A modified pressure-sinkage model for small, rigid wheels on deformable terrains

Bekker’s semi-empirically derived equations allow the designers of off-road vehicles to understand and predict vehicle mobility performance over deformable terrains. However, there are several underlying assumptions that prevent Bekker theory from being successfully applied to small vehicles. Specifically, Bekker’s sinkage and compaction resistance equations are inaccurate for vehicles with wheel diameters less than approximately 50 cm and normal loading less than approximately 45 N. This paper presents a modified pressure-sinkage model that is shown to reduce sinkage and compaction resistance model errors significantly. The modification is validated with results from 160 experiments using five wheel diameters and three soil types.     

Design and mobility evaluation of tracked lunar vehicle

Past lunar vehicles have had difficulty traveling through soft sand areas due to the thick, soft and dry regolith. This paper describes the design and evaluation results of a tracked lunar vehicle which aims at achieving greater mobility, particularly improved climbing ability on pure sand slopes, by reducing contact pressure with a crawler link. The tracked vehicle uses mesh crawler links to reduce complexity, weight and parts count. Single-crawler tests on simulated lunar soil revealed that the crawler’s slip ratio was lower than that of a rigid wheel at any slope angle, and that its power consumption was lower than that of a wheel on slopes of 10° or more. Furthermore, the crawler’s slip ratio was stable or decreasing along the traveling distance on steep slopes, contrary to the wheel. Our tracked lunar vehicle, the “Light Crawler”, is equipped with four such mesh-crawlers, each of which is independently driven and steered. It is intended to realize high climbing ability, a small turning circle, and an obstacle-crossing capability using a unique suspension system. The vehicle’s climbing and obstacle-crossing capabilities were tested on both simulated lunar soil and a rock-scattered field, and its mobility performance was successfully confirmed.     

Performance evaluation of a wire mesh wheel on deformable terrains

Because of the unique lunar environment, a suitable wheel for lunar rover decides the rover’s trafficability on deformable terrains. The wire mesh wheel (hereinafter referred to as WMW) has the advantages of light weight and superior stability, been widely adopted for lunar rovers. But a comprehensive research on performance of WMW on deformable terrains has not been conduct. This paper would provide particular study on a type WMW, including quasi-static pressure-sinkage test and driving performance. A novel pressure-sinkage model for the WMW on deformable soils was presented. In order to investigate the sinkage characteristics of the WMW, tests were performed using a single-wheel testbed for the WMW with different loads and velocities. The effects of load and velocity on sinkage were analyzed, and the relationship between real and apparent sinkage was presented. The research on traction performance of WMW under different slip ratios (0.1–0.6) was also conducted, contrast tests were proceed by using a normal cylindrical wheel (hereinafter referred to as CW). The traction performance of WMW is analyzed using performance indices including wheel sinkage, drawbar pull, driving torque, and tractive efficiency. The experimental results and conclusions are useful for optimal WMW design and improvement/verification of wheel–soil interaction mechanics model.     

Determination of rating cone index using wheel sinkage and slip

It has been known from empirical equations that soil strength can be determined if wheel sinkage and slip of a vehicle can be measured on a soil surface. In this study, field data of wheel sinkage and slip were collected from two platform tractors of different sizes on gravely sandy and sandy loam soils. Using an empirical equation, the rating cone index was determined using the measured wheel sinkage and slip data. The data demonstrated that the same rating cone index can be obtained although the measuring platforms are different. It was also noted that the rating cone index can be estimated in real time by measuring the sinkage and slippage of a driving wheel.     

Further study of the method of approach to testing the performance of extraterrestrial rovers/rover wheels on earth

The current practice for experimentally evaluating the performance of extraterrestrial rovers/rover wheels is to conduct tests on earth on a soil simulant, appropriate to the regolith on the extraterrestrial body of interest. In the tests, the normal load (force) applied by the rover/rover wheel to the soil simulant is set identical to that expected on the extraterrestrial surface, taking into account its acceleration due to gravity. It should be pointed out, however, that the soil simulant used in the tests is subject to earth gravity, while the regolith on the extraterrestrial surface is subject to a different gravity. Thus, it is uncertain whether the performance of the rover/rover wheel obtained from tests on earth represents that on the extraterrestrial surface. This issue has been explored previously. A method has been proposed for conducting tests of the rover/rover wheel on earth with identical mass to that on the extraterrestrial surface, instead of with identical normal load used in the current practice [1]. This paper provides further evidence to substantiate the merits of the proposed method, based on a detailed analysis of the test data obtained under various gravity conditions, produced in an aircraft undergoing parabolic flight manoeuvres [8]. In the study, the effect of slip on wheel sinkage has been evaluated. It is found that gravity has little effect on the slip and sinkage relationship of the rover wheel under self-propelled conditions.     

Discrete element modelling for wheel-soil interaction and the analysis of the effect of gravity

The discrete element method (DEM) is widely seen as one of the more accurate, albeit more computationally demanding approaches for terramechanics modelling. Part of its appeal is its explicit consideration of gravity in the formulation, making it easily applicable to the study of soil in reduced gravity environments. The parallel particles (P²) approach to terramechanics modelling is an alternate approach to traditional DEM that is computationally more efficient at the cost of some assumptions. Thus far, this method has mostly been applied to soil excavation maneuvers. The goal of this work is to implement and validate the P² approach on a single wheel driving over soil in order to evaluate the applicability of the method to the study of wheel-soil interaction. In particular, the work studies how well the method captures the effect of gravity on wheel-soil behaviour. This was done by building a model and first tuning numerical simulation parameters to determine the critical simulation frequency required for stable simulation behaviour and then tuning the physical simulation parameters to obtain physically accurate results. The former were tuned via the convergence of particle settling energy plots for various frequencies. The latter were tuned via comparison to drawbar pull and wheel sinkage data collected from experiments carried out on a single wheel testbed with a martian soil simulant in a reduced gravity environment. Sensitivity of the simulation to model parameters was also analyzed. Simulations produced promising data when compared to experiments as far as predicting experimentally observable trends in drawbar pull and sinkage, but also showed limitations in predicting the exact numerical values of the measured forces.     

Effect of gravity on the mechanical properties of lunar regolith tested using a low gravity simulation device

Simulations of the bearing capacity and shear strength of regolith under Earth’s gravity produce different results from those under low gravity. A low-gravity simulation device was developed in this study, and an internal stress model of regolith simulant was established to correct the errors. The model revealed additional force on both shear plane in the shear test and the press plate area in the pressure–sinkage test. The sinkage and shear test results showed that low gravity decreased the deformable index n, frictional modulus k_φ and cohesion c, whereas there were no obvious changes to the cohesive modulus k_c and internal friction angle φ. The sinkage generally increased as the gravity decreased under a consistent normal load larger than 50 N, but when the wheel load was lower than 50 N, the sinkage of the TYII-1 simulant was larger under 1 G than 1/6 G. Gravity had little effect on the shear strength of the regolith. However, the tractive thrust of the TYII-1 simulant was lower under 1/6 G than 1 G. The smaller difference was due to differences in the way the soils responded to changes in the gravity level for the TYII-2 simulant.     

Systematic design and development of a flexible wheel for low mass lunar rover

Low mass compact rovers provide cost effective means to explore extra-terrestrial terrains. Use of flexible wheels in such applications where the wheel size is restricted, improves traction at reduced slip and sinkage. Design of a flexible wheel for a given mission is a challenging task requiring consideration of stiffness of rim and spokes, stress induced in the wheel, chassis movement during wheel rotation and the operating mode of the wheel. Also, accurate mathematical models are required to save design and development time and reduce the number of prototypes for selection. It is observed that most of the research papers deal with performance testing of flexible wheels and information on analytical formulation is scarce. Therefore, in the present work, a methodology has been formulated to systematically design a flexible wheel for a low mass lunar rover. The prototype performance is tested and compared with analytical estimates and reasons for difference are investigated. Paper contains details of design criteria, mathematical modelling, realisation of wheel prototype, test fixture and analysis test comparison. Authors believe that this work provides a useful aid to the designer to systematically design flexible wheels for low mass lunar rovers.     

Discrete element method simulations of Mars Exploration Rover wheel performance

Mars Exploration Rovers (MERs) experienced mobility problems during traverses. Three-dimensional discrete element method (DEM) simulations of MER wheel mobility tests for wheel slips of i = 0, 0.1, 0.3, 0.5, 0.7, 0.9, and 0.99 were done to examine high wheel slip mobility to improve the ARTEMIS MER traverse planning tool. Simulations of wheel drawbar pull and sinkage MIT data for i ⩽ 0.5 were used to determine DEM particle packing density (0.62) and contact friction (0.8) to represent the simulant used in mobility tests. The DEM simulations are in good agreement with MIT data for i = 0.5 and 0.7, with reasonable but less agreement at lower wheel slip. Three mobility stages include low slip (i < 0.3) controlled by soil strength, intermediate slip (i ∼ 0.3–0.6) controlled by residual soil strength, and high slip (i > 0.6) controlled by residual soil strength and wheel sinkage depth. Equilibrium sinkage occurred for i < 0.9, but continuously increased for i = 0.99. Improved DEM simulation accuracy of low-slip mobility can be achieved using polyhedral particles, rather than tri-sphere particles, to represent soil. The DEM simulations of MER wheel mobility can improve ARTEMIS accuracy.     

Discrete element method-based studies on dynamic interactions of a lugged wheel with granular media

Terramechanics plays an important role in determining the design and control of autonomous robots and other vehicles that move on granular surfaces. Traction capabilities, slippage, and sinkage of a robot are governed by the interaction of a robot’s appendage with the operating terrain. It is important to understand how the terrain flows under this appendage during such an interaction. In this work, dynamics of soil performance and locomotion performance of a lugged wheel travelling on soft soil are numerically investigated. Studies are conducted with a two-dimensional model by using the discrete element method to analyze the interactions between a lugged wheel and the soil. The soil performance is studied by examining the force distribution and evolution of force networks during the course of the wheel travel. For two different control modes, namely, slip-based wheel control and angular velocity-based wheel control, the performance parameters such as, sinkage, traction, traction efficiency, and power consumption of the wheel are compared for various wheel configurations. The findings of this work are expected to be useful for optimal design and control of the lugged wheel travelling on deformable surfaces.     

Influence of atmosphere on lunar rover performance analysis based on soil parameter identification

This paper outlines an analysis of the traveling performance of a lunar rover. The analysis is in the form of numerical simulations and it uses soil properties, identified in vacuum, and mechanics of wheel-based travel. The wheel-to-ground contact model and soil parameters are determined first so they could be used in the numerical simulation. A soil test device is introduced and the soil parameters are identified from plate-pressing and shear tests. Finally, numerical simulations are conducted using the parameters identified and their results are discussed along with those of the traveling tests conducted in vacuum. The soil tests indicated that the wheel sinkage into the ground can increase in vacuum and that the shear stress acting beneath the wheel in vacuum is almost the same as that in the atmosphere. Because of these trends, the simulations and traveling tests showed that the traveling performance of the wheel can decrease in vacuum. Although it has been widely considered that the vacuum environments enhance the traveling performance of the wheel, this study confirmed that it is not always the case.     

Development of in-wheel sensor system for accurate measurement of wheel terrain interaction characteristics

Planetary rovers need high mobility on a rough terrain such as sandy soil, because such a terrain often impedes the rover mobility and causes significant wheel slip. Therefore, the accurate estimation of wheel soil interaction characteristics is an important issue. Recent studies related to wheel soil interaction mechanics have revealed that the classical wheel model has not adequately addressed the actual interaction characteristics observed through experiments. This article proposes an in-wheel sensor system equipped with two sensory devices on the wheel surface: force sensors that directly measure the force distribution between the wheel and soil and light sensors that accurately detect the wheel soil surface boundary line. This sensor design enables the accurate measurement of wheel terrain interaction characteristics such as wheel force distribution, wheel–soil contact angles, and wheel sinkage when the powered wheel runs on loose sand. In this article, the development of the in-wheel sensor system is introduced along with its system diagram and sensor modules. The usefulness of the in-wheel sensor system is then experimentally evaluated via a single wheel test bench. The experimental results confirm that explicit differences can be observed between the classical wheel model and practical data measured by the in-wheel sensor system.     

Analysis of Mars Exploration Rover wheel mobility processes and the limitations of classical terramechanics models using discrete element method simulations

A previous three-dimensional discrete element method (DEM) model of Mars Exploration Rovers (MERs) wheel mobility demonstrated agreement with test data for wheel drawbar pull and sinkage for wheel slips from 0.0 to 0.7. Here, results from the previous model are compared with wheel mobility data for non-MER wheels that cover the range of wheel slip from 0.0 to 1.0. Wheel slips near 1.0 are of interest for assessing rover mobility hazards. DEM MER wheel model predictions show close agreement with weight-normalized wheel drawbar pull data from 0.0 to 0.99 wheel slip and show a similar trend for wheel sinkage. The nonlinear increase in MER wheel drawbar pull and sinkage for wheel slips greater that 0.7 is caused by development of a tailings pile behind the wheel as it digs into the regolith.Classical terramechanics wheel mobility equations used in the ARTEMIS MER mobility model are inaccurate above wheel slips of 0.6 as they do not account for the regolith tailings pile behind the wheel. To improve ARTEMIS accuracy at wheel slips greater that 0.6 a lookup table of drawbar pull, wheel torque, and sinkage derived from DEM mobility simulations can be substituted for terramechanics equation calculations.     

Dynamic behaviour of an open lugged wheel under paddy soil conditions

Many experimental studies of open lugged wheel-soil interaction have been conducted, mainly based on the condition of constant slip and sinkage. As a result the reaction force to lugs seemed to be equal to the soil cutting resistance to a metal surface. However, analyses based on such methods do not appear to represent the actual behaviour of lugged wheel-soil interaction, especially when the lugs are spaced widely. The actual motion the wheel axle. In this study, an experimental device for a model lugged wheel was constructed to investigate the characteristics of the interaction between a lugged wheel and soil. Experiments were conducted under several test conditions of soil including paddy soil with a hard pan. The result of both theoretical and experimental data indicated that slip and sinkage of a lugged wheel showed a fluctuation with rotation angle of which the period is equal to the angular lug spacing. In each test soil condition used, the motion of the lugged wheel and the reaction forces acting on each lug from the soil for a free sinking wheel were different from that of the condition of constant slip and sinkage. It was found that the results obtained from this study could clarify the actual behaviour of lugged wheel-soil interaction.     

The Bekker theory of rolling resistance amended to take account of skid and deep sinkage

The Bekker theory of rolling resistance of free rolling, towed, rigid wheels is amended to take account of both skid and deep sinkage without leading to excessive complexity in the predictive equations. Theoretical relationships between skid and sinkage are derived for a free rolling, towed, rigid wheel on a purely cohesive soil ( = 0) and on a purely frictional soil (c = 0) with a sinkage exponent of unity. Generally, good agreement is found between predicted and measured values of rolling resistance and sinkage at a given vertical load, on both sand and clay soils, at shallow and deep sinkage.     

Discrete element method analysis of single wheel performance for a small lunar rover on sloped terrain

The purpose of this study is to analyze the performance of a lugged wheel for a lunar micro rover on sloped terrain by a 2D discrete element method (DEM), which was initially developed for horizontal terrain. To confirm the applicability of DEM for sloped terrain locomotion, the relationships of slope angle with slip, wheel sinkage and wheel torque obtained by DEM, were compared with experimental results measured using a slope test bed consisting of a soil bin filled with lunar regolith simulant. Among the lug parameters investigated, a lugged wheel with rim diameter of 250 mm, width of 100 mm, lug height of 10 mm, lug thickness of 5 mm, and total lug number of 18 was found, on average, to perform excellently in terms of metrics, such as slope angle for 20% slip, power number for self-propelled point, power number for 15-degree slope and power number for 20% slip. The estimation of wheel performance over sloped lunar terrain showed an increase in wheel slip, and the possibility exists that the selected lugged wheel will not be able to move up a slope steeper than 20°.     

Shape effects of wheel grousers on traction performance on sandy terrain

This paper presents the effects of different wheel grouser shapes on the traction performance of a grouser wheel traveling on sandy terrain. Grouser wheels are locomotion gears that allow small and lightweight exploration rovers to traverse on the loose sand on extraterrestrial surfaces. Although various grouser shapes have been analyzed by some research groups, a more synthetic and direct comparison of possible grousers is required for practical applications. In this study, we developed a single wheel testbed and experimentally investigated the effects of four grouser shapes (parallel, slanted, V-shaped, and offset V-shaped) on the traction performance of linear movement on flat sand. The wheel slip, sinkage, traction and side force acting on the wheel axle, the wheel driving torque, and the efficiency of each wheel were examined. Thereafter, the effects on the lateral slope traversability of a small and lightweight four-wheeled rover with different grouser shapes were also examined. The traversability experiment demonstrated the vehicle mobility performance in order to contribute to the design optimization of rover systems. These experimental results and their comparisons suggested that, of the shapes studies herein, the slanted shape was the optimal grouser design for use in wheeled rovers on lunar and planetary soil.     

Bevameter testing on simulant Fillite for planetary rover mobility applications

This paper examines pressure-sinkage and shearing behavior via bevameter testing of a light-weight, granular simulant called Fillite in support of laboratory modeling of rover mobility in high-sinkage, high-slip environments typically found on Mars, the Moon, and other planetary bodies. Normal bevameter test results helped to determine parameters for the Bekker model, the New Model of Mobility (N2M) sinkage model, and the Bekker-Wong model. A case study used the Bekker-Wong model parameters to predict the possible sinkage of 84% into Fillite of a wheel on the Mars Spirit rover, a value within the observed sinkage of 50–90% of the wheel diameter of the Spirit rover on Mars. Shear bevameter testing of Fillite provided a second set of parameters to assess shear behavior, this time simulating the stresses and shear deformations imparted by rotating wheels. The results compared well to the estimated shear stresses and deformations of Martian soil caused by the wheels of the Spirit rover. When compared to other simulants (e.g. GRC-1), the results confirm that Fillite is possibly more suitable for high-sinkage and high-slip rover studies than other typical simulants derived from natural terrestrial soils and rocks.     

Analysis of a resistance force for the locked-wheel of push-pull locomotion rovers using large subsidence

This paper provides a quantitative analysis of the resistance force of the locked-wheel for push-pull locomotion rovers using intentional sinkage. Our previous study has confirmed that push-pull locomotion using intentional subsidence at an initial position can contribute to improving the traveling performance. The key factor of this scheme is the resistance force of the locked-wheel. However, the resistance force at different sinkage conditions and wheel sizes (e.g., mass, width, and diameter) remains unclear, especially for the individual locked-wheel. The detailed investigation of this interaction can contribute to the accurate estimation of rover mobility. This paper, therefore, investigates the locked-wheel and soil interaction at different sinkage conditions experimentally, especially focusing on the intentional sinkage condition. Additionally, the resistance force is considered theoretically through the knowledge based on the soil flow patterns beneath the locked-wheel. The experimental results confirmed that the resistance force of the locked-wheel rose as the initial sinkage, wheel size, and weight increases. Furthermore, the theoretical calculation suggested the resistance force increased with a similar tendency of the experimental data.     

Traveling and abrasion characteristics of wheels for lunar exploration rover in vacuum

This paper investigates the traveling and abrasion characteristics of rigid wheels for a lunar exploration rover at atmospheric pressure and in a vacuum. For this investigation, a traveling test system that enables the wheel to continuously travel over a long distance was developed. Using this system, tests on traveling performance and abrasion were conducted with the wheel on a lunar regolith simulant surface. In the initial tests, various wheels traveled over different ground conditions and their performances were evaluated based on the relationship between the drawbar pull and slippage. In the later tests, a wheel with grousers traveled a distance of 3 km and the abrasion was analyzed at various intervals. From the traveling performance tests, it was found that for a soft ground condition, the traveling performance of the wheels in vacuum was slightly lower than that in atmosphere. This indicates that ground tests performed in atmosphere overestimate the actual performance on the lunar surface. The abrasion tests suggested that the scratching of wheels occurs more easily in vacuum than in atmosphere. These experiments confirmed that the abrasion of the wheels do not cause any critical problem for a traveling distance of up to 3 km in a simulated lunar environment.