LARGE SCALE MARS MAPPING AND ROVER LOCALIZATION USING DESCENT AND ROVER IMAGERY

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1 LRGE SCLE MRS MIG D ROVER LOCLIZIO USIG DESCE D ROVER IMGERY Rongxing LI *, Fei M *, Fengiang U *, Larry MHIES **, Cark OLSO **, Yaing IOG ** * Departent of Civi and Environenta Engineering and Geodetic Science, he Ohio State University 470 Hitchcock Ha, 070 ei venue, Coubus, OH 430, US i.8@osu.edu ** Jet ropusion Laboratory, Caifornia Institute of echnoogy asadena, Caifornia 909, US HYERLIKHYERLIK Working Group IV/ KEY WORDS: unde djustent, Rover Locaization, Mars Mapping, Descent Iagery, Rover Iagery. SRC he exporation of Mars by anding robotics requires arge-scae apping of the Martian surface and accurate rover ocaization. he resoution of the obiter iagery is too ow to provide terrain inforation for the rover to traverse the Martian surface safey. Future MS (Mars Surveyor rogra) exporation issions wi extend the rover exporation range fro the anding center region to an area of 0kx0k. his cas for high precision argescae apping and rover ocaization with an accuracy of up to 0.%. his paper presents a ethod of arge-scae apping and rover ocaization using descent and rover iagery. set of descent iagery and rover stereo iagery, coected during a fied test at Siver Lake, C, in May 999, is integrated into a bunde adjustent syste to ocaize the rover position. It is deonstrated that rover ocaization with a RMS of 0.4, 0.08 and 0.34 in the x, y and z direction, respectivey, for a distance of up to 500, and 0.3, 0. and 0.46 within.5k can be achieved. his apparenty eets the objective of controing the rover navigation error within 0.% ( for k). IRODUCIO he Mars exporation architecture often consists of an orbiter, ander, and rover. ccurate navigation and ocaization of the over reative to the ander are needed so that the rover ay safey traverse the Martian surface and counicate with the ander as far away as, for exape, 0 k fro the ander. his cas for high precision, arge-scae apping of the surface and rover ocaization with an accuracy of up to 0.% (Matthies, et a. 997; Li, et a. 000). he resoution of the obiter iagery is too ow to provide the needed terrain inforation. he current navigation data, obtained fro a heading sensor, an odoeter and other sensors with an error of approxiatey 0% of the distance fro the ander is not sufficient for this task. he unique characteristics of the descent iagery that wi be avaiabe in the future issions otivate the use of orbita data, descent iages, and rover iages for accurate rover ocaization (Matthies, et a. 997). he Mars athfinder has successfuy conducted a near-ander rover ission. he rover Sojourner provided powerfu cose-range toos for icroscae rock investigation, soi research and other scientific objectives within an area of about 0 x 0 fro the ander. s part of the Mars Surveyor 00 ission, it is panned that the Marie Curie rover, which is very siiar to the athfinder Sojourner Rover, wi be sent to Mars. In the 003 and 005 Mars Missions, the rover FIDO, a prototype of the Mars Sape Return rovers, wi carry the integrated thena Science ayoad to Mars. Research was carried out on rover ocaization using severa different ethods. Vope et a. (995) used a coored cyinder to provide reasonaby accurate position and heading inforation for the rover within a 0 eter range at an accuracy of typicay 5 o for heading and 5% for distance. nother approach tested axiu ikeihood estiation techniques for perforing rover sef-ocaization in natura terrain by atching range aps (Oson, et a. 998). his technique can find the best position in soe discretization of the pose space and does not require an initia estiate of the rover position. his paper discusses arge-scae surface apping and rover ocaization using descent and rover iagery based on photograetric ethods. First of a, a set of descent iages at different resoutions is used to construct a DEM by deterining the descent iagery orientation paraeters. he descent iages taken fro above 5000 to severa eters above the ground have a hierarchy of resoutions (fro coarse to fine), which atch those of the orbita iagery and the ground ander and rover iages. his akes descent iagery extreey vauabe to scientists for ission panning and to engineers for operating the rover. Specificay, for rover ocaization, the descent iagery provides an effective way Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda

2 to enhance the geoetry by integrating orbita, descent and ander/rover iages to for an iage network. raditiona aeria trianguation is perfored on pairs or strips of horizonta iagery at neary the sae atitude and with arge areas of overapping. Here, in contrast, we anayze and test bunde adjustent on descent iagery at severa different resoutions. Second, the rover iage ocations and orientations are precisey deterined within the network using an extended bunde adjustent. he cobined data set of descent and rover iages ensures that rover ocations farther away fro the ander wi be deterined at an accuracy cose to those near the ander. We present the resuts of rover ocaization tests using descent and rover iagery acquired at the fied test site at Siver Lake, C, in May 999 (Li, et a. 000). Different adjustent odes have been used to ocaize the rover, in which ground contro points, tie points, caera caibration paraeters, and various distortion paraeters were taken into account. Using the bunde adjustent syste we deveoped, we are abe to integrate the descent iagery and rover iagery to achieve a RMS of 0.4, 0.08 and 0.34 in the x, y and z directions, respectivey, for a distance of up to 500, and 0.3, 0. and 0.46 within.5k. he objective of controing the navigation error within 0.% ( for k) is apparenty et. D CQUISIIO D REROCESSIG Descent iaging systes have been successfuy used for unar exporation to provide ipressive views of oon. In future Mars exporation issions, the Mars Decent Iager (MRDI), wi acquire data during the oents eading up to the touchdown, fro the tie that the spacecraft's heat shied fas away unti the spacecraft reaches the surface (Main Space Science Systes 000). MRDI wi be abe to iage the anding site at an interesting set of resoutions over a wide fied of view (FOV). MRDI wi be a crucia ink between the orbiter and ander observations, providing the context for panning the traverses of the rovers that wi roa around, ooking for interesting geoogic features to study. MRDI has a foca ength of 7.35, a FOV of 73.4deg and an iage size 0404 pixes. he first iage wi be taken at 5000 height. he resoutions vary fro 8.65 per pixe to 9 per pixe. Radia ens distortion is the doinant distortion in the descent iagery. Suppose r is the distance of a point on the iage fro the principa point, δr is the radia ens distortion, k, k, k 3, k 4 are the coefficients of the radia ens distortion, the correction of radia ens distortion is δ r k r k r k 3 r k 4 r. Decentering distortion is another kind of ens distortion that appears in descent iagery. Suppose x, y are coordinates of a point on the iage, δ x and δ y are decentering distortion corrections in the x and y directions, p and p are coefficients of the decentering distortion, the correction for decentering ens distortion in the x direction shoud be x p r xy p xy δ, and in the y direction y p r y p xy δ. Since the descent iagery wi be taken starting at an atitude of 5000, the correction for the Martian curvature wi be needed. If H is the iaging height, R the Martian radius (3397 k equatoria radius, 3375 poar radius), f the MRDI foca ength, and δ r the correction for Martian curvature, then 3 H δ r r c. R f EMEDEMEDEMEDEMED he fied test at Siver Lake, C conducted in 999 is described in detai in (Li et a., 000). 5 descent iages and severa sets of FIDO avca iagery at 5, 500 and.5k away fro the descent center were acquired. he distortion of the descent iagery is up to 0 pixes. he distortion of the avca iagery is about 0.5 pixe to pixe. c 3 HOOGRMMERIC MODELIG FOR HDLIG DESCE IMGERY 3. otentia of the Descent Iagery Conventiona aeria photograetry is used with horizonta iages that are usuay taken at neary the sae atitude with a reguar overapping area of about 60%. However, the descent iages were acquired at a sequence of decreasing atitudes. Landarks ay appear in utipe descent iages with different resoutions, the degree of detai decreasing as the iage resoution decreases. It is very difficut to find ground features that appear in a the descent iages and are appropriate for seection as tie points. herefore, ost tie points chosen are those that appear in a few adjacent iages whose resoution differences are not too arge. hus, the resuting tie points ink Figure. Geoetry of descent iaging 580 Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda 000.

3 the descent iage sequence hierarchicay in the vertica direction. In the idea situation, the descent iagery can be treated as vertica photography (Wof, 983), and so the rotation 3 cosκ sinκ 0 atrix can be sipified: 3 sinκ cosκ 0. ased on the coinearity equations: ( ) ( Y Y ) ( Z ) and Z ( ) ( Y Y ) ( Z Z ), any two descent iages O O 3 O O O 3 O x f y f p p ( ) ( Y ) ( Z Z ) ( ) ( Y Y ) ( Z Z ) 3 O 3 O 33 O 3 O 3 O 33 O that share the sae feature point can theoreticay deterine the ocation of the corresponding 3-D position. Suppose the descent iage orientation paraeters are fixed, we inearize the coinear equations: v v x y p p ( f cosκ /( Z p Zo ) d ( f sinκ /( Z p Zo ) dy ( x p ( Z p Zo ) dz / ( f sin κ /( Z p Z o ) d ( f cosκ /( Z p Z o ) dy ( y p ( Z p Z o ) dz / Fro the geoetry of vertica photography, we aso know that ( x p f )( Z ZO ) Y ( y f )( Z Z ) Z is, the ower the accuracies of p / O. herefore, the higher the iaging atitude o / and Z, Y are. Furtherore, with the increase of iaging atitude, the descent iagery resoution becoes ower, and aso the ow accuracy of iage easureent eads to the ower accuracies of Z, and Y. Figure iustrates the geoetry of the descent iagery. Fro any two consecutive descent iages, there shoud be enough tie points to deterine the iage orientation paraeters. With a set of consecutive descent iages, a bunde adjustent with enough tie points hierarchicay distributed in the vertica direction eads to a high accuracy that is even cose to that achievabe by horizonta iage bocks. 3. Least squares adjustent of a free descent iage network In the environent of a Mars anding site, there wi be no ground contro. he axiu goba orientation avaiabe ay incude an approxiate ander ocation, and an aziuth pointing to a andark defined in the atest goba Mars contro network with a point accuracy of 750 (Zeiter et a. 000). So the network coputation shoud be perfored as a free network. In our experient, a oca coordinate syste is constructed. ecause the rover position can be reated to the ander, the origin of the oca coordinate syste shoud be the ander ocation. In the bunde adjustent ode we appy three constraints: scae, aziuth, and zenith that can be suppied by a andark reative to the ander. Suppose o, Y o and Z o are the coordinates of the ander position which wi be set to (0,0,0) in the oca coordinate syste, E, Y E and Z E are cooridnates of a andark, and D is the distance between the, then the scae constraint is given as ( O) ( Y YO) ( Z ZO) D. Suppose the aziuth and zenith of the andark in the oca coordinates are β and α, then the zenith constraint and aziuth constraint are represented by ( ) ( ) ( ) ) tan Z Z O / O Y Y O β and tan ( Y YO) /( O) ) α. he network is soved by an extended east squares adjustent. he easureents of iage points with weight constitute observation equations V L, with the constraints represented as H W. ppying the east squares n principe, in( v ) where v i are residua of each of the easureents and iniu nor i in( x ) where x i i i i are unknowns soution, the soution is as foows, and ( ) ( ) ( W H ( L ) L H H H () σ 0 sqrt in r i /( rank ( )) () i Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda

4 Σ σ H ( H H ) H (3) 0 where the nora equation is decoposed into the fu atrices U and V, and the diagona atrix D as d U D V, 0, and the rank of is counted as the nuber of d i >0, the generaized D inverse of is cacuated by 0 d V d n diag. d U j 3.3 Experient Resuts he 0 descent iages shown in Figure with iaging heights ranging fro 085 to 8 were seected to conduct a bunde adjustent using the above agorith. he iaging caera has a foca ength of 5.7 and a fied of view of 6 o. he iage size is pixes. Figure. set of descent iages Within the iaging area, GCs that have known three diensiona coordinates fro the DGS survey were used as check points. s iustrated in Figure 3, the GCs are distributed syetricay around the descent center G and the aternative center of G5 in order to evauate their effect on the accuracy of the network. 7 tie points were anuay seected and hierarchicay distributed in the vertica direction. oca coordinate syste was constructed with the descent center G as the origin. In order to foruate the three constraints: scae, aziuth, and zenith, G0 was suppied as a andark reative to G. nother 9 GCs (G, G3, G4, G5, G6, G7, G8, G9 and G) which are covered by at east of these 0 descent iages were seected as check points. Figure 3. Distribution of ground contro points abe ists estiated standard deviations of the exterior orientation paraeters of the descent iages. he coputationa resuts show that the standard deviations of the exterior orientation paraeters of the descending iagery increase as the atitude increases. Coparing this with the resuts of the bunde adjustent tested on the sae 0 descent iages but with ground contro points (abe of Li, et a. 000), it can be seen that the standard deviations of the exterior orientation paraeters exhibit the sae tendency as the iaging atitude increases. he resuts are neary the sae in ters of accuracy, but the accuracy of the exterior orientation paraeters of higher atitude iages in the free network is sighty 58 Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda 000.

5 iproved. his deonstrates that the bunde adjustent on descent iages without ground contro can achieve the sae accuracy as that with ground contro and the accuracy is ore eveny distributed. he coparison aso tes us that the accuracy of the exterior orientation paraeters of the descending iagery depends on the structure of the network and the distribution of tie points. hoto-id () Y () Z () ω (in:sec) φ (in:sec) κ (in:sec) titude () :6.4 :53.7 : :8.7 :3.0 : :6.8 9:3.7 : :50.8 6:56.0 : :30.3 5:50.0 0: :3.7 5:47.4 : :7.7 5:6.3 0: :4.9 5:9.8 : :53. :5.5 0: :6.6 :.6 0: abe. Standard deviations of exterior orientation paraeters of the descent iagery Furtherore, we aso anayzed the reationship between errors of the ground point cacuated by the adjustent and their distances fro the descent center. he RMS errors cacuated for 9 checkpoints within 500 fro the descent center are 0.4, 0.5 and 0.38 in the, Y and Z directions respectivey. Figure 4 describes the regression resut of this reationship. he curve shows, to soe extent, the genera trend that the farther away a point is, the ower its accuracy is. ut there is no inear reationship between the distance and the point accuracy. In fact, the point accuracy depends on a copex set of factors such as the geoetric strength of the network, and the nuber and distribution of GCs and tie points, aong others. It is cear that Eevation (Z direction) has apparenty ower accuracy than the panietric ( and Y) directions. Fro this experient, it is concuded that at east to 3 tie points shoud be seected in the centra and four corner areas of each iage. Figure 4. Ground point accuracy vs. distance fro the descent center he RMS cacuation resuts of the bunde adjustent under ground contro for 4 check points (G, G5, G9, and G) are 0.4, 0.08 and 0.34 (Li, et a. 000). Moreover, the diagras of ground point accuracy vs. distance fro the descent center have the sae tendency at these different situations. (a) (b) Figure 5. DM of the Siver Lake test fied: (a) DM draped with a descent iage and (b) coor coded DM he above descent iages and the coputed orientation paraeters were used to generate a digita terrain ode (DM) of the test area at Siver Lake, C. First, the DM was fied with an initia eevation coputed fro a few points, for exape, tie points or GCs. Second, a top-down schee was used to register 0 pairs of adjacent descent iages fro high eevations to ow eevations. Corresponding features between pairs were then atched through epipoar ine searching, area-based correation, and east squares atching. hird, an initia DM was buit based on the Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda

6 584 Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda 000. atched features. Finay, a botto-up schee was appied to refine the DM in which each grid point of the DM was back-projected onto a possibe overapping descent iages to find the corresponding features. uti-iage photograetric trianguation provided an iproved eevation of the grid point. his process was appied to a the grid points to generate the fina refined DM dispayed in Figure 5. 4 ROVER LOCLIZIO USIG DESCE D ROVER IMGERY 4. heoretica spects of Rover Locaization Using Descent and Rover Iagery With the oveent of rover, rover position wi be ocated step by step. he foowing increenta bunde adjustent is used to ocate the rover position. First the observations are decoposed into two parts. v, - (4) Y v, (5) where Equation (4) represents the reationship between the observations and unknowns (incuding rover position) at step -, whie Equation (5) represents the next step () observations and the previous unknowns and new unknowns Y. Suppose ( ) H G G K, then the soution at step is deterined by ( ) ( ) ( ) ( ) ( ) H F W G F W Y (6) Y (7) where ( ) ( ) ( ) F, ( ) H I W, ( ) ( ) ( ) F. 4. Experient Resuts and ccuracy Coparison n experient to test rover ocaization using descent and rover iagery was perfored with descent iages centered around the descent center and 4 pairs of rover iages fro 5, 500 and.5k away fro the ander position (descent center). In order to cover the rover ocation in the channe area that is about.5k away fro the descent center, four additiona descent iages that have fying heights of were aso used. he overap between the iages and the two higher atitude descent iages is about 30%. Figure 6 shows the footprint of the descent iagery and the rover ocations. he resoution difference between the highest descent iage (34 atitude) and the owest descent iage is aso significant, for it akes tie point seection difficut. Extensive anua seection and easureent of tie points was required. Figure 7 iustrates the correspondence between descent iagery and rover navigation iagery. Furtherore, to overcoe the difficuty with finding correspondences between the descent iages and rover iages, we utiized the observations of positiona and orientation inforation provided by the rover syste as an approxiation. abe ists the standard deviations of exterior orientation paraeters of rover iages that were taken in three ocations arked in Figure 6. Rongxing Li

7 hoto-id () Y () Z () ω (in:sec) φ (in:sec) κ (in:sec) Distance to descent center () : :4.6 59: :36. 73:.7 57: :7. 54:9.0 33: :4.4 54: : :3.4 3:7.5 6: :59. 3:4.3 6: abe. Standard deviations of exterior orientation paraeters of six rover iages Figure 6. he footprint of descent iagery and rover ocations. Figure 7. Correspondence between descent iagery (botto) and rover navigation iagery (top). he adjustent resut shows that the positions of the rover caeras can be ocaized with an accuracy of within a distance of about.5k fro the descent center. he coputed root ean square errors (RMS) of the ground coordinates of the check points are 0.9, 0.05, and in the, Y, and Y directions, respectivey. Figure 8 deonstrates the reationship between the point accuracy and the distance fro the descent center coputed fro the free network. In fact, ore experients show that the estiated standard deviation of the unit weight observation of the free network adjustent is better than that of the network with ground contro because the entire network is associated with a oca coordinate syste instead of being forced into a goba coordinate syste. Figure 8. Ground point accuracy vs. distance fro the descent center fro the adjustent for rover ocaization 5 COCLUSIOS Large-scae apping of and rover ocaization on the Martian surface using descent and rover stereo iagery has been studied through the processing of the fied data coected at the Siver Lake test site. ased on the above coputationa resuts and anaysis, the RMS of coordinates in the x, y and z directions are around 0.4, 0.08 and 0.34, respectivey, for ground points within 500 fro the descent center using a network with ground contro. hey are around 0.3, 0. and 0.46 for ground points within.5k fro the descent center using a free network adjustent. he rover can be ocaized at an accuracy of about over a distance of.5k. We woud ike to draw the foowing concusions: Rover ocaization through a bunde adjustent using descent and rover stereo iagery has the potentia to achieve an accuracy of 0.% for Mars exporation. he resut of the free network bunde adjustent deonstrated the geoetric and accuracy patterns siiar to the bunde adjustent with ground contro. his ensures that the deveoped coputationa ode wi fit the Mars anding site environent where no ground contro wi be avaiabe. Rover ocations at the boundary of the descent iage coverage area can aso be deterined accuratey if ground features or andarks between the rover iages and higher atitude iages can be recognized and precisey easured. Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda

8 One of the keys in successfu processing the descent and rover iagery is to seect a sufficient nuber of tie points that are eveny distributed in the iaged area. his is even ore crucia to the free network bunde adjustent. High quaity tie points between the descent and rover iagery are essentia to accurate rover ocaization using this ethod. CKOWLEDGMES We wish to thank Dr. C. oth, Dr. D.G. rzezinska and Mr. E.Oshe of the Center for Mapping, the Ohio State University for their assistance in fied data coection and initia data processing. We aso thank Mr. J. Liu and the survey crew of J& Inc. for the DGS ground surveying. Data provided by Dr. R. rvidson of Washington University and JL/S were vauabe to the experient. he project is funded by JL/S. REFERECES Li, R., F. Ma, F. u, L. Matthies, C. Oson and Y. iong, Mars Rover Locaization Using Descent and Rover Iagery Resut of he Fied est at Siver Lake, C. roceedings of SRS nnua Conference, 000, Washington D.C. Main Space Science Systes, 000, (0 March 000) Matthies, L., C. Oson, G. harp and S. Laubach, 997. Visua ocaization ethods for Mars rovers using ander, rover, and descent iagery. Internationa Syposiu on rtificia Inteigence, Robotics, and utoation in Space (ISIRS), pp.43-48, okyo, Japan. Oson, C. and L. Matthies, 998. Maxiu Likeihood Rover Locaization by Matching Range Maps, roceedings of the IEEE Internationa Conference on robotics and utoation, pp Raeburn,. and M. Goobek, 998. Uncovering the Secrets of the Red anet: Mars. ationa Geographic Society, 3p. Vope, R.,. Litwin and L.H. Matthies, 995. Mobie Robot Locaization by Reote Viewing of a coored Cyinder, roceedings of the Internationa Conference on Robots and Systes (IROS), ittsburgh, ugust Wof,., 983. Eeents of photograetry. McGraw-Hi ubishing Copany, 68p. Zeiter, W.,. Ohhof and H. Ebner, 000. Recoputation of the Goba Mars Contro oint etwork. hotograetric Engineering and Reote Sensing, 66(), Internationa rchives of hotograetry and Reote Sensing. Vo. III, art 4. sterda 000.