# An Estimator for the Kinematic Behaviour of a Mobile Robot Subject to Large Lateral Slip
## 1 Introduction  
In recent years, autonomous navigation applied to mobile robots is a rising trend. Within this field, trajectory planning and control is one of the most studied themes. Along with the growth of the mobile robotic fields of application, new and better performance is required from robots. In particular, off-road capabilities, quick manoeuvring at high speed, and particular locomotion architectures require a deep understanding of how the robot dynamically behaves to develop proper trajectory planning and control.  
Lateral and longitudinal wheel slips are two of the most common phenomena to be faced in order to compensate undesired robot behaviour. Many of the existing works in mobile robotics overcome these issues assuming pure rolling conditions of the wheels, neglecting, therefore, wheel slip [1; 2; 3; 4; 5]. These issues are instead largely studied in the automotive field due to similar interest in handling control [6; 7]. Wheel slip is almost impossible to be measured directly; therefore, in most of the cases, it has to be estimated. Thus, many slip estimation approaches have been proposed [8], such as sliding mode control [9; 10], motor current sensing control [11], Kalman [12; 13] or particle filter [14; 15] based estimations, IMU-based slip estimation [16], and vision-based estimation [17]. All these methods have advantages and limitations reported in depth in the literature. Generally speaking, the best-performing solutions require a structured environment (i.e., vision-based systems) or intensive computation load in order to model, estimate, and control the robot correctly. Therefore, it is not always possible to meet the requirements of the various solutions, either because it is not possible to setup in advance the work environment, because the control unit is not capable to manage the slip compensation complexity, or maybe because it is already overburdened by other heavy tasks. For this reason, this paper proposes a very simple approach based on adjusting kinematics parameters to compensate the large lateral wheel slip. A vaguely similar approach was adopted in a couple of cases among tracked robots in order to correlate the complex tracks interaction with the soil with a simpler wheel-ground contact [18; 19].  
The idea behind this approach is to characterise the mobile robot through an experimental campaign with the aim of finding a simple correlation between the ideal andexpected kinematic trajectory and the measured one. Then, by means of the experimental correlation between the desired and observed behaviour, it is possible to adjust some robot control reference input signals with the aim of obtaining a trajectory closer to the kinematic one by compensating undesired handling behaviours due to dynamic phenomena. The experimental correlation between key parameters, such as the yaw rate and path curvature radius, should be simple enough to be easily and quickly computed by any robot control unit. This approach is strongly related to the robot (and the environment) that has been characterised. However, if a good identification is done, it is possible to obtain a very simple correlation between parameters that can be easily used to compute the required corrections.  
This paper briefly introduces a kinematic model of the mobile robot that is then used to fit the experimental results. Post-processing the data, a correlation between the theoretical and experimental results is found and used to compensate the divergence between the two.