## 1 Introduction  
Robots are deployed in a wide range of applications and are, therefore, rapidly becoming an integral component of our everyday life. In particular, with several million units sold worldwide, robots developed and implemented for floor cleaning tasks will become an elemental part of the household in the near future. Such a massive market in robotic floor cleaning products involves dominant market players such as IRobot, Dyson, Samsung, Xiaomi, and Neato. These robots can autonomously navigate through a given area using onboard sensors and are typically characterized by circular, square, and D-shaped morphologies. The suitability of current robots to assist in daily domestic tasks is investigated in [1] from the human user viewpoint. Additionally, the study presented in [2], analyses and models floor-cleaning coverage performances of some commercial domestic mobile robots. Moreover, not only in the commercial market but also in the academic literature, there exist numerous cleaning robot studies within a wide spectrum from mechanical design to autonomy. A Swedish wheeled mechanism for a floor cleaning robot was presented in [3] in order to attain efficient locomotion in a populous area. In terms of robot autonomy, an innovative neural network approach is presented in [4] which is utilized for path planning and obstacle avoidance for a cleaning robot in a random environment. On the other hand, since numerous robotic floor cleaning products are available in the marketplace, it is critical to have benchmark schemes to validate the robot's cleaning performance and coverage efficacy [5]. In addition, multi-robot schemes have been proved to be useful in cleaning applications [6]. Although there are numerous studies that highlight the benefits of cleaning robots, the efficiency of traditional cleaning robots is still affected by factors such as fixed morphology. Since such a rigid structure highly limits the accessible spaces like room corners and narrow corridors, one viable approach to overcome this restriction in a traditional cleaning system is to develop next-generation robots with shape-shifting abilities to maximize the area coverage performance. So far, in the field of reconfigurable robotics, three different architectures are introduced, namely, intra-reconfiguration, inter-reconfiguration, and nested reconfiguration. Intra-reconfiguration deals with a single robotic system that could change its morphology on its own without any external supports [7]. Robots proposed under the inter-reconfigurable principle are basically modular robots that can possess different morphologies by undergoing assembling and disassembling processes [8]. Modular robots can be investigated at higher levels to benefit from swarm intelligence. In this regard, modular swarm robots are utilized to gain advantages on self-reconfigurability, self-replication, and self-assembly [9]. On the other hand, nested reconfiguration can perform both inter and intra reconfigurations. Hinged Tetro presented in [10], is an example of such nested reconfigurable robots. Although numerous studies in the literature address reconfigurable robotics, they are primarily limited to mechanism design and are hardly implemented to an area coverage task like floor cleaning. In order to bridge this gap, in our previous work, we presented a novel reconfigurable floor cleaning robot called hTetro [11; 12]. This Tetris-inspired structure can change its morphology to any of the one-sided Tetris pieces and as a result, could achieve superior coverage performance through its shapesifting ability. In addition, in a couple of our previous works, we utilized polyomino tiling theory to introduce a coverage path planning technique for Tetris-inspired polyomino robots [13; 14]. Polyomino tiling theory has been extensively studied in combinatorial mathematics as a distinct branch of mathematics with [PERSON] 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].