Modeling and Validation of Mobility Characteristics of the Mars Science Laboratory Curiosity 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: [email protected], [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 verti- cal 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 oc- curs 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 terramechan- ics 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.