I Introduction
The Mars Sample Return (MSR) mission was identified as the highest priority planetary science objective in the Planetary Science Decadal Survey [1]. To meet the requirement of the sample return missions, a mobile rover should be able to traverse the terrain safely, quickly, and autonomously to reach its desired targets. In particular, highly accurate realtime localization performance is one of the most demanding abilities for autonomous driving [2], which is especially challenging for planetary rovers with limited energy resources and computational power due to radiation hardened hardware requirements.
Previous Mars rovers have exhibited large onboard localization errors and have had to rely primarily on humanintheloop operations [2]. The Mars Exploration Rovers (MERs) and Mars Science Laboratory (MSL) use a similar approach for localization. When moving, the rover’s attitude angles are propagated through the integration of angularrate measurements [3]
. When the rover is stopped, the rover’s pitch and roll angles are estimated based on the gravity vector which is measured using triaxial accelerometers
[3]. Rover position is estimated from wheel encoderbased odometry and inertial measurement unit (IMU) integration [4]. Stereo visionbased visual odometry (VO) [5]is also used whenever a high probability of wheel slippage is anticipated. Due to limited onboard computational resources, to refine rover position estimates, incremental bundle adjustment is performed on Earth by postprocessing downlinked images
[6] .Wheel slippage is one of the most critical issues to be dealt with for mobile robots driving across loose soil [7]. For example, MERs both became embedded into the soft surface of Mars [8, 9],due to the significant amount of slip. In May 2009, Spirit became permanently entrapped in soft soil [10]. Moreover, Curiosity had to stop to avoid sinking because of severe wheel slippage [11].
One of the most common techniques for estimating rover slip is based on VO [7] [12]. Although VO is an accurate source of information for slip estimation, it is computationally expensive. For instance, each step required 2–3 min of computation time on the MER’s 20MHz CPU [4]. Although MSL’s 200MHz CPU has reduced the onboard processing time to under 40 seconds per step [13] [14], the other limitation of VO arises on lowfeature terrains (e.g., sand dunes, shadowed areas). A low number of detected and tracked features can lead to poor accuracy of motion estimate [15].
For the proposed future MSR mission [16], the rover may be required to traverse up to 20 km from the lander to the cached samples and back to its landing area in less than 99 sols. This required traversal rate is much faster than Curiosity, which has traveled 19.75 km in 6 years [17] and Opportunity that had traversed 45.16 km in 15 years [18] on Mars before the PlanetEncircling Dust Event. It is possible that the MSR rover will need travel up to 1 km per day to the cached sample, which is well beyond the capability for the current daily operations planning. This increased rover autonomy requirement, in turn, requires more accurate and computationally efficient onboard rover localization capabilities.
Zerotype updates (i.e., zero velocity and zero angular rate) are widely used to aid inertial pedestrian navigation[19, 20, 21]. Observability characteristics of zerotype updates on a land vehicle is also detailed in [22]. Zero velocity detection and application in standard road conditions is shown in [23]. Similarly, the method in [24] demonstrates decreased growth in state errors for a land vehicle when stationary updates are used; e.g., stopping at traffic light.
NASA’s Mars rovers move slowly (e.g., MSL has 0.04 m/s top speed on flat hard ground [25]), stop often, and are also equipped with high quality LN200S IMUs [26]. These facts point to the potential that rover localization performance stands to be improved by leveraging zerotype updates for the Curiosity rover as well as the future Mars 2020 and MSR rovers without any hardware changes or significant changes in rover operations.
Ii Methodology
The architecture of the proposed approach is given in Fig.1. The proposed approach offers the following contributions: 1) it is demonstrated that zerotype updates, which simply require stopping, can significantly reduce the rate of inertial navigation error growth for wheeled rovers, 2) we show that wheel slip can be detected as velocity discrepancies between wheel odometry measurements and inertial navigation system (INS) solution, and 3) to show the benefit of the proposed approach, we present experimental tests in which deadreckoning localization estimates are compared to a differential GPS (DGPS) reference solution. As a final contribution, we also make our software, which is designed for use under ROS[27], and presented datasets publicly available.
To improve inertial navigation and provide uncertainty bounds, an errorstate extended Kalman filter (EKF) is implemented based on the method detailed in
[28]. In this formulation, a planetcentered, planetfixed frame is used as the reference frame, while a locallylevelnavigation frame (NED) comprises the resolving axes. In the filter, wheel odometry based wheel velocities and heading rate calculations are treated as an aiding sensor for the INS. In addition, zerotype updates and nonholonomic motion constraints are utilized as additional pseudomeasurement updates whenever they are available. Slip is estimated by using a threshold on the difference between the estimated INS solution and estimated wheel odometry velocity vectors. In this paper, navigation stops are triggered with a manual stopping frequency. Finally, during each navigation stop, backward smoothing to the previous navigation stop is used to further refine state estimates.Iia State Updates
The navigation filter implementation is composed of an attitude update, a velocity update, and a position update. We briefly summarize the integration equations here for completeness. Detailed descriptions can be found in [28]. The attitude update is given as
(1)  
where is the coordinate transformation matrix from the body frame to the locally level frame,
is a 3by3 identity matrix,
is the skew symmetric matrix of the IMU angular rate measurement,
is the skew symmetric matrix of the planet’s rotation vector represented in the locally level frame, is the transport term, and is the IMU sampling interval.Assuming that the variations of the acceleration due to gravity, Coriolis, and transport rate terms are all negligible over the integration interval, the velocity update is given as,
(2)  
where is the velocity update, is the specific force measurements from the IMU acceleration sensors, is the gravity vector.
Finally, assuming the velocity variation is linear over the integration interval, the position update is given as
(3) 
(4)  
(5)  
where , and are updated position estimates (expressed in terms of height, latitude, and longitude, respectively), is the variation of the meridian, and is transverse radii of curvature.
IiB Error State Model
To calculate the INS system matrix, the Jacobian of the errorstate equations is determined. After defining the time derivatives of the errorstate equations, the system matrix and the state transition matrix (STM) are defined. Then, the errors are transformed into the local navigation frame, and the time derivative of the velocity error is constructed by adding the transport rate term. The error state vector is constructed in a local navigation frame,
(6) 
where, is the attitude error, is the velocity error, is the position error, is the IMU acceleration bias, and is the IMU gyroscope bias. The position error is expressed in terms of the latitude, longitude, and height, respectively.
(7) 
The interested reader is referred to [28] for a detailed derivation of the INS errorstate model adopted in this work.
IiC NonHolonomic Constraints
A rover is a nonholonomic system if its number of controllable degrees of freedom is less than its total degrees of freedom. A skidsteer rover, such as a Clearpath Robotics Husky
[29], is subject to two motion constraints if the rover is not experiencing side slip and motion normal to the road surface: 1) the velocity of the vehicle is zero along the rotation axis of any of its wheels, and 2) velocity is also zero in the direction perpendicular to the traversal surface [30]. Due to frame rotations, zero vertical and lateral velocity do not mean that acceleration on these directions are zero.Following the similar process as in [28], it is assumed that the errorstate vector is defined by (6) and the total state vector is
(8) 
The rover velocity constraints can be applied as a pseudomeasurement update, assuming that the axes of the rearwheel frame are aligned with the body frame. This measurement update may be expressed as
(9) 
where is body to rear wheel lever arm, and is angular rate measurement. Then, corresponding measurement matrix may be approximated as
(10) 
where is lateral constraint part. and is the vertical part of the measurement matrix.
(11) 
Although the nonholonomic constraint measurement update is performed whenever the navigation solution is updated, note that the excessive sideslip invalidates the lateral velocity constraint and this adds extra biases to velocity solution. While turning, the heading rate of the rover can be observed and if it exceeds a threshold, the lateral velocity constraint measurement can be omitted.
IiD Zero Type Updates
During stationary conditions, IMU sensor outputs are governed by the planet’s rotation and sensor errors. Since the rover is often stationary during the mission, zerotype updates can be leveraged to maintain the INS alignment. To properly use these updates, stationary conditions must be detected accurately. Otherwise, the rover’s state yields incorrect updates leading to poor navigation performance [24]
. To detect stationary conditions, we used two different indicators, wheel odometry velocity, and the standard deviation of the IMU measurements, which assumes that the rover typically experiences less vibration whenever it is stationary.
Zerotype updates bound the velocity error and calibrate IMU sensor noises[31]. Therefore, the measurement innovation for zerotype update can be given as
(12) 
where is measurement innovation matrix, is estimated velocity vector, and estimated gyro bias. The measurement matrix is given
(13) 
It is also important to note that zerotype updates do not provide any position information; however, because the errorstate model properly accounts for the correlation between the velocity and position errors in the offdiagonal elements of the error covariance matrix, the cubic error growth of INS positioning is reduced to linear growth [32]. This enables zerotype updates to not only limit the error growth and help determine biases to reduce future error growth, but also to mitigate most of the position drift since the last navigation stop.
IiE Wheel Odometry Update
The wheel odometry outputs, wheel forward speed and heading rate, are averaged over the odometry measurement sampling interval. Heading rate is calculated by differencing the average linear velocity values of left and right wheels. It is also assumed that the axes of the rear and front wheel frames are aligned with the body frame.
In our implementation, we adopt a similar procedure as described in [30] and [28] to aid the sensors with an additional vertical velocity constraint as
(14) 
(15)  
where ,, and are predicted longitudinal, lateral and vertical rear wheel speed, respectively. The subscript denotes the estimated INS solution, and denotes the wheel odometry measurements. The measurement matrix is
(16) 
where
(17)  
where
is a 9by9 zero matrix,
and are 3by3 matrices, and are 1by3 row vectors. Note that the coordinate transformation matrix in is from the body to the inertial navigation frame.IiF Slip Detection
Skid steer vehicles rely on differing left and right wheel velocity directions to turn the vehicle. Due to redundant points of contact (i.e., two wheels driven by the same drivetrain on each side), slippage is often expected when turning motion is performed[33]. Since the IMU measurements are independent of the wheel odometry, the motion estimates from the EKF can be compared to the computed velocity based on the vehicle kinematics to determine if any statistically significant slippage has occurred. In order to detect the anomalies in velocity, the residuals between wheel odometry measurements and the EKF solution are computed using the Mahalanobis distance and compared against a threshold. Postfit residuals from the wheel odometry update are used to calculate the Mahalanobis distance as given in (18)
(18) 
where is the predicted covariance matrix. An empirical threshold on the Mahalanobis distance, , is used to specify whether the velocity anomaly is occurred or not.
The slippage is also monitored with the slip ratio calculation for front and rear wheels with respect to the INS velocity solution. The slip ratio, , is checked to specify if the slip is significant (i.e., ) along with the Mahalanobis distance value at the same timestep. We define the slip ratio, i, as follows:
(19) 
where is the translational velocity estimated from INS, is the wheel radius, and is the wheel angular velocity estimated from the wheel odometry measurements.
IiG Backward Smoothing
To smooth out the estimated state along the traversed path between zerotype updates, we used the RauchTungStriebel (RTS) backward recursive method [34], which utilizes all the available state information and goes backward in time.
A backward smoothing algorithm can be summarized as
(20) 
(21) 
(22) 
where is the smoothing gain, and are smoothed state vector and error covariance, respectively. Although zerotype updates correct most of the drift when the rover is stopped, the rover’s position solution still drifts while driving. To utilize the backward smoothing algorithm, the estimated states, state transition matrix, and error covariance between zerotype updates are stored in memory. The smoothing algorithm starts from the current navigation stop and goes back to the most recent previous navigation stop. This further mitigates the solution drift between stopping.
After smoothing between stops, the forward filter continues to provide a realtime available state estimate until the next navigation stop. In this scenario, for an error analysis, it is not simple to present the solution that would be available for realtime over a complete trajectory that includes multiple navigational stops. Therefore, in the presented experimental evaluation, solutions that only include the forward filtering mode are shown, so that the impact of smoothing can be assessed.
Iii Experimental Results
For experimental evaluation, a reference solution was determined using integerambiguityfixed carrierphase DGPS. This setup consisted of two dualfrequency Novatel OEM615 GPS receivers [35] and Pinwheel antennas [36], with one set mounted on a static base station and another affixed on top of the test rover platform. During the experiments, 10 Hz raw GPS pseudorange and carrierphase measurements were recorded on both receivers, and the reference position solutions were then postprocessed using the open source software library, RTKLIB 2.4.2 [37]. Postprocessed ambiguityfixed carrierphase DGPS is expected to provide centimetertodecimeter level accuracy [38].
The IMU incorporated on the rover is an ADIS 16495 [39]. This IMU reports to have an inrun bias and angular random walk values are , for the gyroscopes, and a biasstability and velocity random walk of 3.2 and 0.008 m/sec/ for the accelerometers, respectively. For wheel odometry readings, the ClearPath Robotics Husky’s quadrature encoders with 78,000 pulses/m resolution are used.
Several test runs on different terrain types i.e., concrete, grass, gravel, and sand as shown in Fig.2, were performed on the West Virginia University campus.
To demonstrate the proposed navigation approach, two different scenarios are detailed: 1) “ConcreteTurn”, the rover follows a flat, LShaped concrete path. 2) “RoughTerrain”, the rover traverses a longer path on nonflat, muddy, and grassy terrain with embedded rocks. For both scenarios, navigation stops were periodically commanded. The total distance traversed, Average Driving Time between Stops (ADTS), the number of performed stops, and the total driving time are listed in Table I. The rover has 0.4 m/s commanded velocity while driving in both scenarios.
Additional test scenarios, which are not included in this paper for the sake of brevity, can be found in the public repository associated with this paper.
To assess the relative benefit of each aspect of the approach, many of the update type solution combinations are performed for both test runs. The positioning error values with respect to each of the update combinations are given for each scenario in Tables II, and III, where RMS denotes root mean square, STD denotes standard deviation of the horizontal error, and Max. is the worst case horizontal distance error that rover encounters during each test.
Scenario Type  Distance  ADTS  Stops  Driving Time 

ConcreteTurn  34m  12s  7  85s 
RoughTerrain  151m  9s  42  406s 
Estimation  Horizontal Error (m)  RMS Error (m)  

I O Z N B ^{*}  Median  STD  Max.  East  North  Up 
I  518.44  494.77  1606.2  783.75  64.75  153.07 
I+O  23.73  12.59  34.26  21.80  10.08  7.07 
I+O+N  23.69  11.89  32.34  20.57  10.57  7.84 
I+O+N+B  23.75  12.25  33.30  21.18  10.45  7.57 
I+Z  2.86  6.42  31.09  7.38  4.28  4.46 
I+Z+B  0.60  1.58  31.62  1.23  1.46  1.68 
I+Z+N  0.58  1.19  8.54  1.28  0.81  0.81 
I+Z+N+B  0.63  1.13  7.69  1.28  0.74  0.95 
I+Z+O  0.68  0.31  1.33  0.67  0.31  0.67 
I+Z+B+O  0.66  0.31  1.33  0.66  0.31  0.69 
I+Z+N+O  0.49  0.25  1.20  0.43  0.36  0.71 
I+Z+N+B+O  0.48  0.25  1.21  0.43  0.36  0.73 

I:INS, O:Odometry, Z:ZeroType, N:NonHolonomic, B:Backward
Smoothing.
Estimation  Horizontal Error (m)  RMS Error (m)  

I O Z N B ^{*}  Median  STD  Max.  East  North  Up 
I  14253.  20742.  68676.  29200.  6045.  11334. 
I+O  21.31  18.69  63.90  23.37  17.45  18.07 
I+O+N  30.68  16.30  56.53  29.23  16.94  11.65 
I+O+N+B  30.84  16.35  55.71  28.92  17.06  11.97 
I+Z  1.77  3.13  31.40  4.02  1.09  2.19 
I+Z+B  1.55  1.23  29.75  2.06  0.96  0.86 
I+Z+N  0.93  0.99  4.08  1.46  0.73  0.92 
I+Z+N+B  1.59  1.07  4.01  1.79  1.09  0.58 
I+Z+O  1.36  1.29  4.28  2.16  0.29  1.18 
I+Z+B+O  1.21  1.28  4.29  2.13  0.32  0.90 
I+Z+N+O  0.47  0.90  2.86  1.25  0.27  1.04 
I+Z+N+B+O  0.54  0.93  2.89  1.28  0.41  0.80 

The same estimation types are used as in Table II.
Without using zerotype updates, the rover navigation performance is inadequate due to the accumulated error of the INS integration and the wheel slippage. Wheel odometry helps to reduce drift along with nonholonomic constraints within the INS solution; however, if the zerotype updates are applied, most of the accumulated error is mitigated as explained in Section IID. After the application of zerotype updates, nonholonomic constraints further enhance the solution. Note that, in this formulation, backward smoothing is shown to be most effective only if nonholonomic constraints aren’t applied. This could be useful for a holonomic rover.
To better visualize the effects of the zerotype updates, the estimation of the north error for ConcreteTurn case is given in Fig. 3. As shown in this figure, when the rover stops, the zerotype updates quickly reduce the growth of the position error and also correct most of the position drift.
To test the capabilities of the algorithm while turning, the rover was exposed to a high rate of heading change after a forward drive on a flat concrete surface. Moreover, the rover was purposefully exposed to slippage by commanding an instantaneous maximum velocity (0.4 m/s) and braking after and before zerotype updates. This is evident when velocity anomaly detection and zerotype updates overlap as shown in Fig.
4.Although nonholonomic constraints handle most of the lateral motion drift, when the rover heading rate is significant (e.g., it exceeds 0.1 rad/s), lateral velocity constraint measurement updates become less reliable. However, when using wheelodometry estimated heading rate measurements along with nonholonomic constraints to update the INS solution, less drift in position estimates is noticeable both when driving and when turning. This improvement is illustrated in Fig. 4.
Since the terrain of the “ConcreteTurn” scenario is mostly easy to traverse and less prone to vibration, we also performed another test run on a harsh, nonflat, and diverse terrain. In the “RoughTerrain” case, the rover traversed a longer path. The estimated east and north position estimation with 3 error covariances are given in Fig.5. A 3D view of the positioning estimation when using all of the proposed updates is given in Fig. 6.
Iv Conclusions
This work presents several approaches for enhancing the accuracy of wheeled planetary rover navigation. When using all of the presented update strategies together, the proposed approach was demonstrated to significantly reduce the rate of the rover navigation error growth. In addition, we showed that slippage can be detected by using a threshold on the velocity residuals and the slip ratio estimate. The primary value of this approach is that it can be used within current and future planetary rovers, as well as many other wheeled robots that frequently stops, to improve onboard localization performance without any hardware changes or major alterations in operations.
The software developed for this paper, which is designed for use under ROS, and the datasets used for experimental validation have been made publicly available at:
https://github.com/wvunavLab/CLN.
Future developments of this work will include the extension of the proposed algorithm to autonomously initiating the navigation stops. Additionally, we are investigating ways to improve the backward smoothing for reprocessing the estimated navigation solution to mitigate the error that comes from slipped wheel odometry updates between zerotype updates and methods to improve the navigation solution by using onboard terrain classification techniques.
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