Wheel Sinkage Research Articles

A Real-Time Sinkage Detection Method for the Planetary Robotic Wheel-on-Limb System via a Monocular Camera

When traversing soft and rugged terrain, a planetary rover is susceptible to slipping and sinking, which impedes its movement. The real-time detection of wheel sinkage in the planetary wheel-on-limb system is crucial for enhancing motion safety and passability on such terrain. Initially, this study establishes a measurement of wheel sinkage under complex terrain conditions. Subsequently, a monocular vision-based wheel sinkage detection method is presented by combining the wheel–terrain boundary with the wheel center position (WTB-WCP). The method enables the efficient and accurate detection of wheel sinkage through two-stage parallel computation of the wheel–terrain boundary fitting and wheel center localization. Finally, this study establishes an experimental platform based on a monocular camera and the planetary rover wheel-on-limb system to experimentally validate and comparatively analyze the proposed method. The experimental results demonstrate that the method effectively provides information on the wheel sinkage of the planetary rover wheel-on-limb system, and the relative errors of the method do not exceed 4%. The method has high accuracy and reliability and is greatly significant for the safety and passability of planetary rovers in soft and rugged terrain.

Simulation Research of Motion of Lightweight Wheeled Mobile Robot on Various Types of Soft Ground – a Case Study

A problem of influence of three types of soft ground on longitudinal motion of a lightweight four-wheeled mobile robot is considered. Kinematic structure, main design features of the robot and its dynamics model are described. A numerical model was elaborated to simulate the dynamics of the robot's multi-body system and the wheel-ground interaction, taking into account the soil deformation and stresses occurring on the circumference of the wheel in the area of contact with the deformable ground. Numerical analysis involving four velocities of robot motion and three cases of soil (dry sand, sandy loam, clayey soil) is performed. Within simulation research, the motion parameters of the robot, ground reaction forces and moments of force, driving torques, wheel sinkage and slip parameters of wheels were calculated. Aggregated research results as well as detailed results of selected simulations are shown and discussed. As a result of the research, it was noticed that wheel slip ratios, wheels’ sinkage and wheel driving torques increase with desired velocity of motion. Moreover, it was observed that wheels’ sinkage and driving torques are significantly larger for dry sand than for the other investigated ground types.

An analytical model for stress estimation at the soil-tire interface using the dynamic contact length

The interaction between soil and tire is a complex phenomenon influenced by various factors, such as soil properties, vertical load on the wheel, and tire characteristics. However, estimating stress at the tire-soil interface is a challenging task due to the unpredictable nature of soil. Existing models for investigating the wheel-soil interaction are based on soil mechanical parameters, which are highly variable and require significant time and resources to measure accurately. In contrast, the amount of wheel sinkage into the soil can be measured in real-time and is derived from the mechanical properties of the soil. Therefore, there is a need to establish a relationship between stress and wheel characteristics such as dynamic contact length and tire sinkage in soil. To address this issue, this study introduces an analytical method to estimate the dynamic contact surface between the tire and soil. A mathematical model is then proposed to estimate stress, assuming the contact surface and variable pressure at the interface between the soil and tire. The stress model is validated through experimental tests conducted at three different vertical load levels and four different wheel traffic levels in the soil bin, repeated three times.

Study on hard rock particle size division based on Mars rover traction performance

To simplify the dynamic solution of the contact between the rigid wheel of Mars rover and the spherical hard stone on the mixed terrain, a model for hard stone particle size division based on the traction performance of Mars rover is proposed. On the mixed terrain of hard rock and soft soil, the movement of hard rock will affect the traction performance of the rigid wheels of Mars rover. According to the different effects of the hard stones on the traction performance of rigid wheels, stones are divided into three types. The static sinkage of rigid wheels is calculated according to the Bekker bearing model, and the calculation formula of sliding sinkage of rigid wheels and hard stone sinkage is proposed. The type of hard stones is determined by comparing the sinkage of hard stones and rigid wheels. Finally, three kinds of hard stones with slip ratios of 0.2, 0.5, and 0.7 were substituted into the single wheel simulation platform and the soil trough experiment platform for simulation and experiment. The results show that on mixed terrain, the error of simulation and experimental results of fixed hard stones under three slip rates is below 5.4%, the error of drawbar pull in simulation and experimental results of movable hard stones is above 126%, and the error of simulation and experimental results of scattered small hard stones is below 2%, which verifies the effectiveness of the hard stone particle size division model.

Discrete element modelling of stress propagation in soil under a rigid wheel in a soil bin։ a simulation of probe inducing stress deviation and wheel speed

Discrete element method (DEM) is a suitable technique for simulation of stress propagation in soils, particularly with freshly tilled or aggregated structures. Measurement of true stress, in the absence of a stress-measuring probe inserted in the soil, is not experimentally possible. Stress probes may therefore under- or over-estimate true soil stress. Building on previous work simulating vertical stress propagation under plate sinkage loading, the study modelled stress propagation under a moving rigid wheel. The aim was to determine how vertical stress, with and without a probe, at a given depth may differ under dynamic loading vs. static plate sinkage loading and with varying wheel speed. DEM parameters of the hysteretic spring-linear cohesion contact model were calibrated by a cone penetration test which was validated by wheel sinkage into the soil. Two tests were conducted in a soil bin at a water content of 11% d.b; at a bulk density of 1200 kg m−3 and a wheel loading of 600 N, and at a bulk density of 1350 kg m−3 and wheel loading of 1200 N. Vertical soil stress was measured at 0.15 m depth using a cylindrical load cell probe. The DEM simulation underestimated the measured stress by an average 13%. Average stress overestimation ratio (with/without probe stress) was found to be 1.12, which agreed with measurements beneath the plate during plate sinkage loading. Increasing wheel speed from 0.2 to 6 m s−1 showed a 7% increase in DEM-simulated with-probe stress.

Linear Prediction of High-Slip Sinkage for Planetary Rovers’ Lugged-Wheels Based on Superposition Principle

Planetary rovers with lugged-wheels are the primary equipment for Mars exploration, and as exploration missions become more complex, rovers are expected move into more challenging terrains. When moving over soft sand or slopes, lugged-wheels experience high slip and heavy sinkage, and an explicit sinkage prediction model for lugged-wheels is not available. This limits the motion control of planetary rovers. Here, we show that wheel sinkage can be divided into static sinkage, rolling sinkage, shearing sinkage, and digging sinkage, based on motion decomposition. Static sinkage is in accordance with the modified Archimedes' theorem, shearing sinkage is proportional to the slip ratio, and digging sinkage is proportional to rim displacement. Furthermore, the superposition principle of sinkage has been proved, and the various types of sinkage were superimposed to obtain an explicit prediction model without terramechanics parameters for lugged-wheels. The single-wheel test proves that the linear model can predict sinkage for slip conditions from 0 to 0.9 with a prediction accuracy of over 90%. The decomposition and modeling of the sub-sinkage further explores the intrinsic of the lugged-wheels’ sinkage, and the linear prediction model provides a theoretical basis for high slip control of rovers.

3D DEM-FEM simulation of the flexible metal wheel–soil interaction in low gravity environments

To investigate the driving performance of the flexible metal wheel of the manned lunar rover in a low gravity environment, we established a 3D discrete element method (DEM)-finite element method (FEM) coupling simulation system. The wheel was modeled by FEM and the soil was modeled by DEM. Then, the direct shear tests were performed to verify the validity of the DEM contact parameters. Finally, the driving performance of the flexible metal wheels with different treads under low gravity conditions was studied, and the velocity field of soil particles under the wheels was observed. The results show that the sinkage of the flexible wheel is almost independent of gravity, while the torque and drawbar pull are significantly affected by gravity. Moreover, by comparing the driving performance of the wheel equipped with treads (WT wheel) and without tread (NT wheel), it is found that the tread have great effect on sinkage, torque, and drawbar pull to wheel weight ratio due to the differences in wheel-soil contact area. Also, through the observation of the particle velocity field under the wheel, it is found that the gravity and load also have significant effects on the movement of soil particles. This study provided a reliable method for studies on the interaction between the flexible wheel and soil in low gravity environments.

High-Fidelity Dynamic Modeling and Simulation of Planetary Rovers Using Single-Input-Multi-Output Joints With Terrain Property Mapping

Planetary rovers may traverse terrains with complex geometries and variable physical properties, but their mobility behaviors are complicated and difficult to simulate precisely. This article focuses on high-fidelity dynamic modeling and simulation for a type of rovers that incorporate single-input-multi-output joints to enhance terrain adaptability, which has been used on China's Tianwen-1 Mars rover. A novel multibody dynamic model and its solutions are derived first with consideration of single-input-multi-output joints. Then, a unified terramechanics model is proposed, considering variable terrain surfaces and covering rover's motion states of skidding, slipping, and steering, solved the problem of simulation instability caused by model switching between soft and hard terrains. As the contact areas of wheels with various terrains and resultant sinkage are dominant factors to ensure fidelity but difficult to determine, a new terrain modeling method for calculating contact area and wheel sinkage is developed using digital elevation map with physical properties. A simulation system is developed, integrating all the above models, and verified with physical experiments and commercial software. The relative simulation errors that have been achieved are less than 5.9% for bogie angles, 6.1% for drawbar pull, and 3.4% for slip ratios, demonstrating high fidelity simulation results.

An adapted Burckhardt tire model for off-road vehicle applications

Off-road vehicle mobility is a real challenge in many areas such as agriculture, military, or construction machinery. The introduction of autonomous vehicles in these fields requires more advanced control algorithms. Furthermore, the deformable nature of the terrain has a significant impact on vehicle behavior. In this context, a lot of research has been conducted to describe the wheel-ground interaction phenomena. Among the most significant factors, traction force, lateral force, and wheel sinkage are crucial aspects in the study of vehicle mobility. One of the most used approaches is based on the Bekker-Wong description. However, due to the mathematical complexity of this model, this approach is rather intended for vehicle simulation. Since the design of control laws requires less complex models, this paper proposes a method based on a road tire model structure adapted to deformable surfaces. This modification is based on the original Burckhardt tire model with a modified structure and estimated parameters. Furthermore, the parameter identification is performed by simulating a realistic virtual test bench allowing the data collection for the parameter estimation process. Finally, the obtained results show the applicability of the proposed method through a new tire model called the Adapted Burchardt Tire Model (ABTM).

Linear Expressions of Drawbar Pull and Driving Torque for Grouser-Wheeled Planetary Rovers Without Terrain Mechanical Parameters

Drawbar pull and driving torque are usually applied to characterize the mobility and energy consumption, respectively, of wheeled planetary rovers (WPRs) traversing sandy terrain. Owing to the complexity of the grouser-terrain interaction, neither can be modeled as a closed-form analytical expression of the terrain mechanical parameters. Complexity limits their online applications. Moreover, it is difficult to estimate the terrain mechanical parameters. To solve these issues, based on equivalent wheel sinkage, both the drawbar pull and driving torque can be modeled as a linear function of physically measurable quantities in the absence of terrain mechanical parameters, which is demonstrated using single-wheel experiments conducted with four types of wheels and two sand types. The influence of a sophisticated grouser-terrain interaction on wheel sinkage can be explicitly determined using the linear driving torque model. Furthermore, the validated linear drawbar pull equation is used to estimate the slope-climbing capability of a four-wheeled planetary rover prototype by computing the slope-climbing coefficient, and the relative error can be limited to 10%. In addition, the wheel driving torque of the rover prototype can also be accurately predicted.

A Composite Metric Routing Approach for Energy-Efficient Shortest Path Planning on Natural Terrains

This paper explores the problem of energy-efficient shortest path planning on off-road, natural, real-life terrain for unmanned ground vehicles (UGVs). We present a greedy path planning algorithm based on a composite metric routing approach that combines the energy consumption and distance of the path. In our work, we consider the Terramechanics between the UGV and the terrain soil to account for the wheel sinkage effect, in addition to the terrain slope and soil deformation limitations in the development of the path planning algorithm. As benchmarks for comparison, we use a recent energy-cost minimization approach, in addition to an ant colony optimization (ACO) implementation. Our results indicate that the proposed composite metric routing approach outperforms the state-of-the-art energy-cost minimization method in terms of the resulting path distance, with a negligible increase in energy consumption. Moreover, our results indicate also that the proposed greedy algorithm strongly outperforms the ACO implementation in terms of the quality of the paths obtained and the algorithm running time. In fact, the running time of our proposed algorithm indicates its suitability for large natural terrain graphs with thousands of nodes and tens of thousands of links.

3D DEM analysis on tractive trafficability of a lunar rover wheel with bionic wheel lugs

African ostriches are good at running in the desert, and their toenails can effectively improve the tractivetraction performance in the running process. To improve the tractivetraction trafficability of wheels on the lunar surface loose soil, a wheel with bionic wheel lugs was designed based on the bionic prototype of ostrich toenail and bionic engineering technology. Then, the rolling of the bionic wheel was simulated by using the three-dimensional (3D) discrete element method (DEM) simulation system of the interaction between irregular structure wheel and lunar soil, and the result was compared with that of the wheel with rectangular wheel lugs. Under the same working condition, the drawbar pull, torque, and sinkage of two kinds of wheels at slip ratios of 0.25, 0.375, and 0.625 were analyzed. The simulation results showed that the average drawbar pull and average torque of the bionic wheel are greater than that of the wheel with rectangular wheel lugs at three kinds of slip ratios. When the slip ratios were 0.25 and 0.375, there was almost no difference in the average sinkage of the two kinds of wheels, but the average sinkage of the bionic wheel was significantly less than that of the wheel with rectangular wheel lugs when the slip ratio was 0.625. The results show that, compared with the wheel with rectangular wheel lugs, the bionic wheel has better tractivetraction and anti-subsidence performance. This study provides a new design and research method for improving the tractive trafficability of wheels in the lunar loose surface environment.

Numerical simulation and analysis of mechanized suppression process of seedbed with whole plastic film mulching on double ridges

In order to achieve the construction standard of high mechanized performance of the seedbed with whole plastic-film mulching on double ridges, in this study, the forms of suppression failure were analyzed, and the key factors influencing the suppression performance were determined based on the structure of the seedbed suppression device and its working principles. The discrete element method was adopted for numerical simulation on the suppression process of the seedbed with whole plastic film mulching on double ridges; the parameters during the interaction between the suppression device and seedbed soil were extracted and analyzed, such as contact area, sinkage and horizontal traction resistance trend of press wheels on big ridges and furrows of small ridge. Taking the suppression load on big ridges, suppression load on furrows of small ridge, and advancing velocity of the combined operation machine as the independent variables, qualified rate of suppression as the response value, a mathematical model between the test factors and qualified rate of suppression was established, to explore the influence sequence of the factors on suppression qualified rate. The optimal working parameters of the suppression device were finally obtained: the suppression load on big ridges was 40 N, suppression load on furrows of small ridge was 69.8 N and the machine advancing velocity was 0.98 m/s, and the achieved mean value of suppression qualified rate was 92.6%. Field verification test showed that the mean value of suppression qualified rate was 90.3%, a mere difference of 2.3% compared with the simulation result. The actual operation of the sample machine was basically consistent with the simulation process and could reveal the mechanized suppression operation mechanism of the seedbed with whole plastic film mulching on double ridges, indicating that the established DEM model and its parameter setting were relatively accurate and reasonable. Keywords: seedbed, whole plastic film mulching, double ridges, mechanized suppression, discrete element method, numerical simulation, parameter optimization DOI: 10.25165/j.ijabe.20211401.5866 Citation: Dai F, Song X F, Zhao W Y, Sun B G, Shi R J, Zhang Y. Numerical simulation and analysis of mechanized suppression process of seedbed with whole plastic film mulching on double ridges. Int J Agric & Biol Eng, 2021; 14(1): 142–150.

In-situ wheel sinkage estimation under high slip conditions for grouser-wheeled planetary rovers: Another immobility index

Loose sandy terrain is more likely to induce high slip, making it the most hazardous type of area for grouser-wheeled planetary rovers to traverse. To prevent successfully landed planetary rovers from getting trapped, the rover slip ratio is always selected as a key getting trapped index. Wheel sinkage increases dramatically with slip ratio under high slip conditions, and even though a small uncertainty in the estimated slip ratio could cause a large error in the estimated wheel sinkage. Wheel sinkage contributes directly to entrapment, and thus should also be selected as another important immobility index. Because of the severe soil particle flow caused by the grouser digging effect, the performance of the traditional wheel sinkage estimation algorithm is not acceptable in this context. This study proposes an algorithm to estimate wheel sinkage in-situ using physically measurable quantities, which is validated using single-wheel experiments. Based on the experimental results, the maximum relative error of the estimated wheel sinkage can be reduced from 205% to 14%. The estimated wheel sinkage is then used to compute the drawbar pull to further validate its accuracy, and the maximum relative error of the estimated drawbar pull can be limited to 6%.

Mars curiosity rover mobility trends during the first 7 years

AbstractNASA's Mars Science Laboratory (MSL) Curiosity rover landed on Mars on August 6, 2012. In the 7 years between landing and August 6, 2019 (sol 2488), Curiosity has driven 21,318.5 m over a variety of terrain types and slopes, employing multiple drive modes with varying amounts of onboard autonomy. Curiosity's drive distances each sol have ranged from its shortest drive of 2.6 cm to its longest drive of 142.5 m, with an average drive distance of 28.9 m. Real‐time human intervention is not possible during Curiosity's drives due to the latency in uplinking commands and downlinking telemetry. Instead, the operations team relies on Curiosity's fault protection, autonomous navigation, and visual odometry software to keep the rover safe during drives. During its first 7 years on Mars, Curiosity has attempted 738 drives. While 622 drives ran to completion, 116 drives were prevented or stopped early by Curiosity's fault protection software. The primary risks to mobility success have been wheel damage, wheel entrapment, progressive wheel sinkage, and the potential for hardware or cable failures that result in an inability to command one or more steer or drive actuators. In this paper, we describe Curiosity's mobility subsystem, mobility trends over the first 21.3 km of the mission, operational aspects of mobility fault protection, risks to continued mobility success, and risk mitigation strategies.

Numerical simulation and analysis of mechanized suppression process of seedbed with whole plastic film mulching on double ridges

In order to achieve the construction standard of high mechanized performance of the seedbed with whole plastic-film mulching on double ridges, in this study, the forms of suppression failure were analyzed, and the key factors influencing the suppression performance were determined based on the structure of the seedbed suppression device and its working principles. The discrete element method was adopted for numerical simulation on the suppression process of the seedbed with whole plastic film mulching on double ridges; the parameters during the interaction between the suppression device and seedbed soil were extracted and analyzed, such as contact area, sinkage and horizontal traction resistance trend of press wheels on big ridges and furrows of small ridge. Taking the suppression load on big ridges, suppression load on furrows of small ridge, and advancing velocity of the combined operation machine as the independent variables, qualified rate of suppression as the response value, a mathematical model between the test factors and qualified rate of suppression was established, to explore the influence sequence of the factors on suppression qualified rate. The optimal working parameters of the suppression device were finally obtained: the suppression load on big ridges was 40 N, suppression load on furrows of small ridge was 69.8 N and the machine advancing velocity was 0.98 m/s, and the achieved mean value of suppression qualified rate was 92.6%. Field verification test showed that the mean value of suppression qualified rate was 90.3%, a mere difference of 2.3% compared with the simulation result. The actual operation of the sample machine was basically consistent with the simulation process and could reveal the mechanized suppression operation mechanism of the seedbed with whole plastic film mulching on double ridges, indicating that the established DEM model and its parameter setting were relatively accurate and reasonable. Keywords: seedbed, whole plastic film mulching, double ridges, mechanized suppression, discrete element method, numerical simulation, parameter optimization DOI: 10.25165/j.ijabe.20211401.5866 Citation: Dai F, Song X F, Zhao W Y, Sun B G, Shi R J, Zhang Y. Numerical simulation and analysis of mechanized suppression process of seedbed with whole plastic film mulching on double ridges. Int J Agric & Biol Eng, 2021; 14(1): 142–150.

Real-time Monocular Vision Based Wheel Sinkage and Slip Detection for Planetary Rovers

Real-time Monocular Vision Based Wheel Sinkage and Slip Detection for Planetary Rovers

Physical and Mechanical Characteristics of Lunar Soil at the Chang'E‐4 Landing Site

AbstractChang'E‐4, with the Yutu‐2 rover, is the first lunar probe to successfully land and conduct a tour on the far side of the Moon from early 2019. We analyze the physical and mechanical characteristics of lunar soil through the in situ terrain data collected by the panoramic camera onboard the Yutu‐2 rover. With the slip ratio and wheel sinkage obtained by the derived Digital Orthophoto Map (DOM) and Digital Elevation Model (DEM), the mechanical parameters of lunar soil are derived from the slip‐sinkage model. These mechanical parameters and wheel size of the rover are used to obtain the pressure‐sinkage curves, which can estimate the lunar soil strength. The experimental results indicate that the soil strength at the Chang'E‐4 landing site is much higher than that at the Chang'E‐3 landing site. The discrepancies in lunar soil strength between the two landing sites may be related to the local surface topography and degree of space weathering.

Visualization and analysis of wheel camber angle effect for slope traversability using an in-wheel camera

This paper visualizes and analyzes an effect of a wheel camber angle for the slope traversability in sandy terrain. An in-wheel camera developed in this work captures the wheel-soil contact phenomenon generated beneath the wheel through a transparent section of the wheel surface. The images taken by the camera are then analyzed using the particle image velocimetry. The soil flows with various wheel camber angles are analyzed with regard to the soil failure observed on the slope surface. The analysis reveals that the slope failure and soil accumulation in front of the wheel significantly affect the wheel forces and distributions of the wheel sinkage in the wheel width direction. Further, the side force of the wheel in traversing a slope decreases as the slip ratio increases because the shear stress in the slope downward direction decreases owing to the slope failure.

Research on Application of Wheels with External Track Technology under Soft Road Condition

Wheeled vehicles usually adopt external track when passing through soft road conditions. Taking the large wheelbase four-wheel vehicle as the example, based on recurdyn, the dynamic simulation analysis of two driving modes of wheeled vehicles and wheel with external track was completed, focusing on the comparative analysis of ground specific pressure, hook traction, wheel sinkage and other aspects. The results show that the vehicle passability under the soft condition is improved after the wheels are attached to the track, the vehicle’s theoretical grounding is 86.7% less than the reduction, and the hook traction is nearly 10 times higher. However, for the large wheelbase structure, the track between the two wheels needs to improve the passability by adding load-bearing wheels.