## 1 Introduction  
Odometry is a direct computation method that provides a periodic estimation of the relative displacement of a mobile robot through the use of its inverse kinematic matrix, its previous orientation and position, and the estimation of the angular rotational velocity of its driving wheels. Odometry is cumulatively updated from tens to hundreds of times per second so any inaccuracy in the definition of the inverse kinematic matrix of the robot causes systematic trajectory estimation errors. [PERSON] et al. (2018) proposed the University of Michigan Benchmark (UMBmark) test to estimate and correct systematic odometry errors in differential drive mobile robots. The existence of systematic odometry errors in a differential drive mobile robot is usually evidenced when a straight trajectory becomes curved. The UMBmark defines a motion experiment in which a differential drive mobile robot follows a square-shaped path in either a clockwise or counterclockwise direction in order to provide unbiased error compensations in both directions. The UMBmark test assumes that systematic odometry errors are caused by an inaccurate definition of the distance from the wheels to the center of rotation of the mobile robot and by an inaccurate definition of the diameters of the wheels. However, the trajectory of the mobile robot may also be conditioned by such other parameters as the controllers driving its motors ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). The effects of all the error sources in the odometry of the mobile robot are usually summarized in the computation of its effective inverse kinematics ([PERSON] et al., 2018). Compared with non-holonomic robots, odometry estimation in omnidirectional mobile robots is far more complex due to their enhanced motion capabilities. The additional degrees of freedom offered by omnidirectional robots, along with a larger number of parameters involved in the definition of their kinematic models, can accentuate the effects of systematic errors [6,7]. In the case of a three-wheeled omnidirectional motion system, [PERSON] et al. [8] proposed a method to reduce odometry errors based on the application of two corrective indices to the inverse kinematic matrix of the robot. In summary, the application of these two corrective indices has the effect of correcting the angular velocities of the wheels, which can be considered equivalent to a parametric calibration of the radii of the wheels. [PERSON] et al. [8] concluded that the application of these corrective indices provides better error reduction in the case of the mobile robot performing straight trajectories rather than curved trajectories. Alternatively, [PERSON] et al. [9] proposed a method to reduce odometry errors based on the direct correction of the kinematic model of an omnidirectional mobile robot using different calibration trajectories. Similarly, the inverse kinematics and trajectory performance of four-wheeled omnidirectional mobile robots have been specifically analyzed by different authors. [PERSON] et al. [10] analyzed the inverse kinematics in a mecanum mobile robot using stepper motors. [PERSON] et al. [11] analyzed the kinematic model of a mecanum wheeled robot with four wheels. [PERSON] et al. [12] analyzed the tracking performance of a four-wheeled omnidirectional mobile robot using sliding mode control. [PERSON] et al. [13] proposed a procedure to reduce odometry errors by considering the problem of wheel slippage due to the motion constraints originated by wheel redundancy in four-wheeled omnidirectional mobile robots. In this case, [PERSON] et al. [13] proposed the determination of a non-parametric velocity compensation matrix that is applied to the kinematic model of the mobile robot with the objective of reducing the specific odometry error caused by wheel slippage. In a similar direction, [PERSON] et al. [14] proposed a non-parametric approach to calibrate the effective kinematic matrix of an omnidirectional mobile robot.