Multi-objective traction optimization of vehicles in loose dry sand using the generalized reduced gradient method

A work optimization strategy is combined with algorithms within the vehicle-terrain interface (VTI) model to maximize the traction of a four-wheel vehicle operating on loose dry sand. The optimization model distributes traction among the steered and non-steered wheels with the work optimum coefficient (WOC) of each wheel treated as an independent design objective. Drawbar pull (DBP), motion resistance (MR), longitudinal traction coefficient (LTC), lateral force coefficient (LFC), tire deflection, and wheel slip are key parameters that appear in the VTI model for traction performance analysis. The analysis includes wheels of different diameters, widths, heights, and inflation pressures, under variable wheel slips. A multi-objective optimization problem is formulated over a thirteen-dimensional search space bounded by eight design constraints. The generalized reduced gradient method is used to predict optimal values of the design variables as well as ground and traction parameters such as DBP, MR, LTC, and LFC for maximum slope climbing efficiency. The WOCs are maximized for lateral slip angles between 0° and 24° to find a set of Pareto optimal solutions over a wide range of weight factors. A method to apply the optimization results for predicting vehicle performance and traction control on dry sand is presented and discussed.     

Structure design and traction trafficability analysis of multi-posture wheel-legs bionic walking wheels for sand terrain

Nowadays, the existing walking wheels still have problems with the wheel-legs structure and the traction trafficability on the loose sand. It is commonly believed that African ostrich (Struthio camelus) is a kind of bipedal species with superior running performance on the sandy environment. Being enlightened by this, four bionic walking wheels (herringbone wheel, in-line wheel, V-shaped wheel and combination wheel) were designed and tested by imitating the structure and posture of ostrich’s feet travelling on sand. The results showed that when the wheel load was 20, 30 and 50N respectively and the slip ratio was less than 35%, the herringbone wheel had better traction trafficability than that of other wheels. When the wheel load was 30, 50 and 70N and the slip ratio was more than 35%, the in-line wheel had better performance than that of other wheels. It was shown in this thesis that the bionic walking wheels designed with the multi-posture wheel-legs and the simple structure could reduce the soil resistance and the disturbance to sand, thereby achieving a superior performance of traveling on sand. In addition, a new idea and research method for designing of walking mechanism on soft terrain has been provided in this thesis.     

Improved sinkage algorithms for powered and unpowered wheeled vehicles operating on sand

Modeling and simulation of vehicles in sand is critical for characterizing off-road mobility in arid and coastal regions. This paper presents improved algorithms for calculating sinkage (z) of wheeled vehicles operating on loose dry sand. The algorithms are developed based on 2737 tests conducted on sand with 23 different wheel configurations. The test results were collected from Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating in loose dry sand. The study considers tire diameters from 36 to 124 cm with wheel loads of 0.19–36.12 kN. The proposed algorithms present a simple form of sinkage relationships, which only require the ratio of the wheel ground contact pressure and soil strength represented by cone index. The proposed models are compared against existing closed form solutions defined in the Vehicle Terrain Interface (VTI) model. Comparisons suggest that incorporating the proposed models into the VTI model can provide comparable predictive accuracy with simpler algorithms. In addition to simplicity, it is believed that the relationship between cone index (representing soil shear strength) and the contact pressure (representing the applied pressure to tire-soil interface) can better capture the physics of the problem being evaluated.     

Effect of design parameters on the performance of rigid traction wheels on saturated soils

A dimensional analysis was carried out to study the effect of individual wheel parameters, namely the lug angle, lug height, rim width and lug spacing on the traction performance of rigid wheels in saturated soils. The performance of the test wheels was evaluated on the basis of drawbar pull, slip and torque data obtained at different normal loads ranging between 50 and 100 kg (790–980 N). The data were utilized to compute the performance values such as tractive efficiency and overall performance index. Through the regression analysis, the optimum values of lug angle, rim width and lug spacing were found to be 20°, 200 mm and 110 mm respectively for a wheel of 685 mm dia. However, a definite conclusion regarding the optimum value of lug height could not be drawn, though the analysis for higher loads indicated this value as of 38 mm. The wheel parameter most influencing the traction performance of the wheel was found to be the rim width.     

Traction performance of a pushed/pulled drive wheel

A comprehensive method for prediction of off-road driven wheel performance is presented, assuming a parabolic wheel–soil contact surface. The traction performance of a driven wheel is predicted for both driving and braking modes. Simulations show significant non-symmetry of the traction performance of the driving and braking wheels. The braking force is significantly greater than the traction force reached in the driving mode. In order to apply the suggested model for prediction of the traction performance of a 4WD vehicle, the load transfer effect was considered. Simulated traction performances of front and rear driven wheels differ significantly, due to the load transfer. In the driving mode, the rear driven wheel develops a net traction force greater than that of the front wheel. On the other hand, in the braking mode the front driven wheel develops a braking force significantly greater than that of the rear driven wheel due to a pushed/pulled force affected by the load transfer. The suggested model was successfully verified by the data reported in literature and by full-scale field experiments with a special wheel-testing device. The developed approach may improve the prediction of off-road multi-drive vehicle traction performance.     

Prediction of tractive response for flexible wheels with application to planetary rovers

Planetary rovers are typically developed for high-risk missions. Locomotion requires traction to provide forward thrust on the ground. In soft soils, traction is limited by the mechanical properties of the soil, therefore lack of traction and wheel slippage cause difficulties during the operation of the rover. A possible solution to increase the traction force is to increase the size of the wheel-ground contact area. Flexible wheels provide this due to the deformation of the loaded wheel and hence this decreases the ground pressure on the soil surface. This study focuses on development of an analytical model which is an extension to the Bekker theory to predict the tractive performance for a metal flexible wheel by using the geometric model of the wheel in deformation. We demonstrate that the new analytical model closely matches experimental results. Hence this model can be used in the design of robust and optimal traction control algorithms for planetary rovers and for the design and the optimisation of flexible wheels.     

2D FE–DEM analysis of tractive performance of an elastic wheel for planetary rovers

We have been developing a simulation program for use with soil–wheel interaction problems by coupling Finite Element Method (FEM) and Discrete Element Method (DEM) for which a wheel is modeled by FEM and soil is expressed by DEM. Previous two-dimensional FE–DEM was updated to analyze the tractive performance of a flexible elastic wheel by introducing a new algorithm learned from the PID-controller model. In an elastic wheel model, four structural parts were defined using FEM: the wheel rim, intermediate part, surface layer, and wheel lugs. The wheel rigidity was controlled by varying the Young’s Modulus of the intermediate part. The tractive performance of two elastic wheels with lugs for planetary rovers of the European Space Agency was analyzed. Numerical results were compared with experimentally obtained results collected at DLR Bremen, Germany. The FE–DEM result was confirmed to depict similar behaviors of tractive performance such as gross tractive effort, net traction, running resistance, and wheel sinkage, as in the results of experiments. Moreover, the tractive performance of elastic wheels on Mars was predicted using FE–DEM. Results clarified that no significant difference of net traction exists between the two wheels.     

Improvement of a power tiller cage wheel for use in swampy peat soils

This study was aimed at investigating traction performance of a cage wheel for use in swampy peat soils in Indonesia. The tests were conducted in a soil bin filled with peat soil taken from the swampy areas. A set up was developed to measure tractive performance of a single cage wheel. Deep sinkage and high wheel slip were identified as the major problems of using the existing cage wheel design in swampy peat soils. The results revealed that increasing the lug angle from 15 to 35° and the length of lug improved the tractive performance of the cage wheel significantly, while increasing the number of lugs from 14 to 18 and width of lug did not improve the tractive performance significantly. A cage wheel with lug size 325×80 mm, 35° lug angle, 14 lugs (26° lug spacing), with 2 circumferential flat rings installed on the inner side of the lugs, out performed the other settings for use with power tillers in swampy peat soils.     

Design and traction performance of the movable lug wheel

A movable lug wheel using a rollers-sliding groove mechanism was designed, constructed and tested. Two types of lug moving patterns of the movable lug wheel were proposed and evaluated. Tests were conducted in a soil bin test apparatus to determine the traction performance of the wheel as affected by lug moving pattern, lug spacing, horizontal load and vertical load. Similar tests were also conducted using a fixed lug wheel. Generally, under the same level of vertical load, the fixed lug wheel sank more than the movable lug wheels did. However in general, under various horizontal loads, there was no significant difference of slip between the movable lug wheel and the fixed lug wheel. Among the test lug wheels, the movable lug wheel with lug moving pattern-2 required the smallest driving torque and developed the highest traction efficiency.     

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.     

Design of manned lunar rover wheels and improvement in soil mechanics formulas for elastic wheels in consideration of deformation

Most of the current lunar rover vehicle wheels are inconvenient for changing broken wheels and have poor shock absorbing in driving, so they cannot be used to carry people on the moon. To meet the demands for manned lunar transportation, a new wheel possessing a woven metal wire mesh tire and using hub-rim combination slide mechanism is designed in this article. The characteristics of the new wheel is analyzed by comparing with the same-size conventional rover wheels after demonstrating the validity of FEM simulation. The new wheel possesses lighter structure and superior shock absorbing. It also provides stronger traction because the deformation of the designed wheel increases the contact area between the tire and lunar terrain. In order to establish an on-line soil parameter estimation algorithm for low cohesion soil, the stress distribution along a driven deformable wheel on off-road terrain is simplified. The basic mechanics equations of the interaction between the wheel and the lunar soil can be used for analytical analysis. Simulation results show that the soil estimation algorithm can accurately and efficiently identify key soil parameters for loose sand.     

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.     

Analysis of soil flow and traction mechanics for lunar rovers over different types of soils using particle image velocimetry

Grouser wheels have been used in planetary rovers to improve mobility performance on sandy terrains. The biggest difference between a wheel with and without grousers is the soil behavior beneath the wheel as the grousers shovel the soil. By analyzing the soil flow, we gain insight into the mechanics dominating the interaction between the wheel and the soil, directly impacting performance. As the soil flow varies depending on the soil properties, the effects of soil type on soil behavior and wheel-traveling performance should be studied. This paper reveals the difference in soil flow and wheel performance on cohesive and non-cohesive soils. We conducted a series of single wheel tests over different types of soils under several wheel-traveling conditions. Soil flow was visualized by using particle image velocimetry (PIV). The experimental results indicate that soil flow characteristics highly depend on the shear strength of the soil. The cohesive soil exhibited lower fluidity due to its higher shear strength. At the same time, the wheel displayed a higher traveling performance over the cohesive soil, that is, a lower slip ratio.     

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.     

Measurement of soil parameters useful in predicting tractive ability of off-road vehicles using an instrumented portable device

An instrumented portable device that measures soil sinkage, shear, and frictional parameters in situ was developed to investigate the complexity of soil-traction device interaction process. The device was tested to determine its ability to measure soil frictional and shear characteristics. Extensive laboratory tests were conducted using dry and moist Capay clay and Yolo loam soils. In addition, field tests were also conducted in a Yolo loam field located at the UC Davis Agricultural Experiment Station. The Cohron sheargraph was also tested under the same laboratory experimental conditions to determine adhesion, soil-metal friction, cohesion, and angle of internal friction of soil. The analysis of experimental data indicated that soil adhesion and soil-metal friction were found to be functions of the intercept and slope values of cone torque versus cone index plot (r² = 0.94 and 0.95, respectively). Moreover, soil cohesion was found to be related to adhesion by the constrained adhesion relationship, and soil angle of internal friction was proportional to soil-metal friction as reported by Hettiaratchi [7] and [8]. These results imply that a simpler device consisting of a rotating cone can be developed to measure soil frictional and shear characteristics. Preliminary results showed that the soil parameters determined using this device predicted the maximum net traction developed by four different radial ply tires tested by Upadhyaya et al. [18] under similar soil conditions quite well. These results indicate that the parameters obtained from the device could be useful in obtaining traction related parameters of a soil-tractive device interaction process.     

Bayesian calibration of Vehicle-Terrain Interface algorithms for wheeled vehicles on loose sands

The Vehicle-Terrain Interface (VTI) model is commonly used to predict off-road mobility to support virtual prototyping. The Database Records for Off-road Vehicle Environments (DROVE), a recently developed database of tests conducted with wheeled vehicles operating on loose, dry sand, is used to calibrate three equations used within the VTI model: drawbar pull, traction, and motion resistance. A two-stage Bayesian calibration process using the Metropolis algorithm is implemented to improve the performance of the three equations through updating of their coefficients. Convergence of the Bayesian calibration process to a calibrated model is established through evaluation of two indicators of convergence. Improvements in root-mean square error (RMSE) are shown for all three equations: 17.7% for drawbar pull, 5.5% for traction, and 23.1% for motion resistance. Improvements are also seen in the coefficient of determination (R²) performance of the equations for drawbar pull, 2.8%, and motion resistance, 2.5%. Improvements are also demonstrated in the coefficient of determination for drawbar pull, 2.8%, and motion resistance, 2.5%, equations, while the calibrated traction equation performs similar to the VTI equation. A randomly selected test dataset of about 10% of the relevant observations from DROVE is used to validate the performance of each calibrated equation.     

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.     

Experimental and DEM analyses on wheel-soil interaction

In this paper, the wheel-soil interaction for a future lunar exploration mission is investigated by physical model tests and numerical simulations. Firstly, a series of physical model tests was conducted using the TJ-1 lunar soil simulant with various driving conditions, wheel configurations and ground void ratios. Then the corresponding numerical simulations were performed in a terrestrial environment using the Distinct Element Method (DEM) with a new contact model for lunar soil, where the rolling resistance and van der Waals force were implemented. In addition, DEM simulations in an extraterrestrial (lunar) environment were performed. The results indicate that tractive efficiency does not depend on wheel rotational velocity, but decreases with increasing extra vertical load on the wheel and ground void ratio. Rover performance improves when wheels are equipped with lugs. The DEM simulations in terrestrial environment can qualitatively reproduce the soil deformation pattern as observed in the physical model tests. The variations of traction efficiency against the driving condition, wheel configuration and ground void ratio attained in the DEM simulations match the experimental observations qualitatively. Moreover, the wheel track is found to be less evident and the tractive efficiency is higher in the extraterrestrial environment compared to the performance on Earth.     

Modeling wheel-induced rutting in soils: Indentation

The analysis of indentation of rigid cylindrical wheels into frictional/cohesive soils is presented. Three- and two-dimensional numerical simulations were performed using the finite element code ABAQUS to assess the influence of soil strength parameters, dilatancy, and wheel geometry on the relationship between the indentation force and wheel sinkage. The effect of three-dimensionality in the indentation process is studied in detail. Three-dimensional effects were found to be minor for clays though significant for sands. An approximate analytic approach is also presented, which relates indentation force and wheel sinkage for given wheel geometry and material parameters. Theoretical results are compared with preliminary experimental data obtained from small-scale indentation tests, and satisfactory qualitative agreement is shown. The results described in the paper are regarded as reference for numerical and analytic modeling of wheel rolling, to be presented in a separate paper.     

Experimental analysis of soil reaction on a lug of a movable lug wheel

A movable lug wheel was tested in a soil bin test apparatus to determine its traction performance and to measure the soil reaction forces on its lugs. Similar tests were also conducted using a fixed lug wheel. The effects of the lug motion pattern, lug spacing and horizontal load on pull and lift forces were studied. From the experiments it is confirmed that the movable action of the lug plate could generate superior pull and lift forces in comparison with the fixed lug wheel. Among the test wheels, lug motion pattern-2 generated the highest pull and lift forces. Within the range of the test conditions, there was no significant difference in pull and lift forces of the lug plate between the test lug wheels with 12 lugs and 15 lugs at the same level of horizontal and vertical loads. The increase of horizontal load up to 200 N generally increased the pull force and generated smaller rolling resistance before the lug left the soil, but did not increase the lift force significantly. The patterns of pull force, lift force and drawbar pull generated under a constant slip were slightly different from those under a constant horizontal load. Finally, the results were also elucidated by their actual lug trajectories in soil.