Deformable Terrain Research Articles

Hierarchical Multiscale Modeling of Tire–Soil Interaction for Off-Road Mobility Simulation

A high-fidelity computational terrain dynamics model plays a crucial role in accurate vehicle mobility performance prediction under various maneuvering scenarios on deformable terrain. Although many computational models have been proposed using either finite element (FE) or discrete element (DE) approaches, phenomenological constitutive assumptions in FE soil models make the modeling of complex granular terrain behavior very difficult and DE soil models are computationally intensive, especially when considering a wide range of terrain. To address the limitations of existing deformable terrain models, this paper presents a hierarchical FE–DE multiscale tire–soil interaction simulation capability that can be integrated in the monolithic multibody dynamics solver for high-fidelity off-road mobility simulation using high-performance computing (HPC) techniques. It is demonstrated that computational cost is substantially lowered by the multiscale soil model as compared to the corresponding pure DE model while maintaining the solution accuracy. The multiscale tire–soil interaction model is validated against the soil bin mobility test data under various wheel load and tire inflation pressure conditions, thereby demonstrating the potential of the proposed method for resolving challenging vehicle-terrain interaction problems.

The Effects of Walking Speed and Hardness of Terrain on the Foot-Terrain Interaction and Driving Torque for Planar Human Walking

The foot-terrain interaction mechanics of human is important in understanding the biped locomotion mechanism. This paper aims to investigate the effect of walking speed and the hardness of the terrain on foot-terrain interaction mechanics. In the experiments, mobile portable plantar mechanical measuring insoles with 107 sensor elements were used to gauge the plantar force and contact area in real-time. Seven subjects with healthy feet have participated in typical experiments. The statistical methods including correlation analysis, univariance analysis, and systematic identification are primarily used to obtain several main results. Bimodal functions in describing the total pressure-time relations were performed at slow and regular speeds but only one hump is left if walking at fast paces; they can be unified and summed by three subsections’ unimodal functions. The forefoot produces a large peak impact force in slow and regular quasi-static walking on both hard ground and deformable terrains, while the heel absorbs more dynamic impact shocks in fast walking on hard ground. The torques generated by the ankle joints are calculated based on plantar force or its derived information such as zero moment point. Some implications are drawn, for example, the dynamically changed positions of zero moment point (ZMP) for humans are similar to that generated by reptiles wiggling through the flowable terrains; increasing the stride length on the hard ground produces more impact vibrations than quickening paces but more effective in accelerating walks on deformable terrains.

Optimal Path-Planning of Nonholonomic Terrain Robots for Dynamic Obstacle Avoidance Using Single-Time Velocity Estimator and Reinforcement Learning Approach

A single-time velocity estimator-based reinforcement learning (RL) algorithm, integrated with a chaotic metaheuristic optimization technique is proposed in this article for the optimal path-planning of the nonholonomic robots considering a moving/stationary obstacle avoidance strategy. The additional contribution of the present study is by employing the Terramechanics principles to incorporate the effects of wheel sinkage into the deformable terrain on the dynamics of the robot aiming to find the optimal compensating force/torque magnitude to sustain a robust and smooth motion. The designed systematic control-oriented system incorporates a cost function of weighted components associated with the target-tracking and the obstacle avoidance. The designed velocity estimator contributes to the finite-state Markov decision process (MDP) in order to train the transition probabilities of the problem objectives. Based on the obtained results, the optimal solution for the Q-learning in terms of the adjusting factor for the minimized tracking error and obstacle collision risk propagation profiles is found at 0.22. The results further confirm the promising capacity of the proposed optimization-based RL algorithm for the collision avoidance control of the nonholonomic robots on deformable terrains.

Power consumption of tracked and wheeled small mobile robots on deformable terrains–model and experimental validation

The ability to predict the power consumption of a small mobile robot with either tracked or wheeled configuration is important to its design and control. Accurate and fast prediction of power consumption enables online motion planning that does not exceed the power limits imposed by the propulsion system or the terrain. Skid steering is widely used on small mobile robots because of its simplicity and robust performance. However, modeling of skid steering on deformable terrains is difficult because of the complex vehicle-terrain interaction and the distributed nature of shear stress along the contact surface. This paper first develops a new skid steering model based on terramechanics that is capable of predicting torque and power consumption and is both accurate and computationally efficient. This skid steering model is verified using the experimental data obtained from a track/wheel interchangeable mobile robot driving on dry sand at low speeds. Further, this paper studies the comparison of power consumption between tracked and wheeled mobile robots on deformable terrains focusing on two different aspects: 1) the power losses due to internal friction and damping resistances of both tracked and wheeled configurations, measured from the robot, and 2) the power consumed by deforming the soft soil, using the power consumption model. Overall, this study provides new insights on power consumption of skid steering of both tracked and wheeled mobile robots on deformable terrains.

Online estimation of terrain parameters and resistance force based on equivalent sinkage for planetary rovers in longitudinal skid

Abstract Wheel-soil interaction mechanics plays a crucial role for wheeled mobile robots (WMR) on rough and deformable terrains such as Martian and Lunar surfaces. Skid terramechanics is an essential component for WMRs and generates resistance force when a WMR brakes or on downhill slopes. The basis of classical terramechanics theories for WMRs – Bekker’s normal stress and Janosi’s shear stress equations – are so complex that the wheel-soil interaction force/torque equations are not amenable to closed form solutions, which seriously limits the application of terramechanics theories to WMRs. To establish analytical wheel-soil interaction expressions, the normal and shear stresses that can be characterized linearly by the proposed terrain stiffness and shear strength, respectively, are presented in this paper. Terrain stiffness and shear strength can be used to characterize terrain mechanical properties. Compared with the experimental data, the maximum relative error of the resistance forces estimated using these expressions at steady state is less than 7%. These validated expressions can be applied to estimate terrain parameters and resistance force online with high accuracy. Terrain’s stiffness and shear strength increase first, and then reach a constant. Before wheels entering steady state, the online estimated resistance force’s relative error is much higher, which can be explained using wheel’s vertical velocity.

Multibody simulation of a tracked vehicle with deformable ground contact model

In this paper, the realisation of a multibody model of a tracked machine is described. A new compact modelling of the tracks–soil interaction is presented and soil mechanics laws for terrain response are implemented. Tracked vehicles can be used in different fields such as agriculture, military and construction. The conditions of the terrain on which they operate may vary a lot, in terms of soil composition, slope and roughness. For this reason, performance of tracked vehicles is difficult to predict without a great number of field tests. The model is developed in a multibody code that makes it possible to investigate its dynamic and kinematic behaviour in several operating conditions. A specific routine is implemented in the multibody model in order to simulate the behaviour of the tracked vehicle on deformable terrains. The main hypothesis of this paper is that the terrain deformation could be in a narrow zone affected by the vehicle. Thus, the deformation of the soil is kinematically correlated to the vehicle. Soil mechanics equations are implemented on each track portion and solved only for track links in contact with the soil. The latter is modelled as a rigid body and terrain stress or deformation are not directly computed, thus simplifying solution and terrain modelling despite obtaining coherent results in terms of vehicle traction force, slip and sinkage. Results are reported pointing out performance of the tracked machine on different ground conditions.

UGV with a distributed electric driveline: Controlling for maximum slip energy efficiency on stochastic terrain

Energy saving has been a prominent concern of ground vehicle Original Equipment Manufacturers and research agencies for decades. The search for technological advances that can increase energy efficiency of vehicles has been a relentless quest. The framework of research on energy efficiency improvements has been considerably extended after the introduction of fully electric vehicles with electric motors that individually drive each wheel, i.e., In-Wheel Motors (IWM). Although incoming IWM vehicles can significantly decrease driveline power losses and, thus, improve vehicle energy efficiency compared to conventional mechanical driveline systems, one technical problem related to the vehicle-tire-terrain interaction needs to be addressed in fully electric terrain vehicles. These vehicles are still lacking strategies to manage power distribution between the drive wheels, which are not connected by a driveline system anymore, with the purpose to minimize slip power losses at all tires and maximize vehicle slip energy efficiency. Inappropriate power delivered to each of the wheels, which run in different stochastic terrain conditions, can deteriorate slip energy efficiency of a vehicle with four individually driven wheels. The research work presented in this article addresses the problem of wheel power distribution for an unmanned ground vehicle (UGV) with four IWMs.The goal of this study was to analytically establish and determine conditions for the wheel power split that corresponds to the maximum slip efficiency of the IWM UGV, design a control algorithm that implements the conditions, and verify the effectiveness of the control in experimental research of the vehicle on deformable terrain. The article presents a terramechanics-based IWM UGV mathematical modeling that integrates both vehicle, electric-motor, and wheel dynamics with stochastic soil characteristics. The control algorithm is based on the inverse dynamics approach to control the wheel angular velocity to overcome stochastic terrain load torque and to satisfy a required program of UGV motion given by a UGV velocity profile. Each wheel angular velocity is controlled by varying the wheel torque using a control-by-acceleration principle that provides each wheel with the required angular velocity and the tire rolling radius in the drive mode. Experimental research work, including lab tests at the UAB Vehicle and Robotics Engineering Lab and soil bin experiments of the IWM UGV at the USDA-ARS National Soil Dynamics Lab, was conducted to validate the analytical models and control algorithm.It was found that maximum IWM UGV slip energy efficiency is achieved if the electric motors are controlled to provide the same tire slippages at all four wheels by zeroing the kinematic discrepancy between the theoretical linear velocities of the wheels. At this condition, the total electric current drawn by all four DC motors was minimum. The maximum IWM UGV slip energy efficiency of 89.3% was achieved at a mean tire slippage value of 11.1% on Norfolk Sandy Loam (NSL) soil.

An Apparatus to Measure Wheel–Soil Interactions on Sandy Terrains

Wheeled mobile robots (WMR) have been deployed in Mars/Lunar exploration, military missions, and geological investigations, and they must handle rough and deformable terrains. The dynamics at the wheel–soil interface, including the wheel–terrain contact angle, wheel sinkage, and wheel–soil interaction forces and torque, are major factors in the entrapment of NASA SPIRIT MER and the subsequent mission failure. This paper presents an experimental apparatus that is developed to measure the wheel–terrain contact angle, wheel sinkage, and wheel–soil interaction forces and torque in real time to improve our understanding of the WMR mobility on soft and deformable terrains. A method for wheel sinkage evaluation is presented based on measuring the wheel–terrain contact angle. The wheel–soil interaction forces and torque are measured by installing a force/torque sensor along the axle of the apparatus. The proposed approach is implemented on a testbed, and the experimental results are used to evaluate it; they demonstrate the reliable detection of the wheel–terrain contact angle, wheel sinkage, and wheel–soil interaction forces and torque. Moreover, based on the measured wheel–terrain contact angle, the relative errors in the predicted wheel–soil interaction forces and torque are less than 8% compared with the experimental data.

Modelling optimisation of vehicle velocity for wheeled construction vehicles traversing in off-road terrain

This paper presents the results of an investigation into the effect of terrain conditions on vehicle velocity at each given vehicle speed selection in wet clay and sand terrain beds. Wheeled vehicles face mobility challenges when traversing in deformable terrain resulting in reduced velocity. This experimental modelling-based investigation was carried out using a modified and instrumented wheeled mobility scooter named MOBILITY SF-3713. This vehicle was run on non-deformable pavement in order to obtain reference results. It was then run on wet sand and clay terrain test beds under controlled laboratory conditions. Results from this experiment indicated that terrain type, applied load and tyre inflation pressure all have significant effects on velocity, influenced by tyre rutting in deformable terrain. The results suggest that reliable prediction of this relationship can assist earth moving and deformable haulage road engineers in making economic operational decisions that affect the velocity of wheeled plant.

Modelling optimisation of vehicle velocity for wheeled construction vehicles traversing in off-road terrain

This paper presents the results of an investigation into the effect of terrain conditions on vehicle velocity at each given vehicle speed selection in wet clay and sand terrain beds. Wheeled vehicles face mobility challenges when traversing in deformable terrain resulting in reduced velocity. This experimental modelling-based investigation was carried out using a modified and instrumented wheeled mobility scooter named MOBILITY SF-3713. This vehicle was run on non-deformable pavement in order to obtain reference results. It was then run on wet sand and clay terrain test beds under controlled laboratory conditions. Results from this experiment indicated that terrain type, applied load and tyre inflation pressure all have significant effects on velocity, influenced by tyre rutting in deformable terrain. The results suggest that reliable prediction of this relationship can assist earth moving and deformable haulage road engineers in making economic operational decisions that affect the velocity of wheeled plant.

Trajectory Analysis and Modeling on Longitudinal/lateral Traversing of Slope Terrain for Planetary Exploration Rover

Abstract For a planetary exploration rover, the trafficability is affected by a variety of factors, such as ground hardness, slippage, slope angle on terrain, and so on. In this paper, we focus the development of an analysis model of multi-body dynamics, which consists of forces acting on each wheel based on a wheel and terrain interaction, and a rover dynamics model. From the proposed analysis model, the dynamic behavior for planetary exploration rover on the various inclined terrain during the longitudinal and lateral traversing is predicted. Moreover, we investigate the influence of the steering configuration and load distribution used for the compensation strategies on inclined deformable terrain. These simulation results imply that the appropriate compensation strategy should be adopted so that the rover successfully traverse slope terrain and achieve path following tasks.

A multi-mode real-time terrain parameter estimation method for wheeled motion control of mobile robots

Abstract For motion control of wheeled planetary rovers traversing on deformable terrain, real-time terrain parameter estimation is critical in modeling the wheel-terrain interaction and compensating the effect of wheel slipping. A multi-mode real-time estimation method is proposed in this paper to achieve accurate terrain parameter estimation. The proposed method is composed of an inner layer for real-time filtering and an outer layer for online update. In the inner layer, sinkage exponent and internal frictional angle, which have higher sensitivity than that of the other terrain parameters to wheel-terrain interaction forces, are estimated in real time by using an adaptive robust extended Kalman filter (AREKF), whereas the other parameters are fixed with nominal values. The inner layer result can help synthesize the current wheel-terrain contact forces with adequate precision, but has limited prediction capability for time-variable wheel slipping. To improve estimation accuracy of the result from the inner layer, an outer layer based on recursive Gauss-Newton (RGN) algorithm is introduced to refine the result of real-time filtering according to the innovation contained in the history data. With the two-layer structure, the proposed method can work in three fundamental estimation modes: EKF, REKF and RGN, making the method applicable for flat, rough and non-uniform terrains. Simulations have demonstrated the effectiveness of the proposed method under three terrain types, showing the advantages of introducing the two-layer structure.

Models for Slip Estimation and Soft Terrain Characterization With Multilegged Wheel–Legs

Successful operation of off-road mobile robots faces the challenge of mobility hazards posed by soft, deformable terrain, e.g., sand traps. The slip caused by these hazards has a significant impact on tractive efficiency, leading to complete immobilization in extreme circumstances. This paper addresses the interaction between dry frictional soil and the multilegged wheel–leg concept, with the aim of exploiting its enhanced mobility for safe, in situ terrain sensing. The influence of multiple legs and different foot designs on wheel–leg–soil interaction is analyzed by incorporating these aspects to an existing terradynamics model. In addition, new theoretical models are proposed and experimentally validated to relate wheel–leg slip to both motor torque and stick-slip vibrations. These models, which are capable of estimating wheel–leg slip from purely proprioceptive sensors, are then applied in combination with detected wheel–leg sinkage to successfully characterize the load bearing and shear strength properties of different types of deformable soil. The main contribution of this paper enables nongeometric hazard detection based on detected wheel–leg slip and sinkage.

Measurement of wheel-terrain contact angle for WMRs on rough terrain using laser scanning sensor

PurposeThe purpose of this paper is to explore a novel measurement approach for wheel-terrain contact angle using laser scanning sensors based on near-terrain perception. Laser scanning sensors have rarely been applied to the measurement of wheel-terrain contact angle for wheeled mobile robots (WMRs) in previous studies; however, it is an effective way to measure wheel-terrain contact angle directly with the advantages of simple, fast and high accuracy.Design/methodology/approachFirst, kinematics model for a WMR moving on rough terrain was developed, taking into consideration wheel slip and wheel-terrain contact angle. Second, the measurement principles of wheel-terrain contact angle using laser scanning sensors was presented, including “rigid wheel - rigid terrain” model and “rigid wheel - deformable terrain” model.FindingsIn the proposed approach, the measurement of wheel-terrain contact angle using laser scanning sensors was successfully demonstrated. The rationality of the approach was verified by experiments on rigid and sandy terrains with satisfactory results.Originality/valueThis paper proposes a novel, fast and effective wheel-terrain contact angle measurement approach for WMRs moving on both rigid and deformable terrains, using laser scanning sensors.

Terramechanics-based modeling of sinkage and moment for in-situ steering wheels of mobile robots on deformable terrain

The success of NASA's Mars missions has generated a renewed interest in planetary exploration, along with a need for better mobility of wheeled mobile robots (WMRs)—steering performance, in particular, has not yet reached an acceptable benchmark in high-precision models. This study focuses on the steering mechanics of WMRs, as it can enrich the terramechanics of planetary rovers. An improved sinkage model based on the variable sinkage exponent is proposed, and the sinkage exponent is derived as a function of steering angle. Furthermore, a high-precision steering moment model is proposed based on the steering-sinkage model, which considers the interaction area and the lug effect. The model can fit the results obtained by all of the experimental wheels, based on soil parameter identification. Most of the max relative errors (MREs) for the sinkage are within 5%, and the coefficients of determination are more than 0.97. The MREs of moment increase with increasing vertical load but remain within 10%. This technique can also be applied to other WMRs with rigid wheels steering on deformable terrain.

Particle-based solid for nonsmooth multidomain dynamics

A method for simulation of elastoplastic solids in multibody systems with nonsmooth and multidomain dynamics is developed. The solid is discretised into pseudo-particles using the meshfree moving least squares method for computing the strain tensor. The particle’s strain and stress tensor variables are mapped to a compliant deformation constraint. The discretised solid model thus fit a unified framework for nonsmooth multidomain dynamics simulations including rigid multibodies with complex kinematic constraints such as articulation joints, unilateral contacts with dry friction, drivelines, and hydraulics. The nonsmooth formulation allows for impact impulses to propagate instantly between the rigid multibody and the solid. Plasticity is introduced through an associative perfectly plastic modified Drucker–Prager model. The elastic and plastic dynamics are verified for simple test systems, and the capability of simulating tracked terrain vehicles driving on a deformable terrain is demonstrated.

Finite element modelling of a pneumatic tyre interacting with rigid road and deformable terrain

In this study the dynamic interaction between a pneumatic P235/75R17 tyre and a rigid and/or deformable surface is analysed using the finite element method. After a footprint analysis of the tyre, two models were developed: a) tyre rolling on rigid road with bumps; b) tyre rolling on a deformable terrain, appropriate for off-road vehicle handling. In the first model, a steady-state transport analysis is performed to obtain the free rolling conditions of the tyre, which are then used to simulate the impact of the tyre on a rigid bump, typical of a road cleat or speedbump. In the second model, the transient rolling response of the tyre on a soft cohesive soil layer was simulated under towed and driven conditions. It is shown that the dynamic response of the rolling tyre with off-road terrains is inherently complex and depends on significantly different parameters from that of the on-road tyres.

Computational Studies on Interactions between Robot Leg and Deformable Terrain

Dynamic interactions with soft terrain occur in many natural and engineering systems. These events are usually associated with large deformations and plastic flows, which generate unique challenges for grid-based techniques because of local grid distortions. To overcome this issue, the application of Smooth Particle Hydrodynamics (SPH) method is first extended by the authors to the field of terradynamics, in particular, the continuum simulation of legged locomotion on soft soil media. Soil models with and without consideration of plastic failure are introduced to capture the behavior of loose and dense soil terrain. In one of the models considered for legged locomotion, a pendulum model is used to study a swinging mode. Locomotive interactions across different frequencies are introduced to realize quasi-static deformations and rapid collisional flow phenomena. The results obtained from numerical studies reveal that the soil behavior during locomotive interactions can be realistically simulated with the SPH framework. Compared with a dense soil terrain, a loose soil terrain has better characteristics of energy storage and dissipation. These findings can be helpful for understanding possibilities for robot navigation and exploration in unknown and complex terrains.

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.

Off-Road Tire-Terrain Interaction: An Analytical Solution

A novel semi-analytical solution has been developed for the calculation of the static and dynamic response of an off road tire interacting with a deformable terrain, which utilizes soil parameters independent of the size of the contact patch (size-independent). The models involved in the solution presented, can be categorized in rigid and/or pneumatic tires, with or without tread pattern. After a concise literature review of related methods, a detailed presentation of the semi-analytical solution is presented, along with assumptions and limitations. A flowchart is provided, showing the main steps of the numerical implementation, and various test cases have been examined, characterized in terms of vertical load, tire dimensions, soil properties, deformability of the tire, and tread pattern. It has been found that the proposed model can qualitatively capture the response of a rolling wheel on deformable terrain.