## 1 Introduction  
A holonomic robot is a mobile robot where the number of controllable degrees of freedom (DOF) is the same as the number of total DOF--that is, the robot has no kinematic constraints [1]. In contrast, in a nonholonomic robot, the number of controllable DOF is less than the number of total DOF; thus, the robot may have one or more kinematic constraints. The main advantage of holonomic vehicles over nonholonomic vehicles is their ability to rotate and translate independently and simultaneously [2]--that is, to move in any direction immediately with any orientation, e.g., they can move sideways [3]. In other words, the holonomic vehicle is capable of omnidirectional movement [4]. Among others, mecanum wheels [5] are a special kind of wheel that can be installed on the robotic platform to achieve omnidirectional mobility. This feature of the mecanum-wheeled mobile platforms implies their use in a wide variety of fields [6]: military activities, industrial tasks, medical applications, educational environments, etc. However, they usually present some practical problems such as random wheel slippage and high-speed vibration, which may cause uncertain position errors and low efficiency [7]. In our work, a path-tracking application is developed for a holonomic robot equipped with four mecanum wheels. As no time constraints are required for the mobile platform to converge to and follow the path, the path-tracking application becomes a path-following motion control [8]. The Pure Pursuit path-tracking algorithm (see, e.g., [9]) is used in order to make the robotic platform follow a predefined path approximately. Modified versions of the algorithm can be found in literature. They introduce different approaches with the aim of improving the path-tracking behavior by minimizing oscillations and lateral error. For instance, in [10], the next position of the path is obtained by considering a factor (which is experimentally calculated) multiplied by the path error (the closest distance of the vehicle to the path); in [11], a derivative term is added to the desired curvature equation; in [12], multiple look ahead points along the target path are aggregated to form a spatially filtered steering command; in [13], the ideal vehicle speed is estimated from curvature information; in [14], fuzzy control techniques are applied to dynamically obtain the look ahead distance; in [15], linear interpolation for waypoints and tuning rules for the look ahead distance based on curvature and speed are proposed. In our case, the Pure Pursuit path-tracking algorithm computes reference linear velocities from position estimations provided by a Kalman filter. The novelty of our modified version lies in decomposing the reference linear velocity into Cartesian components, which are parameterized by a variable gain that depends on the distance to the target point. The control solution proposed in this work uses the celebrated Kalman filter [16; 17; 18] via its extended version (see, e.g., [19]) in order to (i) estimate the nonlinear behavior of the mobile platform, provide not available (not measurable) variables, and reduce the possible process and measurement noise effect; (ii) fuse all the data provided by the different sensing devices (encoders and beacons) to be used in the control stage. These data may arrive to the filter at two different rates--that is, whereas rotational velocities and orientation may be sensed at a faster rate, position information is usually obtained at a slower rate. In addition, the possible occurrence of sensor failures or the use of lossy wireless sensor networks may make the presence of the measurements nonuniform. Not facing these facts in the control solution may degrade the path-following control performance. For this reason, a novel, nonuniform dual-rate extended Kalman filter (NUDREKF) is formulated in order to estimate fast-rate robot states from nonuniform, slow-rate measurements.