Accurate Contact Law for Surface Motions of Small-Body Exploration Rovers

This paper develops an accurate contact law for characterizing the hopping motion of exploration rovers on small bodies in the solar system. The availability of such a law is important to provide guidance for rover deployment and mission planning. The contact between a rover and the surface of a small body is set up as a viscoelastic contact problem, for which there have previously been no complete solutions. The proposed new contact law is derived by modifying the equation representing the geometric relation between indentation and surface displacements so that it remains valid after Laplace transformation. The validity of this approach is demonstrated by analyzing the behavior of the Stieltjes convolution involved in the solution, which is found to be consistent with that expected for a viscoelastic material. A numerical verification shows that the new contact law exhibits a good match to results obtained using the finite element method. The new contact law is applied to hopping simulations of an example rover on the asteroid (162173) Ryugu, which reveal that the rover is capable of large traverses, but has a low likelihood of inter-hemispheric traverses from the polar regions.