Improved Terzaghi-theory-based interaction modeling of rotary robotic locomotors with granular substrates

When legged animals and robots move on granular substrates such as loose sand, their legs may sink below the terrain, rowing and paddling within the granular media. However, conventional leg-ground contact models such as elastic and elastoplastic models are unavailable to describe the rotary interaction of penetrated legs which is affected by the flowability of the particles. Therefore, an improved sliding theory was developed to predict ground reaction forces generated by robotic locomotors that rotate through granular media. The conventional sliding assumptions proposed by Terzaghi were developed to estimate the critical forces exerted on the retaining walls of building foundations, whose lateral size are sufficiently large that they are often assumed to be infinitely wide. An improvement to the width of a robotic leg, affected by both the properties of soil and the dimensions of the leg, was developed in the improved sliding model. The results demonstrate the high fidelity of the improved model in predicting interaction forces at a penetration phase during rotation, without considering the digging motion phase, with a goodness of fit larger than 90%.