work [20].…”

“…The experimental results show the superior area coverage performance of the platform in real-time scenarios of the cleaning environmental. We developed another polyform based platform, hTetrakis, that consists of four moniamonds (equilateral triangle) joined by revolute joints [20]. By altering the position and alignment of these moniamonds, the platform attains three distinct configurations [21]- [23].…”

“…After selecting the theorems to tile a specific region, the algorithm enables the tiling process. hTetrakis platform tiles the predescribed environment with three configurations of tetriamonds and the tetriamond tiling theorems which is extensively studied described in our previous work [20], as follows. Theorem 1: A parallelogram of size a×b can be tiled with only 'I' set of tetriamonds if (and only if) the total number of triangles (ab/2) is a multiple of 4, shown in Fig.…”

Modeling and Analysis of hHoneycomb—A Polyhex Inspired Reconfigurable Tiling Robot

“…To enhance cleaning performance in dynamic environments, there is a need to consider the morphology of the cleaning robot when designing a cleaning platform. Considering these aspects, our team has implemented the concept of self-reconfiguration in floor-cleaning robots and built hTetro and hTetrakis platform [22][23][24]. These self-reconfigurable floor cleaning robots include tiling based area coverage path planning algorithms which are inspired by the Tetris game.…”