A hybrid force model to estimate the dynamics of curved legs in granular material

Robot locomotion on rigid terrain or in fluids has been studied to a large extent. The locomotion dynamics on or within soft substrates such as granular material (GM) has not been fully investigated. This paper proposes a hybrid force model to simulate and evaluate the locomotion performance of a legged terrestrial robot in GM. The model incorporates an improved Resistive Force Theory (RFT) model and a failure-based model. The improved RFT model integrates the force components of individual leg elements over the curved leg portion submerged in GM at any moment during a full period of leg rotation. The failure-based model is applied in a bar drag model to yield the normal and the lateral forces of the individual RFT elements as functions of the locomotion depth and speed. The hybrid model is verified by the coincidence between the theoretical predictions and the experimental results. The hybrid model is used to analyze the effects of angular velocity and leg shape with high precision and can guide the design of the legs with any profiles. Our study reveals that the interactions between locomotor and substrate are determined by the locomotor structural characteristics, the nature of the substrate, and the control strategy.