  Legged robots are well-suited for broad exploration tasks in complex
environments with yielding terrain. Understanding robotic foot-terrain
interactions is critical for safe locomotion and walking efficiency for legged
robots. This paper presents a reduced-order resistive-force model for
robotic-foot/mud interactions. We focus on vertical robot locomotion on mud and
propose a visco-elasto-plastic analog to model the foot/mud interaction forces.
Dynamic behaviors such as mud visco-elasticity, withdrawing cohesive suction,
and yielding are explicitly discussed with the proposed model. Besides
comparing with dry/wet granular materials, mud intrusion experiments are
conducted to validate the force model. The dependency of the model parameter on
water content and foot velocity is also studied to reveal in-depth model
properties under various conditions. The proposed force model potentially
provides an enabling tool for legged robot locomotion and control on muddy
terrain.
