|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.