These approaches use output signals of some sensors to detect abnormal conditions and correct odometry. Hardware redundancy, use of special sensors, frequency analysis, and logic reasoning are some methods in this category. Fuzzy logic and expert rule-based techniques were used in (Ojeda et al., 2004) to compare data from redundant encoders with each other, gyros, and motor currents to detect slip and correct odometry for a six-wheel robot with a rocker-boogie suspension system. However, this technique does not estimate the degree of wheel slip. (Ojeda et al., 2006). proposed a slip estimator for odometry correction in the direction of motion that requires accurate current measurements and some specific terrain parameters. They argue that the terrain parameters can be estimated online either using absolute positions provided by GPS or induced slip in a single wheel for a WMR with at least four driven wheels. The slip detection in Mars rover Curiosity, is done based on motor currents and visual sensors (Arvidson et al., 2017). When abnormal currents are detected the vision system is activated to aid the navigation system with VO. In case features are not unique in the scene, using wheel tracks (Maimone et al., 2007) or steering mast cameras are proposed (Strader et al., 2020). Visual odometry correction on deformable terrains were also proposed in (Reina et al., 2010) using fuzzy reasoning and in (Nagatani et al., 2010) using special telecentric lens. These techniques, however, require high computational cost on embedded processors of planetary WMRs. Thermal cameras are another form of special sensors that were used in (Cunningham et al., 2015) to develop a non-geometrical method for predicting traversability of a terrain through analysing its thermal inertia from infrared imagery. However, long observation periods are required to obtain a good prediction.

These methods are based on kinematics models derived from the physics of WMRs and estimation theory tools such as Kalman-based filters. In (Dissanayake et al., 2001), non-holonomic kinematic constraints were used to obtain velocity measurements for aiding the IO within an Extended Kalman Filter (EKF) framework. The method, however, is not applicable on low-traction and uneven terrains of extraterrestrial bodies as the authors modeled slip as a zero-mean noise. Other kinematics-based methods that aim to improve odometry performance were proposed in (Hidalgo-Carrio et al., 2014; Lou et al., 2019). A vision-based method was proposed in (Helmick et al., 2006) which developed a forward kinematics model of rocker–bogie suspension system for a Kalman filter to combine inertial and visual measurements as well as wheel rates and wheel steering angles for slip estimation and compensation. However, permanent shaded regions of Moon, featureless scenes of Mars, and power constrains of WMRs are the main limitations of visual techniques. In (Ward and Iagnemma, 2008) a tire traction model within an EKF framework was incorporated to fuse data of encoders, IMU, and GPS for detecting slip and immobilized conditions. However, GPS signals are not available on extraterrestrial bodies. Although, most research works rely on EKF for estimation, in (Sakai et al., 2009; Reina et al., 2020) two different filters were used. The former proposed a 6-DoF localization solution within an Unscented Kalman Filter (UKF) framework based on the measurements of stereo cameras, an IMU, and wheel encoders. The latter employed a Cubature Kalman Filter (CKF) to estimate terrain properties using vibrations. To reduce odometry error of combined IO and WO, (Kilic et al., 2019), employed non-holonomic constraints and the zero-velocity updates with periodic stops. The autonomous stopping times through estimating and monitoring wheel slip were investigated in (Kilic et al., 2021). However, these methods sacrifice accuracy for traverse rate. In (Malinowski et al., 2022) the effect of integration of predicted slip in WO and VO was investigated using an EKF architecture.

Terramechanics studies soil properties and wheel-terrain interactions to find normal and shear stresses developed at the contact areas using, e.g., empirical Bekker-Wong models (Bekker, 1969; Wong and Reece, 1967) and their recent modification (Higa et al., 2015). The Mars rover Sojourner performed parameter estimation of Martian soil to identify cohesion and internal friction angle relying on Earth-based analyses (Matijevic, 1997a). However, Earth-in-the-loop procedures are time consuming and inefficient. Online estimation of these parameters were proposed in (Iagnemma et al., 2004) based on simplified terramechanic equations and a least squares technique that identifies the parameters using measurements of the rover configuration sensors, encoders, potentiometers, and six-axis force/torque sensors. The simplified terramechanics-based models were also used in (Ishigami et al., 2007) to deal with longitudinal and lateral slip during steering manoeuvres on deformable soil. However, the accuracy of the estimations is under doubt, since simplified models are not a good representation of real interactions. In (Higa et al., 2016), six-axis force/torque sensors and five types of custom-built contact sensors were used to obtain the three-dimensional stress distribution at the wheel-terrain contact area on lunar regolith simulant. The method, however, for a single wheel results in an error of 1–11%. Real-time estimation of terrain parameters was also addressed in (Li et al., 2018) using semi-empirical terramechanic equations and EKF for WMRs driving on deformable slopes. However, this method is not useful for untraversed areas as it requires a history of measurement data. To measure the terramechanic parameters ahead of the rover, (Zhang W. et al., 2022b), proposed use of an articulated wheeled bevameter equipped with force and vision sensors to predict the slip and sinkage of wheels. An in-situ method for estimating sinkage was given in (Guo et al., 2020) that defines a new reference line of wheel sinkage and simplifies terramechanics into closed-form equations using force/torque sensors. The method is limited to moderate and high-traction terrains.

These approaches are mainly based on classification or regression techniques to respectively provide discrete or continuous estimates of the quantities of interest. A terrain classifier was trained using vibration signals measured by an accelerometer, which is subject to noise and bias (Brooks and Iagnemma, 2005). The training process was also offline making the method inappropriate for unknown environments. To alleviate its shortcomings, the same authors proposed a self-supervised learning method that predicts the terrain properties using two distinct classifiers (Brooks and Iagnemma, 2012). The Support Vector Machine (SVM) proprioceptive classifier analyzes vibration signals or combination of torques and sinkage to generate labels for training an exteroceptive terrain classifier. The second SVM classifier uses stereo imagery to identify potentially hazardous terrains from a distance. However, this training method is uni-directional where vibration signals are only used to train the visual classifier. To improve the training procedure, (Otsu et al., 2016), proposed a bi-directional training technique where the two classifiers train each other. In the context of slip estimation, Omura and Ishigami (2017) proposed a SVM learning technique based on the measurements of the normal force and contact angle at the wheel-terrain interaction area to generate correlation labels for the slip and classify wheel slip into three levels: non-stuck, quasi-stuck, and stuck. (Gonzalez et al., 2018a). compared the performance of supervised (artificial neural networks and SVM) and unsupervised (self organizing map and k-means) classification techniques in detection of three discrete levels for longitudinal slip (low, moderate, and high) based on the measurements of IMU, encoders, and motor currents. A vision-based classification method was proposed in Endo et al. (2021) to predict wheel slip via estimating terrain slopes. The computational cost of image processing limits the use of visual approaches. Deep learning techniques were also proposed for proprioceptive terrain classification based on the measurements of motion states and wheel forces/torques (Vulpi et al., 2020). At best its error is around 8.6%. The main limitation of these methods is that slip cannot be estimated in a continuous manner and the outputs are only useful to avoid hazardous terrains. In (Angelova et al., 2007), continuous slip was predicted from a distance based on visual data and non-linear regression models that correlates terrain appearance and geometry with slip. The applicability of the method is under doubt since, it uses visual sensors and it has some difficulties to determine the terrain types. In (Gonzalez et al., 2018b) Gaussian Process Regression (GPR) is used to predict continuous slip and its variance based on the measurements of IMU and motor torques. However, the computational effort of GPR is high as it uses the history of features to perform its predictions. The GPR was also employed on China’s Mars rover Zhurong to estimate the average of longitudinal and lateral slip using the measurements of IMU, encoders, and motor currents (Zhang T. et al., 2022a).

Global localization solutions are incorporated to bypass limitations of the odometry and correct its position drifts. A tele-communication link between Mars orbiter Odyssey and MER platforms enabled the navigation system to obtain position accuracy of about 10 m around 3 days (Guinn, 2001). Skyline signature matching between images captured by a WMR and a global map was proposed in (Chiodini et al., 2017) to initialize the vehicle position after landing on Mars. (Matthies et al., 2022). proposed an onboard global localization technique which involves mapping Lunar craters from orbit and then using stereo cameras or LiDAR for detecting the craters landmarks. The accuracy of this method depends on the resolution of global maps. Learning algorithms such as Siamese Neural Networks were proposed for global localization on Mars and Moon respectively in (i Caireta, 2021) and (Wu et al., 2019).

Table 2 summarizes the methodologies discussed throughout this section and indicates their potential applications for improving mobility and traversability of planetary WMRs. The level of feasibility of these solutions leaves plenty of room for improvement. One major problem is computational limitations of embedded systems within these robots, and future research must be directed toward developing computationally efficient software solutions on available hardware. Distributed sensing, either sensor-level or track-level fusion, can be used in the estimation architecture to enhance its performance. To achieve greater level of autonomy, the prospective learning solutions should be designed based on multi-directional communicating training techniques. Novel terramechanics models based on updated information on planetary surfaces (e.g., soil composition, surface geometry) are needed to simultaneously enhance fidelity and efficiency of the traditional models. Fast and robust vision-based algorithms must be developed to detect and match features in harsh lighting conditions and featureless environments of extraterrestrial bodies. Another prospective solution is combining different approaches, reviewed in this section, to design robust systems for high-speed navigation of future planetary WMRs.