## 1 Introduction  
There has been an increasing demand for flexible production systems that can produce individualized and customized products to meet diverse needs in recent years. For example, the German government has defined such flexible production systems as \"smart factories\" and is promoting Industry 4.0 to realize them [1]. To realize these smart factories, a higher level of automation is required. One of the technologies required for advanced automation is the autonomous transportation of raw materials, products, etc. within an industrial plant, known as internal transport. Conventional internal transport often uses affixed equipment, such as conveyor belts. Changing production lines that use affixed equipment requires considerable additional investment and effort, making it difficult to realize a flexible production system. In recent years, there have been reports of the use of mobile robots to achieve more flexible internal transport [2, 3]. Various forms of mobile robot platforms have been proposed, including wheeled robots [4], quadrupedal [5] and bipedal robots [6]. Leg-type robots are capable of stable transportation on uneven terrain. However, in-house transport is often performed on paved roads, so wheeled robots with high motion efficiency are often employed. In particular, omnidirectional wheeled robots are often preferred for this due to their high maneuverability [7], with various mechanisms already proposed in literature [8]. In general, either omni wheels or mecanum wheels achieve omnidirectional movement. An omni wheel is a wheel with freewheel rollers on a plane perpendicular to its axis of rotation. By sliding in a direction parallel to its rotation axis, omnidirectional movement is achieved. On the other hand, a mecanum wheel uses freewheel rollers that continuously contact the wheel and the floor. As a result, mecanum wheels have the disadvantage of causing the robot to be prone to vibration because the contact point with the floor moves in the direction of the axis of rotation [9]. Due to this issue, we use omni wheels rather than mecanum wheels in this work. The smaller the factory's footprint, the better and more compact equipment is preferred. The same applies to mobile robots for internal transport. \"Compact\" is defined as \"having a dense structure or parts or units closely packed or joined\" [10]. In this work, we consider a robot to be compact if its structure and components leave little dead space. Our design policy is based on this idea. Robots built under the conditions that make them compact have a different wheel arrangement than conventional ones, so their control characteristics may differ. Therefore, special attention is paid to the effects of control errors in the operating characteristics due to intrinsic factors. It is not easy to control a system perfectly to follow the target control volume as internal and external factors influence its operation. It is even more complicated when the cost is a factor, such as in industrial applications. The effect on noise caused by imperfection of control is described as sensitivity to noise. To evaluate the sensitivity to intrinsic factors, we compare and discuss the trajectories of robots using a conventional wheel arrangement and our proposed arrangement, maintaining the same testing conditions. This way, the effect of external factors remains constant and observed differences can be mostly attributed to intrinsic factors. To our knowledge, this is the first work that proposed a design methodology for an omni wheel robot that focuses on compactness, as well as verification of its sensitive to noise. The contribution of our paper is as follows:  
1. From the viewpoint of dead space and kinematics, we propose a design methodology for compact omnidirectional robots. 2. Through experimental validation, we demonstrate the feasibility of our approach and analyze the effects of wheel placement when following different trajectories.