Discrete element modeling of a Mars Exploration Rover wheel in granular material

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Abstract

Three-dimensional discrete element method (DEM) simulations were developed for the Mars Exploration Rover (MER) mission to investigate: (1) rover wheel interactions with martian regolith; and (2) regolith deformation in a geotechnical triaxial strength cell (GTSC). These DEM models were developed to improve interpretations of laboratory and in situ rover data, and can simulate complicated regolith conditions. A DEM simulation was created of a laboratory experiment that involved a MER wheel digging into lunar regolith simulant. Sinkage and torques measured in the experiment were compared with those predicted numerically using simulated particles of increasing shape complexity (spheres, ellipsoids, and poly-ellipsoids). GTSC simulations, using the same model regolith used in the MER simulations, indicate a peak friction angle of approximately 37–38° compared to internal friction angles of 36.5–37.7° determined from the wheel digging experiments. Density of the DEM regolith was 1820 kg/m3 compared to 1660 kg/m3 for the lunar simulant used in the wheel digging experiment indicating that the number of grain contacts and grain contact resistance determined bulk strength in the DEM simulations, not density. An improved correspondence of DEM and actual test regolith densities is needed to simulate the evolution of regolith properties as density changes.

Highlights

► A 3D discrete element rover wheel was developed to model interaction with Mars soils. ► Simulations compared well with laboratory wheel digging experiments. ► Simulation triaxial cell tests determined the soils internal friction angle.

Introduction

In situ characterization of lunar and martian regolith physical and mechanical properties has provided information about the history of surface changes and regolith geotechnical properties since the first Surveyor series of robotic lunar landers. Regolith can record the most recent history of physical and chemical processes modifying an extraterrestrial surface. On the Moon, lunar regolith right at the surface reflects the most recent effects of a complex suite of processes associated with meteorite impacts, including comminution of debris, and deposition of agglutinates, impact melt, and impactor fragments. On Mars, regolith mechanical properties (e.g., bearing strength) sampled by landers and traversed by rovers exhibit values that range from materials similar to regolith found on lunar intercrater plains in cratered terrain, but ranging from very weak loose sandy material to regolith with significant load-bearing crusts [1]. On Mars, cohesion could be due to transient electrostatic charges, or deposition of water-soluble salts, cements, or other bonding agents. Information about regolith strength also is important for guiding designs of lunar and planetary landers and rovers, for assessing the safety of potential rover traverses during flight operations, and to aid recovery efforts when rovers encounter mobility problems due to partial mechanical failures and/or terrain challenges. For example, both rovers from the Mars Exploration Rover (MER) mission have been bogged down at one time or another and the Spirit rover became permanently stuck in May 2009 while attempting to drive with one of its wheels disabled.

We developed a three-dimensional computer simulation of a MER wheel interacting with regolith using the discrete element method (DEM) in order to improve interpretations of rover wheel interactions with martian regolith during the MER mission. These numerical experiments incorporate the essential morphological characteristics of the MER rover wheel and also allow variation of grain-scale regolith properties such as grain size, shape and interparticle friction. In addition, the effects of reduced gravity can be explored (challenging to do in terrestrial laboratory experiments) as well as specific regolith conditions such as compaction, and layering of regolith with different properties.

We also developed a geotechnical triaxial strength cell (GTSC) DEM model to relate grain-scale regolith properties derived from DEM wheel digging simulations to more commonly used bulk strength properties (such as internal friction, and density as a function of regolith deformation). Actual GTSC laboratory experiments are modeled by applying confining pressure to the outer surface of a cylindrical regolith sample and then applying a constant rate of displacement, or load, to the cylindrical ends to produce deformation/load curves for several different confinement pressures [2]. The description of regolith properties as a function of confining pressure derived from GTSC tests represents the fundamental mechanical properties of the regolith. DEM simulations of the GTSC produce simulated regolith deformation (shear and compression) and thus predict shear strength (cohesion and internal friction) as a function of confinement pressure.

The ability to simulate both machine/regolith interactions and GTSC experiments provides powerful tools for predicting bulk regolith mechanical properties, or predicting machine performance in regolith by using known regolith properties from actual GTSC test results. For example, by combining the results of DEM simulations of MER wheel digging tests with GTSC DEM simulations, improved estimates of martian bulk regolith properties can be made. Conversely, data from actual bulk regolith GTSC measurements can be used to define the regolith properties used in DEM simulations of machine/regolith interactions for purposes of design, predicting machine performance, and mission mobility analysis. A flow chart of how regolith property measurements are combined with DEM simulations to determine bulk and DEM grain-to-grain regolith parameters is shown in Fig. 1.

The process shown in Fig. 1 is to simulate torque and sinkage measurements from laboratory or in situ MER digging tests (Fig. 1a and b) using a DEM MER wheel model to estimate DEM grain-parameters (Fig. 1c). The DEM grain parameters are then used in a GTSC DEM simulation (Fig. 1d) to estimate regolith bulk (continuum) parameters. In the reverse direction, simulation of grain-to-grain micromechanical tests (Fig. 1f) and actual bulk regolith GTSC tests (Fig. 1e) are used to determine DEM grain-to-grain parameters. The derived grain-to-grain DEM parameters can then be used to simulate wheel digging (Fig. 1a and b), excavation, or other machine/regolith interactions. Due to the high-computational cost of DEM simulations, the derived DEM particle parameters are optimized to best describe the regolith behavior while keeping the computational requirements within reasonable bounds.

In situ studies of martian surface physical properties (such as grain characteristics, cohesion, bulk density, adhesion, grain size, and angle of internal friction) began with the landings of the Viking spacecraft in 1976 [3], [4]. Six successful Mars lander missions (two Viking landers [1976–1982], the Pathfinder lander [1997] [5], the two MERs [2004–present] [6] and the Phoenix lander [2008] [7], [8]) have returned data informing us about physical properties of martian regolith.

Specialized instruments designed to measure regolith properties (such as density, strength, and deformation response to load) have not been deployed on Mars missions due to mass and power constraints guided by other exploration priorities. Instead, procedures with available spaceflight hardware, such as wheels or arm-mounted scoops, have been developed to estimate forces and torques associated with pushing or digging activities [1]. This can involve analyzing pictures of hardware imprints into regolith for sinkage (with implications for regolith strength), or evaluating electromechanical resistance to regolith deformation recorded in motor telemetry from arm scoops or wheels interacting with regolith. In all cases, the goal is to relate the observed deformations, or electromechanical resistances, to more widely applicable and comparable properties like angle of internal friction, cohesion, and bulk density [3], [5], [8], [6]. An essential element of all these analyses has been calibration testing of spaceflight hardware with soils on Earth. However, such calibrations generally are challenging for three reasons: (1) access to flight hardware before launch typically is very limited or even precluded (e.g., to maintain flight hardware in “clean room” condition) and resource limitations also limit access to flight-like hardware after launch of the flight hardware itself; (2) the full range of regolith properties that might be encountered during flight operations on Mars generally cannot be perfectly anticipated in any set of calibration test soils; (3) gravitational self-packing of loose, cohesionless calibration soils on Earth will be greater than for the same materials on Mars, which has ∼38% of terrestrial gravity.

Section snippets

Description of the discrete element model

We use a discrete element approach to model the regolith grains, the MER rover wheel and the GTSC. In a DEM model, individual grains and the forces between them are modeled explicitly. Each particle is defined by its shape, size, position, velocity and orientation at all times in the simulation. Most large-scale DEM simulations use spherical grains for efficiency, however, spheres poorly represent the irregular grains found in most regolith. The chief drawbacks to spherical grains are their

Rover wheel simulations

The simulations are compared with physical experiments performed at Cornell University [6]. The experiments used an actual MER wheel and lunar regolith simulant, JSC-1A, with a bulk density of 1660 kg/m3. The effective mass of the wheel and arm assembly was 11 kg and the length of the arm was 947 mm. The wheel rotation rate was a constant 0.3 rad/s. The mean particle size of the lunar simulant JSC-1A was approximately 100 μm, although the material is not well sorted. Sullivan et al. [6] estimated

Geotechnical tri-axial strength cell simulations

The DEM simulation of the GTSC is shown in Fig. 6. Both the test grains and the GTSC apparatus are modeled using the DEM. As with the wheel digging simulation, each grain is defined by its shape, size, position, velocity and orientation. After the contact and body forces on each grain are found, the equations of motion are solved for new positions and velocities and the program advances one time step. To simulate a GTSC test, a cylindrical core of grains was taken from the model MER regolith

Conclusions

A three-dimensional computer simulation of the MER wheel interacting with regolith was developed using the discrete element method (DEM), to improve interpretations of rover wheel interactions with martian regolith during the MER mission. The rover vehicles that landed on Mars, though not designed to do more than transport cameras and instruments over a wide area, have been able to complete some basic tests that allow us to attempt to infer martian regolith properties [6]. By combining the

Acknowledgement

This work was supported by the NASA Lunar Science Institute supported project “Scientific Exploration Potential of the Lunar Poles”, NASA’s Kennedy Space Center Technology Development project “Lunar regolith mechanical properties, the NASA’s Mars Fundamental Research Program project “The relationship between the physical and mechanical properties of Mars soils and their simulation”, and the NASA Mars Exploration Rover Program-NNH05ZDA001N-MERPS project “Physical and geologic Investigations of

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