The role of epistemic uncertainty of contact models in the design and optimization of mechanical systems with aleatoric uncertainty

Epistemic uncertainty, the uncertainty in the physical model used to represent a phenomenon, has a significant effect on the predictions of simulations of mechanical systems, particularly in systems with impact events. Impact dynamics can have a significant effect on a system’s functionality, stability, wear, and failure. Because high-fidelity models of systems with impacts often are too computationally intensive to be useful as design tools, rigid body dynamics and reduced order model simulations are used often, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The choice of impact model, though, can have significant ramifications on design predictions. The effects of both epistemic and aleatoric (parametric) uncertainty in the choice of contact model are investigated in this paper for a representative multiple-degree of freedom mechanical system. Six contact models are considered in the analysis: two different constant coefficient of restitution models, a piecewise-linear stiffness and damping (i.e., Kelvin–Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. Results show that the optimal mechanism design for each contact model appears extremely different. Further, the effects due to epistemic uncertainty are differentiated clearly in the response from the effects due to aleatoric uncertainty. Lastly, when the mechanisms are optimized to be robust against aleatoric uncertainty, the resulting designs show some robustness against epistemic uncertainty.     

Measurement and modeling for two-dimensional normal stress distribution of wheel on loose soil

On the Moon or Mars, typical target environments for exploration rovers are covered with fine sand, so their wheels easily slip on such weak ground. When wheel slippage occurs, it is hard for the rover to follow its desired route. In the worst case, the rover gets stuck in loose soil and cannot move anymore. To reduce the risk of the rover getting stuck, analysis of the contact mechanics between the soil and wheel is important. Various normal stress distribution models for under the wheel surface have been proposed so far. However, classical models assume a uniform stress distribution in the wheel’s width direction. In this study, we measured the two-dimensional normal stress distribution of a wheel in experiments. The results clarified that the stress distribution in the wheel’s width direction is a mountain-shape curve with a peak located at the center of the wheel. Based on the results, we constructed a stress distribution model for the wheel’s width direction. In this paper, we report our measurements for the two-dimensional stress distribution of a wheel on loose soil and introduce our stress distribution model for the wheel’s width direction based on our experimental results.     

A method for on-line soil parameters modification to planetary rover simulation

In planetary exploratory rover simulation, the contact model between wheel and terrain inevitably has some differences in contrast with the real one, which can make rover depart the planned track. To eliminate the dynamic errors caused by it, this paper presents a method for on-line soil parameters modification. This paper classifies data errors between virtual rover and real rover as model errors and asynchronous errors. Before modification, data identification is utilized to eliminate asynchronous errors and get a group of effective data with least additional errors. Based on the simplified terramechanics model, the origins of model errors are analyzed in detail from static status and kinetic status; meanwhile, some soil parameters are decoupled from the complicated model, and it makes on-line soil parameters modification feasible. An effective coefficient is also proposed to maintain the stability and convergence of modification. Lastly, through simulations on ROSTDyn (ROver Simulation based on Terramechanics and Dynamics), it is demonstrated that the soil parameters modification method is effective and useful for rover simulation to eliminate dynamic errors of predictive model.     

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.     

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.     

Predicting the performances of rigid rover wheels on extraterrestrial surfaces based on test results obtained on earth

With a growing number of nations interested in planetary exploration, research and development of extraterrestrial rovers have been intensified. The usual practice is to test the performances of rovers on soil simulants on earth, prior to their deployment to extraterrestrial bodies. It is noted that in the tests the soil simulant is subject to the earth gravity, while the terrain on the extraterrestrial surface is subject to a different gravity. Therefore, it is uncertain whether the rover/rover wheel would exhibit the same performance on the extraterrestrial surface as that obtained from tests conducted on earth. This paper describes a practical methodology that can be employed to predict the performances of rover wheels on extraterrestrial surfaces, based on test results obtained on earth. As rigid wheels are used in many extraterrestrial rovers, this study focuses on examining the effects of gravity on the sinkage and compaction resistance of rigid rover wheels. Predictions obtained using the methodology are shown to correlate reasonably well with test data.     

Expanding scissor-based UGV for large obstacles climbing

This research proposes a new extendable platform for an unmanned ground vehicle to overcome the obstacle climbing issue. The new platform is basically established on scissor mechanism principles which have been innovated to achieve long and rigid displacement. A couple of scissor mechanisms are embedded in the rover platform adjusting the mass center of rover respect to the rear and front wheels. Accordingly, it yields geometric control of the contact forces, which can simultaneously reduce the slip of the wheels and increase the performance of the obstacle climbing up. To demonstrate the performance of the proposed platform, the 3D kinematics is derived. Subsequently, the stick-slip Euler-Lagrange dynamics is derived and a three-level controller including the torque optimization is implemented to simulate the rover facing obstacles. Finally, without any hardware prototyping, the extendable rover is simulated and compared with a typical fixed-geometry rover to show the enhancement of the climbing ability by using the proposed concept. Moreover, controlling the normal contact forces of the wheels yields the slip reduction, which subsequently, increases the traction force.     

Uncertainty quantification and global sensitivity analysis of mechanistic one-dimensional models and flow pattern transition boundaries predictions for two-phase pipe flows

The prediction of uncertainties is a growing interest in flow assurance industrial applications, but only few works have been presented on this topic. In this work, an uncertainty quantification and a global sensitivity analysis are performed to quantify the level of confidence in predictions of one-dimensional mechanistic models considering different two-phase flow regimes. A method is proposed for this purpose accounting for the effect of several variables on pressure drop and hold-up predictions by the well-known one-dimensional two-fluid model, such as fluid flow rates, geometry (the inclination angle and the pipe diameter), and fluid properties (density and viscosity); the case of a non-Newtonian shear-thinning fluid behaviour is also considered. Flow pattern transition boundaries, including the stability of the stratified flow regime, are included in this analysis. Monte Carlo simulations were used for the uncertainty quantification while different approaches for the sensitivity analysis (scatter plot, linear regression, the Morris’s method, and the Sobol’s Method) were used and compared to identify the best tool for this family of models. The Sobol’s method appears to be the most convenient approach and a discussion is provided considering different practical cases for gas/liquid and liquid/liquid systems. The most critical input parameters in terms of uncertainty are rigorously identified case by case. A way to reduce the output uncertainty is indicated by the interpretation of the results of the global sensitivity analysis. The conclusions of this analysis gives new insights regarding the degree of uncertainties in predictions of one-dimensional mechanistic models.     

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.     

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.     

Prediction of traction and soil compaction using three-dimensional soil-tyre contact profile

Prediction of traction and compaction in the soil profile based upon two-dimensional (2D) and three-dimensional (3D) representations of the dynamic soil-tyre contact area and an assumed pressure distribution over the profile are presented for two tyre sizes at two inflation pressures, two levels of dynamic load and two slip levels in a tilled Yolo Loam soil condition. A soil model based upon a semi-logarithmic porosity-stress relationship was used to obtain the pressure distribution. Traction predictions based upon the 3D surface were significantly better than those based upon the 2D surface. Compaction predictions were similar for both surfaces except for immediately below the soil surface.     

A systematic approach to reliably characterize soils based on Bevameter testing

Although a lot of information about soil parameter identification exists in literature, there is currently no algorithm who makes use both of state of the art identification methodologies and incorporating statistical analysis. In this paper a state of the art soil parameter identification method is presented including the calculation of its standard deviations and a proper weighting of the objective function. With this algorithm and a Bevameter with advanced sensor and actuator technology a test campaign is started to find a reliable soil preparation, which is applicable to a large planetary rover performance testbed. Furthermore, the preparation method has to be valid and stable for various types of dry, granular and frictional soils, typically used for planetary rover testing in space robotics, since the result of pre-tests show that the soil parameters are highly depending on the preparation. Besides preparation, the soil parameters are also influenced by different Bevameter test setup variables. Thus, the effect of the penetration velocity as well as the penetration tool geometry for pressure–sinkage tests on soil parameters is investigated. For shear tests the influence of the dimension of the shear ring is analysed as well as the variation of the grouser height, the number of the grousers and the increase of the rotational shear velocity. The results of the extensive test campaign are evaluated by the proposed identification algorithms.     

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.     

The ExoMars rover locomotion subsystem

ExoMars is the European Space Agency (ESA) mission to Mars planned for launch in 2018, focusing on exobiology with the primary objective of searching for any traces of extant or extinct carbon-based micro-organisms. The on-surface mission is performed by a near-autonomous mobile robotic vehicle (also referred to as the rover) with a mission design life of 180 sols. The rover has a 6 × 6 × 6 with 6 wheel-walking drive configuration (all 6 wheels are driven, steered and have a ‘walking’ capability) and has flexible wheels providing enhanced traction compared to rigid wheels of the same diameter. The suspension is a passive ‘3-bogie’ system which offers the same 6 wheel contact on uneven ground and mobility performance as the NASA-JPL ‘rocker-bogie’ suspension used on previous Mars rovers, but permits elimination of the differential linkage present in that design. Mars presents several challenges to the rover locomotion subsystem with its rock-strewn surface, sand dunes, rocky outcrops, craters and slopes. The unknown nature of the terrain to be traversed imposes several constraints on the locomotion subsystem design that need to be evaluated and incorporated within the flight model for its successful operation on Mars. In addition, accommodation within the confines of the lander and successful egress from it over deflated airbags places stringent constraints on locomotion subsystem mass, stowage envelope, deployment and wheel design. This paper documents the evolution of the ExoMars rover vehicle locomotion configuration from an early design concept to the current mission baseline design. The discussion involves various tradeoffs supported by mechanical and terramechanical analyses, simulations and testing performed on full-scale locomotion breadboard models at single wheel level and system level.     

Soft soil track interaction modeling in single rigid body tracked vehicle models

Single rigid body models are often used for fast simulation of tracked vehicle dynamics on soft soils. Modeling of soil-track interaction forces is the key modeling aspect here. Accuracy of the soil-track interaction model depends on calculation of soil deformation in track contact patch and modeling of soil resistive response to this deformation. An algorithmic method to calculate soft soil deformation at points in track contact patch, during spatial motion simulation using single body models of tracked vehicles, is discussed here. Improved calculations of shear displacement distribution in the track contact patch compared to existing methods, and realistically modeling plastically deformable nature of soil in the sinkage direction in single body modeling of tracked vehicle, are the novel contributions of this paper. Results of spatial motion simulation from a single body model using the proposed method and from a higher degree of freedom multibody model are compared for motion over flat and uneven terrains. Single body modeling of tracked vehicle using the proposed method affords quicker results with sufficient accuracy when compared to those obtained from the multibody model.     

Smooth static and dynamic indentation of a cantilever beam

The static and dynamic indentation of structural elements such as beams and plates continue to be intriguing problems, especially for scenarios where large area contacts are expected to occur. Standard methods of indentation analyses use a beam theory solution to obtain an overall load–displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: the stress distribution in the contact region will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. The indentation models developed herein are improvements over existing GLOBAL/LOCAL models for static and dynamic indentation of cantilever beams. Maximum contact stresses, beam displacements, and contact force time histories are obtained and compared with the predictions of current static and dynamic indentation models. The validity of the solutions presented herein is further assessed by comparing the results obtained to the predictions of modified beam theory solutions.     

Modelling of crack growth under cyclic contact loading

The paper describes a general computational model for modelling of subsurface fatigue crack growth under cyclic contact loading of mechanical elements. The model assumes that the initial fatigue crack develops along the slip line in a single crystal grain at the point of the maximum equivalent stress. The position and magnitude of the maximum equivalent stress are determined with the Finite Element Analysis of the equivalent contact model, which is based on the Hertzian contact conditions with the addition of frictional forces. The Virtual Crack Extension method is then used for simulation of the fatigue crack propagation from the initial to the critical crack length, when the surface material layer breaks away and a pit appears on the surface. The pit shapes and relationships between the stress intensity factor and the crack length are determined for various combinations of contacting surface curvatures and contact loadings. The computational results show that the model reliably simulates the subsurface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.     

Characterisation of martian soil simulants for the ExoMars rover testbed

The European Space Agency (ESA) ExoMars mission involves landing a rover on the surface of Mars on an exobiology mission to extend the search for life. The locomotion capabilities of the ExoMars rover will enable it to use its scientific instruments in a wide variety of locations. Before it is sent to Mars, this locomotion system must be tested and its performance limitations understood. To test the locomotion performance of the ExoMars rover, three martian regolith simulants were selected: a fine dust analogue, a fine Aeolian sand analogue, and a coarse sand analogue. To predict the performance of the ExoMars rover locomotion system in these three regolith simulants, it is necessary to measure some fundamental macroscopic properties of the materials: cohesion, friction angle, and various bearing capacity constants. This paper presents the tests conducted to determine these properties. During these tests, emphasis was placed on preparing the regolith simulants at different levels of density in order to evaluate its impact on the value of the parameters in particular. It was shown that compaction can influence the Bekker coefficients of pressure-sinkage. The shear properties are consistent with the critical state model at normal stresses similar to those of the ExoMars rover in all but one of the simulants, which showed behaviour more consistent with transitional soil behaviour. It is necessary to give due consideration to these variations to ensure a robust test regime is developed when testing the tractive ability of the ExoMars mobility system.     

A comparison of ground vehicle mobility analysis based on soil moisture time series datasets from WindSat,LIS, and in situ sensors

Soil moisture is a key terrain variable in ground vehicle off-road mobility. Historically, models of the land water balance have been used to estimate soil moisture. Recently, satellites have provided another source of soil moisture estimates that can be used to estimate soil-limited vehicle mobility. In this study, we compared the off-road vehicle mobility estimates based on three soil moisture sources: WindSat (a satellite source), LIS (a computer model source), and in situ ground sensors (to represent ground truth). Mobility of six vehicles, each with different ranges of sensitivity to soil moisture, was examined in three test sites. The results demonstrated that the effect of the soil moisture error on mobility predictions is complex and may produce very significant errors in off-road mobility analysis for certain combinations of vehicles, seasons, and climates. This is because soil moisture biases vary in both direction and magnitude with season and location. Furthermore, vehicles are sensitive to different ranges of soil moistures. Modeled vehicle speeds in the dry time periods were limited by the interaction between soil traction and the vehicles’ powertrain characteristics. In the wet season, differences in soil strength resulted in more significant differences in mobility predictions.     

A Computational Intelligence-Based Genetic Programming Approach for the Simulation of Soil Water Retention Curves

Soil water retention curves are a key constitutive law used to describe the physical behavior of an unsaturated soil. Various computational modeling techniques, that formulate retention curve models, are mostly based on existing soil databases, which rarely consider any effect of stress on the soil water retention. Such effects are crucial in the case of swelling soils. This study illustrates and explores the ability of computational intelligence-based genetic programming to formulate the mathematical relationship between the water content, in terms of degree of saturation, and two input variables, i.e., net stress and suction for three different soils (sand–kaolin mixture, Gaduk Silt and Firouzkouh clay). The predictions obtained from the proposed models are in good agreement with the experimental data. The parametric and sensitivity analysis conducted validates the robustness of our proposed model by unveiling important parameters and hidden non-linear relationships.