Modeling and Validation of Mobility Characteristics of the Mars Science Laboratory Curiosity Rover

Home , Mars rover, Mars Science Laboratory, Opportunity (rover)

C. Senatore*, N. Stein**, F. Zhou**, K. Bennett**, R. E. Arvidson**, B. Trease***, R. Lindemann***, P. Bellutta***, M. Heverly***, K. Iagnemma*

*Laboratory for Manufacturing and Productivity, MIT, USA e-mail: [email protected], [email protected] **Earth and Planetary Remote Sensing Laboratory, University of Washington in St. Louis, USA e-mail:[email protected], [email protected], [email protected], [email protected] ***Jet Propulsion Laboratory, NASA, USA e-mail: brian.p.trease@jpl.nasa.gov, [email protected], [email protected], [email protected]

Abstract barchan dunesto get to Mount Sharp and duringthe ascent of Mount Sharp, which contains steeply sloped terrain and This paper describes recent work toward developing bedrock surfaces covered by loose, sandy soils of varying a terramechanics-based modeling and validation infras- depth. tructure for characterizing the Curiosity rovers mobility Realistic simulations of rover-terrain interactions dur- properties on the Mars surface. The resulting simula- ing traverses are needed to help engineers define safe and tion tool, ARTEMIS (Adams-based Rover Terramechan- ffi ics and Mobility Interaction Simulator), is composed of a e cient paths to waypoints for robotic systems such as Opportunity and Curiosity. A spin-off of such a capability MSC-Adams dynamic rover model, a library of terrame- is that the rover can also be used as a virtual instrument, chanics subroutines, and high-resolution digital elevation maps of the Mars surface. sensing the terrain slope distributions, together with soil and bedrock properties. Registration of model and flight Rover-terrain interactions that are modeled include data can be used to retrieve surface properties and also longitudinal, lateral, and vertical wheel-terrain interaction increase the confidence with which future traverse path forces, the effect of slip sinkage, and multi-pass effects. options can be simulated. A single wheel ARTEMIS model was also developed. Model validation has been performed via several comple- This paper describes recent work toward developing mentary methods. Mobility properties of a Curiosity rover a terramechanics-based modeling and validation infras- flight spare wheel have been analyzed at the Robotic Mo- tructure for characterizing the Curiosity rovers mobility bility Groups terramechanics lab at MIT using a single properties on the Mars surface. The resulting simula- wheel test rig capable of reproducing forced-slip and free- tion tool, ARTEMIS (Adams-based Rover Terramechan- slip conditions. In order to evaluate ARTEMIS potential ics and Mobility Interaction Simulator), is composed of a in full, the simulation was used to model the performance MSC-Adams dynamic rover model, a library of terrame- of the Mars-weight Curiosity test rover (a.k.a. Scarecrow) chanics subroutines, and high-resolution digital elevation while operating in realistic scenarios. maps of the Mars surface [11]. Rover-terrain interactions that are modeled include longitudinal, lateral, and vertical wheel-terrain interaction forces, the effect of slip sink- 1 Introduction age, and multi-pass effects. ARTEMIS has previously The Mars Science Laboratory (MSL) Curiosity rover been successfully employed to model MER rover mobility successfully landed on Mars on the plains of Gale crater properties [11, 1]. on August 6th 2012 [5]. From a mobility standpoint, The paper is organized as follows. Section 2 briefly the ongoing mission has thus far encountered mostly be- introduces ARTEMIS; section 3 presents the MSL single nign plains composed of soil-covered surfaces with em- wheel terramechanics test bed; section 4 describes the re- bedded rock clasts, together with some bedrock outcrops golith simulants utilized for this study; section 5 shows [2]. However, it is likely that Curiosity will face more single wheel forced-slip and free-slip experiments and full challenging terrains when crossing the longitudinal and vehicle experiments on inclined terrains. 2 ARTEMIS [4]. The angle at which the maximum normal stress occurs can be calculated as: ARTEMIS (Adams-based Rover Terramechanics and Mobility Interaction Simulator), is composed of a MSC- θm = (a1 + a2i)θ f (4) Adams dynamic rover model, a library of terramechanics subroutines, and high-resolution digital elevation maps The wheel is divided into “slices” normal to the axis of the Mars (or other candidate terrains) surface. Rover- of rotation and the entry and exit angle are calculated for terrain interactions that are modeled include longitudinal, each slice. The normal stress in each patch is computed lateral, and vertical wheel-terrain interaction forces, the independently. Shear stress in the longitudinal direction effect of slip sinkage, and multi-pass effects. ARTEMIS (i.e. the direction of travel) is the primary source of driv- is able to handle interactions with soft soil (i.e., regolith) ing traction. Shear stress is function of soil parameters and hard terrains (i.e., bedrocks, flagstones, etc.). For the and the measured shear deformation, j: deformable soil interaction model, formulations are based − j − k on the traditional terramechanics theory by Bekker and τ = (c + σtanφ) 1 e x (5) Wong [3, 10]. where c is the soil cohesion, φ is the angle of internal fric- To facilitate understanding of the parameters dis- tion, kx is the shear modulus(a measure of shear stiffness), cussed in this paper, a brief introduction of the key ter- and j is shear deformation: ramechanics formulations is presented here. ARTEMIS has previously been successfully employed to model t0 θ f dθ = = MER rover mobility properties and more details on j vtdθ vt (6) Z0 Zθ ω the terramechanics subroutine can be found in [11, 1]. where vt is the tangential slip velocity and kx is the shear The model relies on terramechanics relations first devel- modulus. oped by Bekker and later modified by Wong and Reece Traction forces generated by a wheel can be decom- [wong67a,wong67b]. Figure 1 indicates the chosen coor- posed in two components: a thrust component, which acts dinate frame and introduces a schematic representation of to move the vehicle forward; and a compaction resistance the stresses acting on the wheel. component, which resists forward motion. Thrust, T, is The normal stress at the wheel-terrain contact patch computed as the sum of all shear force components in the is assumed to be purely radial, and is calculated using the direction of forward motion: Wong and Reece equation [wong67a] θ f T = br τ cos θdθ (7) Zθr σ = ψzn θ <θ<θ = 1 1 m f σ n Compaction resistance, Rc, is the result of all normal σ2 = ψz θr <θ<θm  2 force components acting to resist forward motion, and can = − z1 r(cos θ cos θ f ) be thought of as the net resistance force provided by the θ − θr soil: = − − − θ f z2 r cos θ f − (θ f θm) cos θ f (1) θm θr ! ! Rc = br σ sin θdθ (8) Zθr where θ f is the soil entry angle, θr is the exit angle, θm is The net longitudinal force, also termed the drawbar the angle at which the maximumnormal stress occurs, and pull, is calculated as the difference between the thrust r is the wheel radius (see Figure 1). ARTEMIS can utilize force and resistance force. DP is the resultant force that either Bekker or Reece pressure-sinkage formulation: can provide a pulling/braking force at the vehicle axle.

DP = T − Rc + Fg (9) kc + k Bekker ψ = b φ (2) ck′ + ρgbk′ Reece where Fg is the thrust produced by grousers. More detail  c φ about grousers force calculation can be found in [11].  ′ ′ Parameters kc, kφ, n, kc, kφ depend on soil properties, The importance of drawbar force is obvious, since a while g is gravity, ρ is terrain density, and b corresponds positive drawbar force implies that a rover can generate to the smallest dimension between the wheel width and forward motion on a particular patch of terrain, while a contact patch length. To better model slip-sinkage effects negative drawbar force suggests that forward motion is the sinkage exponent n is expressed as function of slip as difficult or impossible. Torque, M, is the resultant of follows: shearing action along wheel rim, and can be calculated n = n0 + n1i (3) as: θ f where n is the nominal sinkage exponent and n is the M = br2 τdθ (10) 0 1 Z slip-sinkage exponent, which is determined empirically θr Figure 1. Schematic representation of nor- Figure 2. MSL terramechanics test bed at mal and tangential stress profile along MIT. This rig allows for forced-slip and the wheel-soil interface. free-slip tests.

3 Single Wheel Test Bed handled by a NI PCIe-6363 card through Labview soft- ware. The Robotic Mobility Group at MIT has designed and The rig is capable of approximately 3.5 meters of lon- fabricated a multi-purposeterramechanics rig based on the gitudinal displacement at a maximum velocity of approxi- standard design described by Iagnemma [7]. The test bed mately 60 mm/s with a maximal wheel angular velocity of is pictured in Figure 2 and it is composed of a Lexan soil approximately 15 deg/s. The bin width is 1.2 meters while bin surrounded by an aluminum frame where all the mov- the soil depth is 0.5 meters. Considering the wheel sizes ing parts, actuators and sensors are attached. A carriage and vertical loads under study, these physical dimensions slides on two linear bearings to allow longitudinal trans- are sufficient for eliminating boundary effects. Moreover, lation while the wheel, attached to the carriage, is able to the same testbed, with some adaptations, can be used to rotate at a desired angular velocity. The wheel mount is perform soil penetration tests. also able to freely translate in the vertical direction. This typical setup allows control of slip and vertical load by 4 Test-Bed Soils modifying the translational velocity of the carriage, angular velocity of the wheel, and applied load. Alterna- The experiments presented in this paper are con- tively, it is possible to disconnect the longitudinal drive ducted on two different types of dry granular materi- system and actuate the wheel independently, hence recre- als. For the single wheel experiments, performed at MIT, ating free-slip conditions. a new simulant has been developed from commercially Horizontal carriage displacement is controlled available sands. This granular material was created with through a toothed belt actuated by a 200 W Maxon DC the intent of reproducing grain size distribution and me- motor, while the wheel is directly driven by a 250 W chanical properties of the most challenging terrains ob- Maxon DC motor. The motors are controlled through two served on Mars. The simulant is obtainedblendingof 75% identical Maxon ADS 50/10 4-Q-DC servo-amplifiers. Mauricetown NJ70 sand and 25% SilCoSil250 ground sil- The carriage horizontal displacement is monitored with ica (percent represents mass fraction). The resulting mix a Micro Epsilon MK88 draw wire encoder while wheel was tested under direct shear and plate penetration tests vertical displacement (i.e., sinkage) is measured with a to evaluate mechanical properties under different loading Turck A50 draw wire encoder. conditions. A 6-axis force torque ATI Omega 160 transducer is Direct shear tests showed that the simulant has a shear mounted between the wheel mount and the carriage in or- modulus of 0.001 m, presents a cohesion of 0.43 kPa, and der to measure vertical load and traction generated by the an angle of internal friction of 34 degrees. Direct shear wheel. Finally, a flange-to-flange reaction torque sensor tests were conducted under three different vertical loads from Futek (TFF600) is used to measure driving torque repeating each experiment 4 times. Results, presented in applied to the wheel. Control and measurementsignals are Figure 3, show little variation between each trial. 4 60 x 10 9 Direct Shear Tests 7 cm Plate 8 5 cm Plate 50 Mohr−Coulomb Fit Bekker Fit 7 Bekker Fit 40 6

5 30 [kPa] τ 4 Pressure [Pa] 20 3

2 10 1

0 0 0 10 20 30 40 50 60 70 80 0 0.005 0.01 0.015 0.02 0.025 0.03 σ [kPa] Sinkage [m]

Figure 3. Mohr-Coulomb failure envelope Figure 4. Pressure-sinkage characteristics for the MIT sand. of the MIT sand.

Table 1. Mechanical properties of the MIT Table 2. MIT sand properties for sand measured through direct shear and ARTEMIS simulations. plate penetration tests.

kx [m] n1 a1 a2 Symbol Value Units 0.0146 0.54 0.38 0.44 n 1.26 n/a n+1 kc -404 kN/m n+2 kφ 15500 kN/m tions utilizing measured sand parameters first. Then, it is c 430 Pa shown how it is possible to use ARTEMIS to characterize φ 35 deg in-field tests. kx 0.001 m 5.1 Single Wheel Experiments vs. ARTEMIS Single wheel experiments have been conducted us- The simulant was also tested under penetrating plates ing two testing methodologies: forced-slip and free-slip. in order to extrapolate Bekker pressure-sinkage parame- For the forced-slip experimentsthe wheel longitudinal and ters. The experiments were conducted with two plates of angular velocities were fully controlled, thus imposing 0.05m x 0.16m and 0.07m x 0.16m area. For each plate wheel slip during the test. For the free-slip experiments 15 repetitions were conducted and the fit was conducted the wheel longitudinal velocity was not constrained, and on the average of the 15 trials, as shown in Figure 4. MIT dead weights were used to increase longitudinal motion regolith simulant properties are summarized in Table 1. resistance. For this experimental setup the slip becomes a The Dumont Dunes test area in the Mojave Desert free variable. is dominated by well-sorted, rounded, wind-blown sands Results for forced-slip and free-slip experiments are dominated by quartz and feldspar. For the experiments presented in Figures 5, 6, 7. For the forced slip experi- conducted at this site, the topography was characterized ments 5 repetitions at each normal load and slip combina- using a scanning laser altimeter. Soil properties were tions were conducted. Boxplots represent average with the not determined but rather treated as an unknown, and whiskers showing one standard deviation for these experi- ARTEMIS simulations were tuned to achieve best perfor- ments. It is evident that torque and drawbar measurements mance. are very repeatable while sinkage shows more variance. This is a consequence of the inability to precisely pre- 5 Results pare the surface back to its original topographic state after each run. Experimental data for the free-slip experiments The results are divided in two subsections. Single overlap with the forced-slip experiments, which suggests wheel experiments are compared to ARTEMIS simula- that the two testing methodologies are indeed equivalent. 120 400

350 100

300

80 250

60 200

F = 480 N (Forced) Drawbar [N] F = 480 N (Forced) Torque − [Nm] z 150 z F = 480 N (Free) F = 480 N (Free) 40 z z F = 480 N (ARTEMIS) F = 480 N (ARTEMIS) z 100 z F = 750 N (Forced) F = 750 N (Forced) 20 z z F = 750 N (Free) F = 750 N (Free) z 50 z F = 750 N (ARTEMIS) F = 750 N (ARTEMIS) z z 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Slip Slip

Figure 5. Torque vs. longitudinal slip for Figure 6. Drawbar vs. longitudinal slip for ARTEMIS model and single-wheel ex- ARTEMIS model and single-wheel experimental data. perimental data.

90 Also, for the free-slip experiments, sinkage shows signifi- 80 cant variability. For the ARTEMIS simulations, the parameters kx, n1, 70 a1 and a2, were used as tuning parameters while all other 60 parameters were taken from Table 1. More details on the reasons for this approach are presented in [11, 9, 8] while 50 Table 2 shows the values for the tuning parameters. Single wheel ARTEMIS simulations show good 40 Sinkage − [mm] agreement with drawbar and torque measurements while 30 sinkage is underestimated. Although this is not ideal, it reflects the known limitations of semi-empirical terrame- 20 chanics models. In the next section it will be shown that, 10 notwithstanding its limitations, ARTEMIS can be utilized 0 to characterize full vehicle operations. 0 0.2 0.4 0.6 0.8 1 Slip 5.2 ARTEMIS vs. Field Tests A series of field tests were conducted at the Dumont Figure 7. Sinkage vs. longitudinal slip for Dunes site utilizing the Scarecrow platform [6]. Scare- ARTEMIS model and single-wheel ex- crow is a fully functional mockup of the rover Curiosity perimental data. weighting approximately 3/8 of Curiosity in order to reproduce on earth similar ground pressures to the ones ex- perienced on Mars (Figure 8). The Dumont Dunes were simulations including weight transfer effects. selected in the Mojave Desert as wind-blown dune field analogous to wind-blown sand dunes seen from orbit cov- 3. Simplified analysis based on ARTEMIS single wheel ering a portion of the roverslanding target ellipse on Mars. simulations neglecting weight transfer effects. An extensive report of these field tests is reported in The first approach essentially utilizes the ARTEMIS [6]. In this paper, the focus is on the climbing perfor- full vehicle model to replicate the actual drive that the mance of Scarecrow. The analysis of the rover climbing rover performed. This is the most complete analysis and capabilities is conducted following three approaches: it is also the more computationally intensive. Since soil 1. ARTEMIS simulations of the full vehicle. properties for the Dumont Dunes site were not available this analysis was also utilized to extrapolate terrain prop- 2. Simplified analysis based on ARTEMIS single wheel erties. Sand properties are obtained from the SSTB-lite Figure 8. Scarecrow at the Dumont Dunes Figure 9. Load transfer during upslope site while attempting an upslope drive. drives. Values represent the additional load that is carried by each wheel. Con- sidering that the nominal load is approximately 550 N, the rear axle can experi- rover simulations as presented in [11] and are utilized to ence up to 50% surcharge during a 20 model scarecrow drive. Sand properties are summarized degrees slope ascent. in Table 3. The second approach utilizes single wheel ARTEMIS simulations (conducted on flat ground) and weight transfer information to estimate the amount of slip necessary Table 3. Sand properties for the Dumont to drive up a slope of varying grade. Figure 9 shows verti- Dunes site obtained from ARTEMIS cal load distributions for the three axles of the rover once simulations. steady state climbing has been reached on slopes of different inclinations. These values have been obtained from Symbol Value Units the ARTEMIS full vehicle simulation and show how more ρ 1650 kg/m3 load is transferred to the rear axle while less is carried by n 1.45 n/a the frontaxle when the vehicle travels on an incline. Given 0 n1 0.45 n/a the vertical load for each wheel it is possible to calculate ′ kc 9.1 n/a the slip required to climb by solving: ′ kφ 500.8 n/a 6 c 200 Pa DPn(Fzn cos α, i) − Fzn sin α = 0 (11) φ 30 deg Xn=1 kx 0.029 m / where DPn is the drawbar force at the n-th wheel, Fzn is a1 0.33 n a the reaction force under the wheel in the direction parallel a2 0.11 n/a to the earth gravity vector, α is the slope inclination, and i is slip. Equation 11 can be solved for slip in order to yield slip vs. inclination curves. 3 are also able to produce predictions close to the actual The third approach is similar to the second, but dis- rover performance. This is an interesting result because regards the load transfer and simply assumes that each it shows that, for the rover configuration, soil type, and wheel carries the same amount of load, reducing the anal- range of wheel slip considered here, it is possible to use ysis to: single wheel experiments conducted on flat ground to es- DP(Fz cos α, i) − Fz sin α = 0 (12) timate the performance of a full MSL vehicle without the need of knowing the vertical load distribution among the where Fz is simply a sixth of the total vehicle load. Con- axles. sidering the non-linear nature of the drawbar vs. slip vs. normal load surfaces, approaches 2 and 3 are expected to produce different results. 6 Conclusions Results of Scarecrow climbing capabilities are presented in Figure 10. Full vehicle simulations conducted This paper presented recent work toward developing a with ARTEMIS are capable of accurately describing slope terramechanics-based modeling and validation infrastruc- climbing capabilities of the rover. The approaches 2 and ture for characterizing the Curiosity rovers mobility prop- 100 Dumont Dunes Experiments References 90 ARTEMIS Full Vehicle ARTEMIS Single Wheel w/o ∆ F z [1] R. E. Arvidson, J. W. Ashley, J. F. Bell, M. Cho- 80 ARTEMIS Single Wheel w/ ∆ F z jnacki, J. Cohen, T. E. Economou, W. H. Farrand, 70 R. Fergason, I. Fleischer, P. Geissler, R. Gellert, 60 M. P. Golombek, J. P. Grotzinger, E. A. Guinness, R. M. Haberle, K. E. Herkenhoff, J. A. Herman, 50 K. D. Iagnemma,B. L. Jolliff, J. R. Johnson,G.Klin- Slip [%] 40 gelhfer, A. H. Knoll, A. T. Knudson, R. Li, S. M.

30 McLennan, D. W. Mittlefehldt, R. V. Morris, T. J. Parker, M. S. Rice, C. Schrder, L. A. Soderblom, 20 S. W. Squyres, R. J. Sullivan, and M. J. Wolff. Op- 10 portunity mars rover mission: Overview and selected results from purgatory ripple to traverses to endeav- 0 0 5 10 15 20 our crater. Journal of Geophysical Research: Plan- Slope Inclination [deg] ets, 116(E7):n/a–n/a, 2011. Figure 10. Scarecrow climbing characteristics at the Dumont Dunes site. [2] R. E. Arvidson, P. Belutta, F. Calef, A. A. Frae- man, J. Garvin, O. Gasnault, J. Grant, J. Grotzinger, V. Hamilton, M. Heverly, K. Iagnemma, J. Johnson, N. Lanza, S. Le Mouelic, N. Mangold, D. Ming, erties on the Mars surface. The Adams-based simulator M. Mehta, R. V. Morris, H. Newsom, N. Renno, ARTEMIS was utilized to reproduce single wheel experi- D. Rubin, J. Schieber, R. Sletten, A. R. Vasavada, ments conducted at MIT and full vehicle experiments con- J. Vizcaino, and R. C. Wiens. Terrain physical prop- ducted at the Dumont Dunes site. erties derived from orbital data and the first 360 sols The results show that it is possible to utilize single of mars science laboratory curiosity rover observa- wheel simulations conducted on flat terrain to quickly es- tions in gale crater. J. Geophys. Res. - Planets, in timate rover climbing capabilities. It should be noted that review. it was unfortunately not possible to perform experimental single-wheel tests on soil gathered from the Dumont [3] M. G. Bekker. Introduction to Terrain-Vehicle Sys- Dunes site. For this reason, ARTEMIS simulations of tems. The University of Michigan Press, Ann Arbor, single-wheel tests were used to predict upslope driving 1969. performance. [4] Liang Ding, Hai-bo Gao, Zong-quanDeng, and Jian- ARTEMIS is intended to be used on a continuing ba- guo Tao. Wheel slip-sinkage and its prediction sis as a tool to help evaluate mobility issues over candidate model of lunar rover. Journal of Central South Uni- Mars Science Laboratory Curiosity rover drive paths. The versity of Technology, 17(1):129–135, 2010. model will be employed to help plan drives for Curiosity, providing a set of outputs to help the engineers analyze [5] J. P. Grotzinger, J. Crisp, A. R. Vasavada, R. C. An- routes to desired target sites that minimize wheel sinkage derson, C. J. Baker, R. Barry, D. F. Blake, P. Con- and slip, and thus minimize the probability of embedding. rad, K. S. Edgett, B. Ferdowski, R. Gellert, J. B. In addition, ARTEMIS enables the possibility of retriev- Gilbert, M. Golombek, J. Gmez-Elvira, D. M. Has- ing Mars soil, bedrock and topographic properties, by it- sler, L. Jandura, M. Litvak, P. Mahaffy, J. Maki, erative registration of model outputs against actual drive M. Meyer, M. C. Malin, I. Mitrofanov, J. J. Sim- results. monds, D. Vaniman, R. V. Welch, and R. C. Wiens. Mars science laboratory mission and science inves- tigation. Space Science Reviews, 170(1-4):5–56, Acknowledgment 2012. [6] Matt Heverly, Jaret Matthews, Justin Lin, Dan This work was supported by contracts from the Fuller, Mark Maimone, Jeffrey Biesiadecki, and Jet Propulsion Laboratory through the Mars Exploration John Leichty. Traverse performance characteriza- Rover and Mars Science Laboratory missions. The au- tion for the mars science laboratory rover. Journal thors gratefully acknowledge the work of the field crew, of Field Robotics, 30(6):835–846, 2013. led by Matthew Heverly, who conducted the tests at the Dumont Dunes site, and Thuan Doan and Gregory Puszko [7] K. Iagnemma, H. Shibly, and S. Dubowsky. A for their help in designing and fabricating the terrame- laboratory single wheel testbed for studying plane- chanics test bed at MIT. tary rover wheel-terrain interaction. MIT Field and Space Robotics Laboratory Technical Report, 1:05– 05, 2005. [8] C. Senatore and K. Iagnemma. Direct shear be- haviour of dry, granular soils subject to low normal stresses. In Proceedings of 17th International Con- ference of the ISTVS, Blacksburg, VA, 2011. [9] C. Senatore and K. Iagnemma. Analysis of stress distributions under lightweight wheeled vehicles. Journal of Terramechanics, 51(0):1 – 17, 2014. [10] J. Y. Wong. Terramechanics and Off-Road Vehicle Engineering. Elsevier, UK, 2nd edition, 2010. [11] F. Zhou, R. E. Arvidson, K. Bennett, B. Trease, R. Lindemann, P. Bellutta, K. Iagnemma, and C. Senatore. Simulations of mars rover traverses. Journal of Field Robotics, 31(1):141–160, 2014.