# Model-Based Slippage Estimation to Enhance Planetary Rover Localization with Wheel Odometry
## 1 Introduction  
Robotic exploration of the surface of celestial bodies in the Solar System is a key phase of planetary science investigations. In situ measurements are fundamental to significantly expand our knowledge of surface formation and evolution, habitability, geology and geophysics. Rovers on the Martian surface have led to unprecedented measurements (e.g., [1]), studying the planet's habitability and seeking signs of past microbial life [2, 3]. To conduct science investigations across a wide region of the body's surface, the navigation of a rover must fulfil tight engineering constraints. Safe mobility is one of the main requirements, and is directly related to the morphology of the explored area and the properties of the terrain [4]. Serious risks are caused by high-slippage terrains, slopes and hazards, which strongly affect locomotion. The NASA rover Spirit, for example, got stuck in soft soil leading to the descoping of the mission as a stationary science platform [5]. An accurate characterization of the soil properties is then fundamental to prevent these undesired motion failures. Onboard systems can then be designed to identify a terrain type by using images of the environment [6]. The predicted terrain class can then be used to predict the slippage conditions and correct nonsystematic errors of wheel odometry [7]. The reconstruction of the rover's pose through the processing of encoder measurements is also limited by systematic errors [8, 9]. WO and inertial measurement unit (IMU) data are directly used to compute a vehicle's motion from wheel displacements. This approach is generally based on a simplified modeling of the kinematic equations, leading to a significant error propagation [10]. To enhance the determination of the rover's pose additional measurements are collected by onboard instrumentation, as, for example, navigation cameras for visual odometry [11, 12, 13] and light detection and ranging (LiDAR) [14]. Images can also be used to estimate the rover's slip by jointly measuring the pose of the wheels' traces and the rate of turn [15]. A correction of WO and IMU measurements is fundamental to absorb mismodeling errors when imaging and ranging data are not available. A novel method was introducedby [PERSON] et al. [16] to detect the wheel-slippage for WO corrections by measuring motor current. Terramechanics and regression functions were adopted by [PERSON] et al. [17] to improve the localization accuracy that is obtained using IMU-based systems. [PERSON] et al. [18] developed a technique based on WO and an exteroceptive sensor to simultaneously calibrate odometry and sensor parameters. Here, we present a method to compute the velocity slippage correction, which is the difference between the linear speed of the vehicle and the relative speed of the wheel measured by WO [16], with an accurate modeling of a rover's dynamics. To accurately determine the rover's motion on different terrain types, we implemented a detailed wheel-soil interaction that accounts for rover's wheel and terrain deformability [19; 20; 21]. Previous works were in general based on the assumption of a rigid wheel on different terrain types [10; 22; 23]. This hypothesis, however, is not well-suited for rovers equipped with flexible wheels, i.e., ESA ExoMars rover [24]. In this work, the rover was modeled by using size and mass of ESA ExoMars rover [25]. Different terrain types were included in our software, including cloddy, mixed drift-cloddy and drift soils. Their physical properties rely on Martian soil simulants retrieved from semi-empirical Earth-based observations [26; 27]. Numerical simulations of different scenarios are reported to test the advantages of the proposed method for WO correction.