# Omni Wheel Arrangement Evaluation Method Using Velocity Moments
## 1 Introduction  
Recently, mobile robots have been developed widely in the industrial, medical, and service fields [1]. Various modes of locomotion for these robots have been proposed, including wheeled robots [2], quadruped robots [3], and biped robots [4]. When operating robots in production, robots must be able to move in all directions (for use in confined work environments) and with precise locomotion. In addition, it is preferable for robots to operate with less energy, as it improves efficiency. Leg-type robots can move in all directions, run over bumps, and have flexible posture control. However, they are generally less energy efficient than wheel-type robots. On the other hand, although ordinary wheeled robots are efficient in operation, they are limited in the direction they can move, making precise movement difficult in some cases. Therefore, the development of omnidirectional wheels has been promoted [5, 6], as it allows for precise and energy-efficient robots. Figure 1 shows examples of wheeled omnidirectional mobile robots that are in use or under development for industrial and service fields; such as loading and towing cage carts in factories, patrolling and monitoring at construction sites as well as customer service and advertising activities in commercial facilities, hotels, and airports. Typical omnidirectional wheels are the Omni wheel and the mecanum wheel. The two wheels are shown in Figure 2. Both wheels achieve omnidirectional movement by sliding the freewheel rollers. An Omni wheel is a wheel with freewheel rollers on a plane perpendicular to its axis of rotation. Many Omni wheels use two rows of freewheel rollers, as shown in Figure 1(a), to contact the ground continuously. A mecanum wheelis a wheel with freewheel rollers arranged diagonally, as shown in Figure 2b, which are arranged ingeniously so that the next roller can be grounded by itself. Compared to the Omni wheel and the mecanum wheel, the mecanum wheel performs better over bumps than the Omni wheel because it allows for a car-like wheel arrangement. On the other hand, many products of Omni wheels have slimmer widths per wheel diameters than mecanum wheels. For example, the Omni wheel in Figure 2a is 29 mm in width and the mecanum wheel in Figure 2b is 50 mm in width. As a result, the mecanum wheel is known to have a more significant contact point shift than the Omni wheel when switching the freewheel roller, and the robot is prone to vibration [7]. Since floors in factories, hospitals, and commercial facilities are often flat, the Omni wheel with less vibration is preferable. Another disadvantage common to both was the small load capacity. In response to this problem, the company to which the author belongs has developed a high-load-bearing Omni wheel. Against this background, this manuscript describes the development of a robot using an Omni wheel. Omni wheel robots can achieve omnidirectional mobility with only three wheels. On the other hand, it is known that stability can be improved by increasing the number of wheels [8]. Attempts have also been made to increase the number of wheels to increase the load-bearing capacity of robots [9]. Because stability and payload are essential in industrial applications, robots with more wheels are considered in this manuscript. In agricultural machinery, asymmetric structures prevent tipping over and improve work efficiency [10]. Parts may also be arranged asymmetrically in industrial applications to prevent tipping over and compactness. On the other hand, Omni wheel robots are generally designed with point-symmetrical wheel arrangements. Some wheel arrangements cause poor operability [11]. However, we investigate asymmetric wheel arrangements that do not compromise operability to develop more compact robots with greater payload capacity. We define this wheel arrangement as an \"easy-to-operate Omni wheel arrangement\" in this manuscript. Figure 1: Practical omnidirectional robot.