Interaction Modeling and Dynamic Control Strategy for C-Shaped Leg with Sandy Terrain in Terradynamics

High trafficability and robustness on terrain surfaces composed of granular substrates can be obtained through configurations of C-shaped legs. Recently, C-shaped configuration has been widely used in the locomotion mechanism design of the legged mobile robots on harsh grounds, especially for sandy terrains. In case of rotational gait, based on the stress-macro deformation relationship according to the Resistive Force Theory (RFT) in terradynamics, an interaction model between a C-shaped leg and the sandy terrain is established in this paper. Considering the influence of velocity field of C- leg particle systems on Fourier linear coefficient in fitting precondition, the inversion characters of mechanical parameters through integral derivation and linearized expression of the model are established. Then, the experimental data samples are employed to identify the mechanical parameters of the sandy terrain, followed by checking its validity through setting a limit for the tolerance between predicted results and experimental data. Furthermore, mechanical behaviors under swing gaits are analyzed, for which some basic dynamic control strategies are suggested in this study. In this work, the outputs of driving torque within the range of a feasible region experienced at the joint are explored. It is concluded that the mechanical properties dominated by the sandy terrain and leg geometry can be revealed by the identified parameters, some driving outputs can be evaluated through interaction models in terradynamics.