The main objective of this research is the development of a volumetric wheel-soil ground contact model that is suitable for mobile robotics applications with a focus on efficient simulations of planetary rover wheels operating on compliant and irregular terrains. To model the interaction between a rover wheel and soft soil for use in multibody dynamic simualtions, the terrain material is commonly represented by a soil continuum that deforms substantially when in contact with the locomotion system of the rover. Due to this extensive deformation and the large size of the contact patch, a distributed representation of the contact forces is necessary. This requires time-consuming integration processes to solve for the contact forces and moments during simulation. In this work, a novel approach is used to represent these contact reactions based on the properties of the hypervolume of penetration, which is defined by the intersection of the wheel and the terrain. This approach is based on a foundation of springs for which the normal contact force can be calculated by integrating the spring deflections over the contact patch. In the case of an elastic foundation, this integration results in a linear relationship between the normal force and the penetration volume, with the foundation stiffness as the proportionality factor. However, due to the highly nonlinear material properties of the soft terrain, a hyperelastic foundation has to be considered and the normal contact force becomes proportional to a volume with a fractional dimension --- a hypervolume. The continuous soil models commonly used in terramechanics simulations can be used in the derivation of the hypervolumetric contact forces. The result is a closed-form solution for the contact forces between a planetary rover wheel and the soft soil, where all the information provided by a distributed load is stored in the hypervolume of interpenetration. The proposed approach is applied to simulations of rigid and flexible planetary rover wheels. In both cases, the plastic behaviour of the terrain material is the main source of energy loss during the operation of planetary rovers. For the rigid wheel model, a penetration geometry is proposed to capture the nonlinear dissipative properties of the soil. The centroid of the hypervolume based on this geometry then allows for the calculation of the contact normal that defines the compaction resistance of the soil. For the flexible wheel model, the deformed state of the tire has to be determined before applying the hypervolumetric contact model. The tire deformation is represented by a distributed parameter model based on the Euler-Bernoulli beam equations. There are several geometric and soil parameters that are required to fully define the normal contact force. While the geometric parameters can be measured, the soil parameters have to be obtained experimentally. The results of a drawbar pull experiment with the Juno rover from the Canadian Space Agency were used to identify the soil parameters. These parameters were then used in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain. Comparison of the simulation results with the experimental data validated the planetary rover wheel model developed in this work.

More than 50 percent of the land area of the Nordic countries Finland, Norway, and Sweden are covered by dense forests and they are among the most important producers of forest products in the world. Forestry in these countries is based on sustainable management principles – reforestation follows harvesting. Furthermore, increasing demands for more gentle techniques and technologies with less negative impact on the environment ask for development and implementation of new processes and new machine solutions. The increasing interest in developing forest management approaches that are based on gentleness to the environment requires better understanding of the interaction between the forestry machines and the terrain in the harvesting process. / <p>QC 20150827</p> / Gentle Forest Machines

The main objective of this research is the development of a volumetric wheel-soil ground contact model that is suitable for mobile robotics applications with a focus on efficient simulations of planetary rover wheels operating on compliant and irregular terrains. To model the interaction between a rover wheel and soft soil for use in multibody dynamic simualtions, the terrain material is commonly represented by a soil continuum that deforms substantially when in contact with the locomotion system of the rover. Due to this extensive deformation and the large size of the contact patch, a distributed representation of the contact forces is necessary. This requires time-consuming integration processes to solve for the contact forces and moments during simulation. In this work, a novel approach is used to represent these contact reactions based on the properties of the hypervolume of penetration, which is defined by the intersection of the wheel and the terrain. This approach is based on a foundation of springs for which the normal contact force can be calculated by integrating the spring deflections over the contact patch. In the case of an elastic foundation, this integration results in a linear relationship between the normal force and the penetration volume, with the foundation stiffness as the proportionality factor. However, due to the highly nonlinear material properties of the soft terrain, a hyperelastic foundation has to be considered and the normal contact force becomes proportional to a volume with a fractional dimension --- a hypervolume. The continuous soil models commonly used in terramechanics simulations can be used in the derivation of the hypervolumetric contact forces. The result is a closed-form solution for the contact forces between a planetary rover wheel and the soft soil, where all the information provided by a distributed load is stored in the hypervolume of interpenetration. The proposed approach is applied to simulations of rigid and flexible planetary rover wheels. In both cases, the plastic behaviour of the terrain material is the main source of energy loss during the operation of planetary rovers. For the rigid wheel model, a penetration geometry is proposed to capture the nonlinear dissipative properties of the soil. The centroid of the hypervolume based on this geometry then allows for the calculation of the contact normal that defines the compaction resistance of the soil. For the flexible wheel model, the deformed state of the tire has to be determined before applying the hypervolumetric contact model. The tire deformation is represented by a distributed parameter model based on the Euler-Bernoulli beam equations. There are several geometric and soil parameters that are required to fully define the normal contact force. While the geometric parameters can be measured, the soil parameters have to be obtained experimentally. The results of a drawbar pull experiment with the Juno rover from the Canadian Space Agency were used to identify the soil parameters. These parameters were then used in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain. Comparison of the simulation results with the experimental data validated the planetary rover wheel model developed in this work.

For realistic predictions of vehicle performance in off-road conditions, it is critical to incorporate in the simulation accurate representations of the variability of the terrain profile. It is not practically feasible to measure the terrain at a sufficiently large number of points, or, if measured, to use such data directly in the simulation. Dedicated modeling techniques and computational methods that realistically and efficiently simulate off-road operating conditions are thus necessary. Many studies have been recently conducted to identify effective and appropriate ways to reduce experimental data in order to preserve only essential information needed to re-create the main terrain characteristics, for future use. This thesis focuses on modeling terrain profiles using the finite difference approach for solving linear second-order stochastic partial differential equations. We currently use this approach to model non-stationary terrain profiles in two dimensions (i.e., surface maps). Certain assumptions are made for the values of the model coefficients to obtain the terrain profile through the fast computational approach described, while preserving the stochastic properties of the original terrain topology. The technique developed is illustrated to recreate the stochastic properties of a sample of terrain profile measured experimentally. To further analyze off-road conditions, stochastic soil properties are incorporated into the terrain topology. Soil models can be developed empirically by measuring soil data at several points, or they can be created by using mathematical relations such as the Bekker's pressure-sinkage equation for homogeneous soils. In this thesis, based on a previously developed stochastic soil model, the polynomial chaos method is incorporated in the soil model. In a virtual proving ground, the wheel and soil interaction has to be simulated in order to analyze vehicle maneuverability over different soil types. Simulations have been created on a surface map for different case studies: stepping with a rigid plate, rigid wheel and flexible wheel, and rolling of a rigid wheel and flexible wheel. These case studies had various combinations of stochastic or deterministic terrain profile, stochastic or deterministic soil model, and an object to run across the surface (e.g., deterministic terrain profile, stochastic soil model, rolling rigid wheel). This thesis develops a comprehensive terrain and soil simulation environment for off-road mobility studies. Moreover, the technique developed to simulate stochastic terrain profile can be employed to simulate other stochastic systems modeled by PDEs. / Master of Science

This research has investigated the effect of tyre rutting of wheeled construction plant performance traversing in wet and deformable terrain, specifically clay and sand. The purpose was to translate the wheel rutting into performance reduction measured in drawbar-pull. The ultimate goal was to translate the power loss into practical effects on cost, time and other economic variations on construction projects that are characterised by movement of wheeled plant on long haulage deformable roads. In order to achieve this aim, mathematical modelling was deployed based on Newton’s laws of motion, principles of energy conservation and numerical integration. The model is based on a single rigid wheel because construction plant tyres are inflated to high pressure in order to support heavy loads thereby translating the flexible tyres into rigid mode. The results from the mathematical model were verified using a three stage robust verification process which included computational analysis based on two existing semi-empirical methods and real experimental data. Laboratory experiments using Mobility SF- 3713 were also used to check the validity of the results. The results from the mathematical model verify that a flexible tyre can operate in rigid mode if it encounters softer and wet ground. Results further indicate that the soil cohesion, angle of shearing resistance and moisture content play key roles in the subsequent power loss created by motion resistance. All the results from computational analysis and the experiments were found to be consistent with the mathematical model results. The study concludes that there is ample evidence to suggest that there is significant power loss associated with wheeled construction plant traversing in soft terrain which can be assessed. The study further concludes that a combination of economic decisions on variables must be considered with respect to existing ground conditions. This will considerably reduce uncertainty levels in cost and resource management on construction projects.