## 1 Introduction  
An omnidirectional mobile platform is characterized by its capability to simultaneously translate and rotate in any direction without kinematic constraints [1; 2; 3]. Omnidirectional wheels have free rollers on their perimeters [4] to combine rotation around the wheel axis and translation in the rotation direction of the rollers. The angular orientation of the free rolling direction of the rollers relative to the wheel hub (\(\gamma\)) determines the type of omnidirectional wheel. The most commonly used are Mecanum (\(\gamma=\pm 45^{\circ}\)) [5; 6; 7] and omni wheels (\(\gamma=0^{\circ}\)) [8; 9; 10]. Omnidirectional wheels are implemented in a significant number of robot applications [11; 12; 13]. Compared with conventional wheels, their main disadvantages are the generation of vibrations and the susceptibility to slippage. The combination of several omnidirectional wheels in a system does not ensure omnidirectional motion; only when wheel placement and orientation is adequate, the platform can achieve three degrees of freedom (DOF). Proposals of omnidirectional mobile robots with different wheel configurations are presented in the scientific literature [14; 15; 16]; their selection depends on the field of application. The most frequent omnidirectional platforms are based on symmetric designs [17; 18] with three omni wheels [19; 20] or four Mecanum wheels [21; 22; 23]. Less common implementations include asymmetric distributions [17; 24] and systems with six [25; 26; 27] or eight wheels [28]. Specific approaches such as navigation within tunnels to inspect nuclear sites rely on compact designs [29] or systems with joints to change the alignment of the Mecanum wheels [30]. Other designs include omnidirectional wheels on a bending platform so that robots can climb and inspect ferromagnetic structures such as walls and circular constructions [31]. Hybrid mobile robots combining legs and Mecanum wheels are convenient in heterogeneous environments with irregular terrains [32], and proposals such as the collinear Mecanum drive are interesting omnidirectional alternatives to typical two-wheeled inverted-pendulum robots [33]. Similarly, hybrid quadruped spherical robots combine the structure of spherical robots and four legged robots [34]. Other omnidirectional proposals extend the operation sceneries to terrain and water by implementing oloid-like paddlewheels based on Schatz linkages [35]. The analysis of omnidirectional mobile platforms is often addressed with the aim of refining their design and operability [36]. For example, [PERSON] et al. [18] proposed a model for systems with symmetrical distributions of N omni wheels to optimize robot trajectories, [PERSON] et al. [37] presented a model predictive control to compensate for frictional effects on trajectories, and [PERSON] et al. [38] considered orthotropic friction to model roller-ground contact of Mecanum wheels and developed an efficient wheel model. With respect to their constructive characteristics, [PERSON] et al. [39] analyzed the effect of the angles of the rollers on motion performances, [PERSON] et al. [40] presented an overview of three-wheeled omnidirectional motion strategies, and [PERSON] et al. [41] proposed an alternative wheel arrangement of four omni wheels in a mobile robot, suggesting that wheel arrangement changes the effect of imperfect control on the motion. Reconfigurable and asymmetric wheel arrangements are useful in case of motor failure [24; 42]. In this context, [PERSON] and [PERSON] [43] studied the maximum velocity of omnidirectional robots with arbitrary wheel arrangements, and [PERSON] et al. [19] analyzed the front and back movement of a three-wheeled omnidirectional robot by varying the angles between its wheels. Several authors have analyzed the omnidirectional mobility of a system on the principle that if the Jacobian matrix of the inverse kinematics model is full rank, the system has three DOF [44]. [PERSON] et al.