LOCALIZATION OF A MARS ROVER IN MARSHELICOPTER-GENERATED MAPS

Kamak Ebadi*, Ali-akbar Agha-mohammadi*, Kyohei Otsu*

*NASA Jet Propulsion Laboratory, 4800 Oak Grove Dr, Pasadena, CA 91109, USA*E-mail: ebadi, aliagha, kyohei.otsu@jpl.nasa.gov

ABSTRACTNASA has been investigating the feasibility of de-ploying a low-flying rotorcraft scout on Mars toassist in the exploration of the planet. The coor-dination between Mars helicopter and rover is thenext challenge ahead. In this paper, we study thefeasibility and performance of high fidelity visualsensing for localization of a Mars Rover in Marscopter-generated-maps (CGM). Using a sequenceof aerial imagery captured by Mars helicopter fly-ing ahead of the rover, a map of the environmentis constructed and represented by a set of salientimage features. Accordingly, we study the per-formance of aerial-to-ground (A2G) image simi-larity evaluation embedded in a Bayesian filteringscheme for the purpose of robust rover localiza-tion. We test the system empirically at the JetPropulsion Laboratory’s Mars Yard and demon-strate its feasibility and performance.

1 INTRODUCTIONOver the past few decades, Mars exploration mis-sions have delivered a wealth of knowledge andinformation about the history, composition andevolution of Mars and the solar system. In or-der to improve the productivity of future roboticsmissions to Mars, NASA has been developing anautonomous solar powered helicopter that couldscout the terrain for future Mars rovers (Figure 1).The Mars Helicopter [1] significantly improvesthe distance traversed by the rover in a Martianday (Sol). In nominal conditions, the helicopterwould undertake daily autonomous flights, dur-ing which it would fly for several hundred metersand provide high resolution aerial map at altitudesranging from 3m to 10m above the ground. Therover needs to obtain accurate localization on theaerial map in order to safely navigate toward thescience targets for exploration.

Localization methods that rely on scene imagematching, have proven to be successful in envi-ronments where sufficient salient landmarks andfeatures at known locations can be extracted fromfeature-rich images of the environment [2, 3, 4].In such methods, once a query image is matched

Figure 1: A Mars helicopter would scout the localterrain ahead of the rover, and provide a high res-olution map of the environment. The rover needsto obtain localization on the aerial map, in orderto safely navigate toward the science goals - Im-age credit: NASA/JPL-Caltech

with a geotagged image, the location of the queryimage can be inferred from the matched image.As shown in Figure 2, in a Mars-like environ-ment due to presence of repetitive surface featuresacross multiple scenes, and sparsity of salientlandmarks in the environment, feature-based im-age matching often lacks sufficient distinctive-ness, and could result in perceptual aliasing andambiguity in rover localization. This problem isfurther exacerbated in case of aerial-to-ground im-age matching, due to the change in viewing anglebetween aerial and ground imagery.

An illustration of exploration by a team of Marsrover-copter is presented in Figure 3, which showsa 3D reconstruction of the JPL’s Mars Yard froma sequence of aerial images provided by the heli-copter. The map provides a high resolution rep-resentation of the local terrain along with regionsof interest and science targets for further surfaceexploration. Natural landmarks with known loca-tions on the map can serve as information sourcesthat rover can use to estimate its state.

In this work, we study the feasibility of obtainingaccurate rover localization on an aerial map, byrelying on A2G image similarity evaluation inte-grated with a probabilistic Bayesian filtering.

The rest of this paper is organized as follows: inthe rest of this section we provide a review of the

Figure 2: Different Martian terrain types - (a) rep-resents a feature-rich environment. (b) and (d)represent feature-poor environments. (d) repre-sents an environment with repetitive features - Im-age credit: NASA/JPL-Caltech

related work. Section 2 outlines the problem for-mulation. In Section 3, presents the problem ofperceptual aliasing in feature-poor environmentsand introduces our an image similarity evalua-tion pipeline in order to reduce the ambiguity inimage matching. Section 4 presents the integra-tion of the proposed image similarity evaluationpipeline with a Bayesian filtering algorithm in or-der to enable a robust vision-based localization forthe rover. Section 5 presents the results of our ex-periments in the JPL’s Mars Yard. Conclusion andfuture work are discussed in section 6.

1.1 Related Work

A2G Localization: Accurate vision-based local-ization is a fundamental prerequisite for reliableautonomous navigation, and over the past decadea growing body of literature has been focused onthis topic. In [4], authors address the problemof vision-based localization of a micro aerial ve-hicle (MAV) in an urban environment. The lo-calization with respect to surrounding buildingsis achieved by air-ground image feature match-ing between low-altitude MAV-based imagery andground level street view images. In a similar work[5], authors introduce an image-based localizationin urban environments based on the use of a wide-baseline matching technique. Accurate locationestimation is established from triangulation be-tween query image and the closest reference im-ages in geotagged database.

Authors in [6] propose a feature-based localiza-tion method between air and ground, by usingparticle filter and leveraging features associatedwith vertical structures. They obtain localizationby relying on robust descriptorless features suchas edges of buildings, and matching them to pre-determined locations of vertical structures in anorthographic overhead map. In [7], a ground-to-

Figure 3: By performing structure from motion onthe aerial imagery, the 3D reconstruction of theterrain in JPL’s Mars Yard is obtained. The aerialimagery is provided by a helicopter taking imagesof the terrain while flying in a zig-zag motion. Themap encodes information about the traversabilityof the terrain and location of autonomously dis-covered science targets. Using the onboard cam-era, the rover needs to obtain accurate localiza-tion on the map, in order to successfully traversethe terrain toward the science target.

air localization between a team of two aerial vehi-cles and a ground vehicle is presented. Using theUAV’s onboard cameras a map of the environmentis obtained. The ground vehicle then obtains poseestimates from a dedicated aerial robot that tracksand localizes the ground robot on the map.

Even though such methods perform well forvision-based localization in feature-rich environ-ments, it is not known if localization by relyingon feature-based image matching can perform ef-ficiently and robustly in Mars-like environmentswith sparse and repetitive features.

Mars Rover Localization: Rover localizationbased on satellite imagery has been a subjectof interest in the past decade. Authors in [12],warp rover’s images to obtain a birds eye viewof the ground, before comparing it against a gridof satellite imagery. In similar studies [13, 14],a rover localization approach using HiRISE [15]orbital imagery is introduced, where outstandinglandmarks such as craters, cliffs, and hills are usedfor image matching between ground and orbitalimagery. However, due to the low resolution ofHiRISE imagery, such methods are typically ef-fective in feature-rich areas with large and distinc-tive surface features.

2 PROBLEM FORMULATIONIn this paper, we address the problem of localiza-tion of an autonomous Mars rover in an aerial mapof a Mars-like environment, provided by a heli-copter scouting the terrain ahead of the rover.

Environment Representation: High resolutionaerial imagery of a Mars-like environment is ob-tained from a helicopter scouting the local terrain.From a sequence of n aerial images A = {ai}

ni=1, a

copter-generated-map (CGM) of the environmentis obtained.

Rover state and dynamics/sensing models: Therover dynamics is denoted by xk+1 = f (xk, uk,wk),where rover’s state (position) is denoted by x,which encodes rover’s location in CGM coordi-nate system.uk denotes the rover’s action obtained from visualor wheel odometry, and wk is the state-dependentprocess noise. Rover is equipped with on-boardcameras and zk = h(xk, vk) denote the rover’s ob-servation model (rover’s query images) at timestep k, where vk is the state-dependent observationnoise.

Objective: Given a copter-generated-map of aMars-like terrain, determine the rover’s state inthe CGM, relying on a sequence of observationsmade by the rover’s onboard cameras.

3 A2G IMAGE SIMILARITYEVALUATION

A Mars-like environment often lacks highly dis-tinctive visual landmarks that can be reliably usedfor image registration and retrieval. In addition,illumination variations, and changes in the view-ing angle between the aerial and ground imagerymakes it more difficult to reliably match the ex-tracted image features. As a result, feature-basedimage matching in such environments often lackssufficient distinctiveness, and leads to percep-tual aliasing. Figure 4 depicts our proposed im-age similarity evaluation pipeline, which enablesus to reduce the ambiguity in feature-based im-age matching and evaluate the similarity betweenground and aerial imagery.

Feature Extraction: With no global positioningsystem on Mars, the aerial imagery obtained bythe helicopter is not geo-registered and the rela-tive location of autonomously detected landmarksand science targets in the aerial imagery is un-known. In order to geo-register the images, andobtain the 3D structure of the terrain (Fig. 3), wefirst need to extract salient image features from the

Figure 4: Image similarity evaluation pipeline,enables reduction in data association ambiguityand similarity evaluation of rover’s observation tothe provided aerial imagery

aerial imagery. As presented in Section 5, we relyon the Speeded-up Robust Features (SURF) [16],that has a higher performance in terms of inliercorresponding features between aerial and groundimagery when tested on our dataset.

Structure form Motion: In the next step, weuse the iterative and robust structure from mo-tion (SfM) method presented in [17]. Structurefrom motion involves image feature extractionand matching, camera pose estimation, cameramotion estimation (from the estimated camera po-sitions), and recovery of the 3D structure of theterrain using the estimated motion and features.SfM estimates relative camera locations, as wellas relative locations of landmarks in aerial im-agery. For an aerial image ak, we denote the es-timated camera location by ck

A, and define CA =

{(ciA)}ni=1, the set of camera locations estimated for

n aerial images in A.

Copter-Generated-Map: We denote the copter-generated-map by CGM = {(pi

A)}ni=1, a set of nfeature keypoints extracted from the aerial im-agery A, where each keypoint pA, consists of aSURF feature descriptor and a 3D location (ob-tained from SfM) which represents the pose ofthe point in CGM. In addition, we define a map-ping, Points, between the feature keypoints andtheir corresponding camera locations and aerialimages. For instance, Points(pk

A) maps featurepoint pk

A to its corresponding camera location ckA,

and the aerial image ak where the point was ob-served.

Onboard Sensing: We denote rover’s observa-tions of the environment (query images) by zk =

{(piz)}

mi=1, a set of SURF feature keypoints ex-

tracted from rover’s image of the local terrain.

Similarity Evaluation: For every feature in zk,we perform the search in feature descriptor do-main for its closest neighbor in CGM by usingthe Fast Library for Approximate Nearest Neigh-bors (FLANN), that is proven to be efficient andfast when working on high dimensional spaces[18, 19]. FLANN uses multiple randomized KD-tree or K-means tree forests for search in high di-mensional spaces, which results in significant im-provement in computation and speed, compared tomethods that rely on the nearest neighbor search.

Outlier Rejection: After finding the correspond-ing features points, the Random Sample Consen-sus (RANSAC) algorithm [20] is used to detectand remove outliers from the set of correspond-ing points. Due to presence of repetitive and simi-lar surface features (Figure 2), RANSAC cannotcompletely remove the outliers from the set ofcorresponding points. Thus, in order to furtherreduce the number of outliers in the correspond-ing points, for every point P j

a for 0 < j < k weuse the mapping Points(p j

a), in order to find thecorresponding aerial image where the point wasobserved. If the number of inlier points that aremapped to the aerial image a j is less than 20, weconsider this as a weak match and remove all theinlier points from consideration. We denote thepair of inlier image features by Pz = {(pi

z)}ki=1 and

Pa = {(p ja)}kj=1 for the remaining points in rover’s

query image and the CGM respectively.

Perceptual Aliasing: After reducing the numberof outliers by using RANSAC and weak match re-jection, we define perceptual aliasing as the am-biguity in data association where the remaininginlier keypoints belong to multiple aerial images,each of which represent a different location onthe map. Figure 5, presents a typical example ofsuch perceptual aliasing in a Mars-like environ-ment. After applying RANSAC and weak matchrejection, there are a large number of inlier featurepoints between the query image of the terrain, andfour different aerial images.

3.1 Average Hausdorff Distance

After removing the outliers from the set of cor-responding points, using the mapping Points thatmaps each point to its corresponding aerial image,we group the corresponding points into subsets,Pa =

⋃ki=1 Fi and Pz =

⋃ki=1 Gi, such that all point

in a subset F j belong to aerial image a j and allpoints in G j are the inlier points corresponding toF j where 1 < j < k. In this step, we rely onthe pixel locations of F j and G j in the aerial and

ground images, in order to estimate a 2-D geomet-ric transformation between the two image. Thetransformation T , that maps the points from onesubset to another is then used to obtain F′j = T F j.In the next step the reprojection error, ha(F′j,G j),is obtained by finding the Hausdorff [21] averagedistance, which enables an accurate measure ofsimilarity between the two sets of projected pointsand measured points. We define the Hausdorff av-erage distance by

ha(F′j,G j) = (∑f ′j∈F j

ming j∈G j || f′j − g j||)(|F′j|)

−1 (1)

where |F′j| is the cardinality of F′. The similarityscore of an aerial image, a j ∈ A, to observation, zk

is given bys(zk, a j) = (1 + ha(F′j,G j))−1 (2)

Using this method, for an observation zk a sim-ilarity score is obtained for all aerial images inA. For images that are flagged as a weak match,or images with no corresponding points, a simi-larity score of 0 is assigned. Using the mapping,Points that maps a group of keypoints to a cameralocation where the points were observed, we canpresent the final result as a probability distributionthat represents the likelihood of observation zk foreach camera location in CGM

p(zk |xi) = s(zk, ai)(∑j∈A

s(zk, a j))−1 (3)

This computed distribution, is then used in theBayesian filtering scheme presented in Section 4,in order to compute and update the posterior prob-ability.

4 ROBUST LOCALIZATIONAs discussed in Section 3, A2G image matchingin a Mars-like environment leads to multi-modaland ambiguous results. The best one can obtainfrom A2G image similarity evaluation is a dis-tribution that represents the likelihood of everyobservation in CGM. This ambiguity in imagematching can be considered as a non-Gaussiannoise in visual sensing of the environment.

We rely on a Bayesian filtering scheme [22], tocope with such multi-modal similarity distribu-tions. As depicted in Figure 6, by relying onBayesian filtering, the localization uncertainty ofthe rover can be reduced when feature-rich se-quence of observations are obtained by onboardvision sensors.

Figure 5: A typical example of perceptual aliasing in a Mars-like environment - Due to sparsity of salientlandmarks and similarity between different scenes, extracted SURF features of a query image are matchedwith four aerial images, where each matched image represents a different location in the environment. OnlyFigure (a) is considered a true positive, as it represents the same location in the environment.

Figure 6: Evolution of belief over time - As rovertraverses the terrain, using Bayesian filtering, thelocalization uncertainty of the rover can be re-duced when feature-rich sequence of observationsare obtained by onboard vision sensors.

We denote the belief state of the rover by bk =

p(xk |z0:k), to represent a probability distributionover all possible states in CGM. Let B be theset of all belief states (belief space) of the rover.To capture the non-Gaussianity of the distribution,we represent the belief by a finite set of particles,where each particle consists of a state x in CGM,and an importance weight w, which is a measureof compatibility with new measurements.

At time t = 0, the prior belief that represents theinitial distribution of state for the rover is givenby p(x0|z0) ≡ p(x0). Since at this time no obser-vations of the environment are available, an accu-rate rover state estimation in CGM is not possi-ble. Thus, we assume it is equally likely for therover to be at any location in environment. Thiscan be shown with a set of n particles uniformlydistributed over the aerial map.

Prediction: In the prediction step, by relyingon rover’s motion model and data obtained fromrover’s odometry sensors (e.g., visual or wheelodometry), the prior distribution is propagated.

b−k+1(x) = conv(bk(x),N(uk,Q‖uk‖))=: τ−(bk(x), uk). (4)

Update: As the rover traverses the terrain and anew observation zk+1 is obtained, the similarity ofthe observation to the aerial imagery is evaluatedand using the distribution obtained from Eq.3 theimportance weight of each particle is updated as:

b̀k+1(x)=b−k+1(x)p(zk+1|x)=:τ+(b−k+1(x), zk+1). (5)

Resampling: We denote the importance resam-pling by

bk+1 = τs(b̀k+1(x)), (6)

where, τs is the resampling function. The prob-ability of a particle being selected during the re-sampling process is proportional to its importanceweight, which represents the likelihood of beingthe correct representation of rover’s state, giventhe motion and measurement models.

Bayesian Recursion: This recursive algorithmcontinues as the rover traverses the terrain andmakes new observations. The evolution of be-lief using the sequence of obseravtions and rover’smotion model is given by

bk+1 = τ(bk, uk, zk+1) = τs(τ+(τ−(bk, uk), zk+1)) (7)

where bk+1 is the new belief based on set of parti-cles that are sampled from the state space.

5 EXPERIMENTAL EVALUATIONMars Yard: We conduct a set of experimentsat the Mars Yard (Figure 7) in Jet PropulsionLaboratory. The Mars Yard is an outdoor sim-ulated Martian landscape environment that pro-vides a large test area (21m x 22m), to test dif-ferent robotic applications under natural lightingconditions. The soil characteristics, the rock col-ors, and their sizes and distribution are intended tomatch images from the Martian landscape.

Figure 7: A prototype rover for earth-based test-ing of Mars Rover in the Jet Propulsion Labora-tory’s Mars Yard

The Aerial Image Database: A Sony ICX445camera with a 2.7mm FUJINON Fish-eye lenswas used for acquiring the aerial imagery. Theaerial image dataset consists of 1400 color imagesat 640×480 resolution, and was created by movingalong a zig-zag trajectory at an altitude of ∼ 2mabove the surface. Figure 8 represents a top-view3D reconstruction of the Mars Yard terrain, ob-tained by performing structure from motion on theset of copter’s aerial imagery.

Figure 8: 3D Reconstruction of the terrain inJPL’s Mars yard, by performing structure frommotion on the aerial imagery. The flight path ofthe helicopter is shown on the map.

5.1 A2G Feature-Based Image Matching

Feature detection, description and matching areessential components of localization algorithmsthat rely on feature-based image matching. In aMars-like environment, with sparse salient fea-tures, viewing angle variations between aerial andground imagery can significantly impact the per-formance of feature-based image matching. Ro-bust image feature detectors and descriptors en-able the detection of discriminative local features

that can be repeatably detected at consistent loca-tions under illumination variations, image trans-formation and different viewing angle conditions.

In this experiment a reference image of the terrainwas obtained using a downward-looking camera.In the next step, the same part of the terrain wascaptured from different viewing angles. Figure 9-(a) represents the total number of extracted fea-tures (SURF, FAST, BRISK, Harris) from imagesof the terrain under different viewing angles.

Figure 9: Image feature matching performanceevaluation for different feature detectors and de-scriptors under different viewing angles

Extracted image features are then matched withthat of the reference image. Figures 9-(b) and (C),represent the total number of corresponding fea-tures, and total number of inlier features respec-tively. For our dataset, the Speeded up robust fea-tures (SURF) [16] outperformed other methodsand provided the largest number of inlier imagefeatures under all viewing angles.

Rover Localization in CGM: In this experimentthe objective is to establish rover localization onthe provided aerial map by capturing pictures ofthe terrain and matching them against the pro-vided aerial imagery. In the first step, as presentedin Figure 8, a high resolution map of the environ-ment is obtained from helicopter’s aerial imagery.

In the next step, the relative location of the camerain every aerial image is estimated using the struc-ture from motion. The rover is then initialized ata random location within the mapped area, and asequence of observations at random locations areobtained as the rover traverses the terrain. As pre-sented in Figure 10-(a), since no measurementsare available at time t = 0, particles representingthe initial state of rover are distributed uniformlyover the entire map, representing an equal like-lihood for the rover to be at any location on theaerial map. The ground truth location of the roveris shown in the map.

Figure 10: An example of proposed localizationmethod. Image (a) represent the initial belief attime t= 0. Images (b) and (c), represent the distri-bution of the posterior belief after making 3 and 8observations of the environment respectively.In the prediction step the particles are propagatedby relying on rover’s visual odometry. As new ob-servations become available, the similarity of newobservations to aerial imagery is evaluated, andthe result is used to update the importance weightof propagated particles. Particles are then resam-pled, where the probability of a particle being re-sampled is proportional to its importance weight.

As shown in Figure 10-(b), after making few ob-servations particles are mostly converged aroundfour locations in CGM. This ambiguity in lo-calization is due to multi-modal outcome of theimage similarity evaluation pipeline. Terrain im-ages in these four locations are shown in Figure 5which shows the high level of perceptual similar-ity between the scenes. Relying on more observa-tions and iterating through the Bayesian filteringalgorithm, particles are converged to the locationof the correct state of the rover in CGM as shownin Figure 10-(c).

6 CONCLUSIONIn this paper, we discussed various challenges inaerial to ground localization, including percep-tual aliasing, significant view-point changes, andhandling feature-poor areas in a Mars-like envi-ronment. We studied the feasibility of A2G lo-calization of a Mars rover in a Mars helicopter-generated map from a relatively sparse sequenceof images. Specifically, we studied the A2Gimage similarity evaluation embedded in a non-Gaussian recursive filtering scheme, to enable arobust localization.

For future work, we will evaluate the performanceof the proposed system on different terrain types(sandy and smooth terrain, rocky terrain, and ter-rain with repetitive features), and under differentillumination conditions. In addition we will studyhow active perception methods (e.g. POMDP-likemethods [23, 24]) can enhance the localizationperformance by actively taking actions that lead tohigher perceptual information gain and ultimatelya higher situational awareness.

ACKNOWLEDGEMENTThe research was carried out at the Jet Propul-sion Laboratory under a contract with the NationalAeronautics and Space Administration. U.S. Gov-ernment sponsorship acknowledged.

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