Towards Langevin equations of locomotor-obstacle interaction dynamics

In complex 3-D terrain like forest floor and earthquake rubble, animals and robots often physically interact with cluttered large obstacles to traverse them. Our previous studies established a potential energy landscape approach to modeling this problem. An animal or robot's self-propelled interaction with obstacles results in a potential energy landscape. The gradients of this potential energy landscape, which are conservative forces and torques, dominate the obstacle contact forces and torques, which also include non-conservative components. Here, we take the next step by extending our model to describe the system's stochastic dynamics. We developed a dynamic simulation of our established robophysical model traversing grass-like beam obstacles. We validated the simulation in two scenarios. First, we matched the simulated obstacle contact forces against experimental measurements during forward propulsion with prescribed body posture and without noise. Second, we matched the simulated obstacle traversal probability against measurements during forward propulsion with free body rotations and noise. For the second scenario, we will approximate the non-conservative forces from the simulation with simple force models, and we will test how well a Langevin equation with the potential energy landscape and these non-conservative force terms can predict the system's stochastic dynamics. Our work will help establish a statistical physics framework for self-propelled obstacle traversal.