I Introduction
Achieving accurate realtime localization performance is challenging for planetary rovers with limitedperformance computers traversing on harsh and unknown terrains that cause wheel slippage. Rover slip is often estimated using visual odometry (VO)
[26, 34]. Despite its safety and reliability, using VO for long periods comes with some concerns: 1) substantial traversal rate reduction since the rover needs to stop to acquire images [41], and needs to drive slow due to limited computational resources [25]; 2) the low number of detected and tracked features on indistinguishable terrains (e.g., bright areas, sand dunes, shadowed areas) can lead to poor accuracy of motion estimates [14] and limit the usage of VO. Specifically, Mars Science Laboratory (MSL) rover reaches a maximum speed of 140 m/h in blinddrive mode (without VO), 45 m/h in hazard avoidance mode (VO update every 10 meters), and only 20 m/h in fully autonomous mode (VO update every halfvehicle length) [16].For current Mars rovers, the slow pace driving can be alleviated by using the blinddriving mode, which makes use of wheel odometry (WO) and inertial measurement unit (IMU) to keep track of the rover’s motion if the terrain ahead is considered to be safely traversable by the rover operation team. However, using only blinddriving causes unbounded pose error growth over time and increasing uncertainty in the rover state due to wheel slippage and INS drift. For this reason, the rover localization is corrected with computationally expensive methods after a short period of blinddriving [26].
Leveraging “free” information without affecting any other operations and using observations for multiple purposes are desirable characteristics for planetary missions [3]. In planetary missions, stopping is inevitable for the rovers due to hardware constraints, and so far, the autonomous planetary rovers are stopping approximately every 110 meters of driving for various reasons [16, 41]. As the rover is mostly stationary due to these frequent stops, ZUPT can be leveraged to maintain INS alignment. The main advantages of ZUPT for the localization task is that it can bound the velocity error, calibrate IMU sensor biases, and limit the rate of INS localization drift [17]. Using ZUPT in a planetary rover deadreckoning system can provide a computationally efficient and accurate realtime rover localization capability, even in featurepoor areas, without any major changes to the rover operations. Furthermore, having a more reliable onboard proprioceptive localization approach may help to reduce the frequency of using computationally expensive visualbased corrections. However, knowing how often ZUPT should be employed requires consideration to avoid unnecessarily reducing traverse rate.
In our previous work [22], we presented an approach to enhance planetary rover deadreckoning localization performance by making use of ZUPT with periodic stops. In this study, we propose an autonomous stopping framework by monitoring wheel slippage and predicting the time when the rover needs to stop to keep the localization drift rate to an acceptable level using only an IMU and wheel encoders. Our contributions are listed as:

We develop a novel method for predicting localization error, using a timeseries Gaussian process model for prediction of slip uncertainty as a function of time, such that ZUPTs can be actively initiated with respect to the wheel slippage frequency and magnitude.

We evaluate our approach in a set of field tests and demonstrate that the proposed method is able to improve blinddriving localization on different terrain types (e.g., paved, unpaved, graveled, and rough areas) that yield different stopping times.
The rest of the paper is organized as follows. Section II provides a comprehensive overview of related works. In Section III, we introduce the preliminaries for the problem formulation. In Section V, we describe the details of the proposed framework. Section VI explores the concept further and carries out a qualitative analysis of experimental results. Finally, conclusions are presented in Section VII.
Ii Related Work
Wheel slippage can occur when the terrain traversed fails [19] or when there is a kinematic incompatibility between wheels (i.e., different wheel speeds) encountered [13]. Because of slippage and imperfect measurement of the wheel radius, WO based localization is inherently subject to drift.
Knowledge of the terrain geometry is a critical asset for the rovers in unknown environments for safe traversal. For example, MSL uses stereo vision to generate a digital elevation map (DEM) of the surrounding terrain enhanced by leveraging High Resolution Imaging Science Experiment (HiRISE) images [4] similar to Mars Exploration Rovers (MERs) [34]. VO is an accurate and reliable source of information for slip estimation; however, it is computationally expensive for planetary rovers. Even with the fieldprogrammable gate array (FPGA) processors [24], the other limitations of VO arise that it suffers from lowfeature terrains and it relies on proper lighting conditions [39]. Similarly, insufficiently detected and tracked features may lead to poor accuracy of motion estimate [14].
Various studies have modeled slip as a function of terrain geometry. Past studies have yielded important insights into the relationship between visual terrain information and the measured slip using training examples by casting the problem into a Mixture of Experts (MoE) framework [2]. However, this terrain geometry knowledge does not guarantee to localize the rover relative to terrain traversed since the rover slip is measured infrequently, and it causes a substantial reduction of the traversal rate due to computational expenses [41].
Moreover, the wheelterrain interactions (terramechanics) are not dictated by the visible topsoil of the terrain [14]. To address this, a recent line of research has focused on datadriven cubic regression metrics to predict slip with respect to the slope by using proprioceptive and exteroceptive sensors [38]. Although slippage is strongly affected by increasing absolute value of a slope, wheel slippage can also be observed on flat terrains while encountering local obstacles (e.g., small rocks that rover can traverse on) due to kinematic incompatibility [13].
Martian soil is extremely challenging for traversability; even throughout a single drive, Mars rovers traverse various terrains [4]. Employing a terramechanics model to estimate slip requires the knowledge of terrain parameters and variables, which are challenging to measure or estimate accurately online. Due to the complexity of terramechanics modeling, considerable research has been devoted to simplified models. For example, [19] presented a tool for online estimation of terrain parameters based on a simplified terramechanics model for deformable terrains.
Apart from terramechanics modeling, machine learning algorithms have also been utilized as slip estimation tools. Locally adaptive slipmodel learning with respect to slope values is demonstrated in
[9]using a Gaussian process (GP) regression for visually classified terrain types. Using visual information is one of the common ways to classify a terrain and estimate an equivalent slip value for planetary missions. However, unexpected small variances on the terrain can be deceptive for a vision based sliplearning approach
[6].The methodology in [18] demonstrated an offline wheel slippage learning approach, where the model is learned on training runs and evaluated in a test environment using SLAM in a planetary rover navigating an unstructured environment. On the other hand, [36] suggested that the mapping between inputs and resultant behavior depends critically on terrain conditions which vary significantly over time and space (spatiotemporal). Therefore, offline techniques for slip estimation are most likely to suffer from learning changes in wheelterrain interactions.
Leveraging ZUPT is a natural fit for wheeled planetary robots because rovers are in stationary conditions in many instances [5] such as capturing images for obstacle avoidance, replanning, processing VO, and conducting scientific experiments. When a rover is in stationary conditions, localization performance can be improved by using the pseudomeasurements generated (i.e., ZUPT) as detailed in our previous work [22]. ZUPT is a wellknown concept that was initially popularized to aid inertial pedestrian navigation [12, 28]. Zerovelocity detection and application on paved road for automobile applications are shown in [44, 32, 7].
Iii Preliminaries
This section introduces several essential framework elements for planetary rover proprioceptive localization from our previous study for the sake of completeness. Detailed descriptions can be found in [22].
Iiia Rover Filter States
An error state extended Kalman filter (ESEKF), based on the method detailed in
[17], is implemented to enhance proprioceptive localization and provide uncertainty bounds. The error state vector is formed in a local navigation frame,
(1) 
where, is the attitude error, is the velocity error, is the position error, is the IMU acceleration bias, and is the IMU gyroscope bias.
It is assumed that the errorstate vector is defined by (1) and the total state vector is
(2) 
where each of the nine total states correspond to the first nine errorstates.
IiiB NonHolonomic Constraints
A nonholonomic rover is subjected to two motion constraints: 1) zero velocity along the rotation axis of the rover wheels, and 2) zero velocity in the direction perpendicular to the traversed terrain [10]. These constraints can be leveraged as a pseudomeasurement update. Assuming that the rearwheel frame axes are aligned with the body frame, this measurement update can be given as
(3) 
where is the coordinate transformation matrix from the body frame to the locally level frame, is body to rear wheel lever arm, and is angular rate measurement. The approximate measurement matrix can then be found as
(4) 
Note that the lateral velocity constraint is invalid in excessive sideslip conditions. The sideslip angle estimation (see Subsection VA) can be used to verify whether the rover is experiencing an excessive sideslip and this verification can be used to decide the lateral velocity measurement should be omitted or not.
IiiC ZeroVelocity Update  (ZUPT)
During stationary conditions, IMU output is dominated by planetary rotational motion and sensor errors. Therefore, ZUPT can be used to maintain INS accuracy.
ZUPT bounds the velocity error and calibrates IMU sensor biases [37]. Hence, the measurement innovation for ZUPT can be expressed as
(5) 
where is measurement innovation matrix, is estimated velocity vector, and is estimated gyro bias. The measurement matrix is given as
(6) 
Iv Gaussian Process with TimeSeries Modeling Overview
In this study, we employ a GP to model the wheel slippage as timeseries data. The primary reason for choosing the GP is to leverage its prediction of uncertainty estimates, which are used for predicting the errorcovariance of odometry measurements (see Section VD).
A GP is uniquely defined by its mean function and covariance function [43].
(7) 
For any collection of input points,
, with defining a probability distribution
, has a joint Gaussian distribution such that
(8) 
where the matrix is the kernel matrix whose entries are given by , , and is the corresponding mean vector. The covariance (kernel) function encodes the similarity between the outputs in GP [11]. To model the different characteristics of the training dataset, which is collected while the rover is in motion, we combine two kernels as a product to capture the different slip behavior of the rover with respect to the terrain.
Assuming that the slip can be occurred randomly and significantly (e.g., impulsive high slippage) due to unexpected kinematic incompatibility, we adopted the Brownian kernel,
. On the other hand, from the mathematical expression of Radial Basis Function (RBF) kernel,
, it can be assumed that if inputs are similar, then the outputs would be similar [42]. In the case that the rover does not encounter significant slippage, we assumed the subsequent measurements should be similar to each other for a short timeinterval (the timeinterval between two successive slip measurements is 0.1s in our setup) resulting to a repetitivelow slippage. Based on this intuition and a heuristic approach from field test results, we also used RBF kernel in our GP model, resulting in a composite kernel (i.e., multiply kernels together)
[11] such as . Note that the assumptions mentioned above are for blinddriving mode, and the mode can be activated when the terrain is considered safe to be driven for planetary rovers. The aim of a regression problem is to learn the mapping from inputs to outputs [35], given a training set of input and output pairs , where is the number of training examples, predictions can be made at test indices by computing the conditional distribution and with assuming a zero mean , results in a Gaussian distribution and given by:(9) 
where
(10)  
(11) 
V Methodology
The proposed wheeledrobot localization framework consists of a series of actions in currenttime and futuretime, both of which are computed onboard the rover. The currenttime portion consists of our previous work [22], an INS mechanization aided with WO, pseudomeasurements, and kinematic constraints in an ESEKF as briefly summarized in Section III. The futuretime part of the framework uses the estimated slip events and prior estimated error state information to predict the robot’s localization error. A depiction of the proposed framework and its elements is demonstrated in Fig. 1.
Va Slip Detection
The slippage is monitored with the slip ratio calculation for front and rear wheels velocity with respect to the INS velocity. Example estimates of WO based velocity, INS (filter) estimated velocity, and truth (DGPS) velocity are shown in Fig. 2 (a).
The longitudinal slip ratio, , is defined as:
(12) 
where is the translational velocity estimated from INS, is the wheel radius, and is the wheel angular velocity estimated from the WO measurements. The motion estimates from the filter are compared to the computed velocity based on the vehicle kinematics to determine if any slippage has occurred. Detected slippage input is demonstrated in Fig. 2 (b).
Also, sideslip can be expressed using the slip angle, , and can be given as the angle between lateral velocity, , and translational velocity
(13) 
Although there are several methods to detect slippage as discussed in Section II, we adopt this proprioceptive slip detection since it is computationally efficient and not required any visualsensor information to observe the wheel slippage for the proposed method.
VB Wheel Slippage with GP TimeSeries Modeling
In our case, there is one input and one output in the GP. The input is the time tags of each corresponding slip ratio value, and the output is the estimated slip ratio value, assuming training input and output pairs such that .
The collected training data for wheel slip ratio values, , and corresponding time tags for a time window are used to learn the model
(14) 
The time window for learning is kept short to capture the most current (the last 12 m of drive) terrainwheel information based on the MSL Hazard Avoidance slip check interval (10 m) [16]. In that time window, the rover is in free driving (i.e., rover does not perform any stops). The learned model is then processed in the GP forecast model to make predictions at future test indices for future unknown wheel slip ratio observations where is the number of test indices which in our case it corresponds to a future time tag. For a detailed demonstration of slip input and slip prediction by using the slip ratio definition, see Fig. 1(b). A python GP library [15]
is used in our rover’s ROS framework to optimize the hyperparameters (e.g., the length parameter
in the RBF kernel), and to predict the slip values while the rover is in motion.VC Wheel Odometry Velocity Prediction
To predict the simulated odometry velocity error boundaries, a statistical sigma point transformation inspired by unscented transformation [21] where the slip ratio definition in (12) is used to generate this transformation function:
(15) 
where is the time when the prediction is being generated, is the time when the generated prediction ends (i.e., s, see Fig. 1(c)), is the number of the sigma points, is velocity term mapped from slip measurement, defined as , , and where and are mean and variance of , respectively, and is the mean of values for .
In constituting the observation noise covariance matrix in the localization forecasting phase, , we assumed that the constant WO velocity related values on the filter could be interchangeable with varying values between and come from predicted observation covariance.
(16) 
These mapped velocity values and their prediction with this statistical sigma point transformation method are depicted in Fig. 1(c).
VD Forecasting Localization Error
When the forecasted GP data arrives, the algorithm uses the latest filter error covariance estimate, , to initialize the error covariance prediction.
(17) 
The most recent state transition matrix, , process noise covariance, , and WO observation matrix, are being kept fixed during the forecasting error covariance process (see the left side of the Fig. 1).
(18) 
Then, the algorithm simulates an INS error covariance propagation. In our setup, simulated odometry update is assumed to take place in every 5th IMU time step (IMU data rate is 50 Hz, WO data rate is 10 Hz). When this simulated odometry update is available, transformation function predicts the simulated odometry velocity error boundaries. Finally, the simulated Kalman gain is calculated and simulated estimate covariance is updated.
(19) 
(20) 
For each updated covariance prediction, the algorithm calculates the position error covariances as a function of time. An example calculation is illustrated in Fig. 1(d). When the horizontal error gets more prominent than a predetermined threshold, the algorithm takes the corresponding time for that event, calculates the remaining time to stop with respect to the current time, and alerts the rover to stop. If there is no need for stopping (e.g., the positioning error prediction is below the threshold within the prediction time limit), the rover keeps driving. Otherwise, the rover stops traversing, applies ZUPT, then keeps driving. A detailed example scenario is given Fig. 2. The details to model state transition matrix , process noise covariance , observation matrix and the observation noise covariance can be found in [22] and [17].
Vi Experimental Results
Via Setup
Pathfinder, a custombuilt testbed rover, is employed for the experimental evaluation of the proposed method (see Fig. 3). The platform is a lightweight, 4wheeled, skidsteered robot. Rover uses a rocker system with a differential bar connected to the front wheels. In general, planetary rovers use wheels with grousers, which increase traction and traversability performance (e.g., MSL, MERs, ExoMars). However, Pathfinder is utilized with slick wheels to test our localization algorithm against significant slippage. Slick wheels lead to encounter more slippage with larger frequency and occurrence which aid to detect slippage but degrade the localization performance significantly.
The IMU used on the rover is an ADIS16495 with 50 Hz data rate [1] and the quadrature encoders are used for WO readings with 10 Hz data rate. Integerambiguityfixed carrierphase differential GPS (DGPS) is used to determine a truth reference solution. Just as in [22], dualfrequency Novatel GPS receivers and L1/L2 Pinwheel antennas [29] are mounted to the rover and a stationary base station. During the experiments, 10 Hz carrierphase and GPS pseudorange measurements were logged on both receivers. Rover state is initialized with a looselycoupled GPSIMU sensor fusion algorithm, such as driving straight with a short distance (10 m) for estimating initial heading and being stationary for a period of time (
30 s) to initialize position before testing. After initialization, GPS measurements are collected only externally for generating the truth through postprocessing. The opensource software library, RTKLIB 2.4.2
[40], is used to postprocess the DGPS solutions with a cmtodm expected level accuracy [27]. Rover is teleoperated and commanded for 0.8 m/s forward speed in field tests.ViB Evaluation
A series of tests were performed on several terrains, including paved, unpaved, gravel, and rough terrains. Paved terrains are relatively flat roads with minimal slippage observation.
Unpaved terrains are also rigid roads with small scattered rocks that rover can easily traverse. Gravel terrain consists of small broken rock materials. Due to the shape of these materials, there is less traction on the wheels on the gravel road. This loose surface creates slippage primarily due to wheel kinematic incompatibilities. This letter particularly focuses on the rough terrain results because of its similarities with the Martian terrain (see Fig. 3). This terrain is a burnt coal ash pile located at Point Marion, PA, with complex geometric (e.g., sloped, pitted, fractured, and sandy areas) and chemical terrain properties [33] similar to the abundant chemical compounds found in Martian regolith [30].
A stopping time comparison analysis against four terrain types is shown in Fig. 4. In this analysis, the rover is driven on different terrains and the corresponding stop time intervals are stored. Paved and unpaved roads are rigid, and the terrain underneath the wheels is not moving, and the robot wheels do not encounter significant slippage, resulting in better WO. However, the rover encounters significant slippage on gravel (kinematic incompatibility) and rough terrain (sinkage, slope, and kinematic incompatibility). The important result of this analysis is that the average stopping time intervals are shorter on gravel and rough terrain than on benign roads. Correspondingly, the algorithm enforces the rover stops more often on more slippery terrains (minimum stop frequency is 15 s).
To further evaluate the method, the localization accuracy of the proposed estimation is compared against the DGPS solution. As detailed in Table I, we achieved approximately 1% of 3D localization error (ENU) in short (152 m) and medium (339 m) range distances on rough terrain with keeping the stopping error threshold as 2 m. Also, in long (650 m) range distances, the threshold is varied as 2 m, 3 m, and 5 m to observe the localization accuracy performance against stopping time prediction. In these field test results, the algorithm reasonably predicts the stopping time to keep the localization drift approximately 3 for the 5 m threshold and less than 2 for the 3 m threshold. We also monitored that the rover often does not need to stop for the 5 m threshold due to not exceeding the threshold in the prediction time limit.
Ash Pile  Test Specifics^{*}  Error ()  
(m)  (m)  Stop Count  (s)  ENU  Median  
Test1  671  5  8  879  3.07  1.73 
Test2  663  3  19  924  1.78  1.04 
Test3  652  3  20  915  1.14  1.05 
Test4  339  2  9  469  0.91  0.58 
Test5  152  2  5  215  0.94  0.82 
Horizontal Error (m)  RMS Error (m)  
Median  STD  Max.  East  North  Up  
Test1  11.60  12.01  34.48  17.84  7.26  7.25 
Test2  6.89  5.68  18.78  9.49  3.08  6.24 
Test3  6.84  2.88  11.10  5.67  4.44  1.75 
Test4  1.96  1.27  5.86  1.74  1.83  1.78 
Test5  1.24  0.80  2.72  1.34  0.47  0.13 

: Traversed Distance, : Error Threshold, : Traversal Time.
Groundtrack depiction of an example scenario from ashpile field testing is given in Fig. 5. The results show that traditional 2D deadreckoning (WIO) is reliable only for short distances due to slippage, whereas the proposed estimation (3D WIO+ZUPT) can be used for longer distances if the terrain is safe to drive blindly. The localization design goal for MER was to maintain a position estimate that drifted less than 10 during a 100 m drive [26]. Without using ZUPT and kinematic constraints in blinddriving, the drift can quickly elevate and exceed that design limit, as shown in Fig. 5.
Moreover, a comparison analysis between autonomous (proposed) and periodic [22] stopping methods is provided in Table II. Using autonomous stopping leads to an average stop rate ) decrease over 65% compared to periodic stopping while keeping the localization accuracy more than 98%. Consequently, when using ZUPT, autonomous stopping increases the traversal rate by stopping less, and keeps the localization accuracy to an acceptable level.
Periodic  (m)  (s)  Error(%)  (%)  Stop 
Rough_A  151  504  0.85  25.02  42 
Unpaved_A  87  133  1.53  18.08  8 
Unpaved_B  128  181  1.02  11.60  7 
Autonomous  (m)  (s)  Error(%)  (%)  Stop 
Rough_B  152  215  0.94  7.32  5 
Unpaved_C  183  244  1.17  6.15  5 
Unpaved_D  161  210  1.56  4.28  3 

, : Same as Table I, : Stop rate, Stop: Stop count
A comparison between our localization approach against a commercially offtheshelf RealSense T265 tracking system [20] visualinertial odometry (VIO) solution is provided in Fig. 6. In this field test, rover traversed for 150 m on a lowfeature terrain. The tracking system is able to provide reliable solution in feature rich areas whereas it suffers in the areas with a lack of detectable and trackable features. This is a common issue of visualbased localization approaches because these approaches require reasonable distinct visual features in view to operate accurately [8, 39, 34].
Vii Conclusion and Future Work
We presented a slipbased localization error prediction framework, which effectively balances the traversalrate and localization accuracy for wheeled planetary rovers. Instead of periodic stopping, ZUPTs can be autonomously initiated with respect to the wheel slippage frequency and magnitude using a timeseries GP model for prediction of slip uncertainty as a function of time. Planetary robot slip related localization drift can be alleviated with ZUPTs and can provide reliable localization performance for longer distances. The main value of the proposed approach is that it can be easily integrated into planetary rover operations (and many other wheeled robots) to improve onboard localization performance with no hardware changes and minimal operational changes. Since planetary rovers are already stopping frequently for using VO or other operational reasons, using ZUPT along with the blinddrive is a natural fit.
Future work will focus on 1) using deformable planetary spring tires with a traction control mechanism to help alleviating the limitation of the method when stopping on a steep slope and sliding down, 2) improving the method with adaptive and robust filtering techniques.
Collected dataset for experimental validation is available in [23] for the community to use. Developed software and supplementary analyses for this paper are available at:
https://github.com/wvunavLab/CNGP.
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