Modeling Quadruped Leg Dynamics on Deformable Terrains using Data-driven Koopman Operators. Issue 37 (2022) - Krolicki, Alexander
Abstract: Quadruped locomotion over soft deformable terrain is a challenging problem. It is difficult to accurately model the nonlinear dynamics associated with the terrain-leg interaction during the stance phase of the gait motion. In order to overcome this challenge, we utilize Koopman spectral theory to obtain a linear dynamical system in the space of observable functions. We propose an experimental framework to obtain a data-driven Koopman model of the quadruped's leg dynamics over deformable terrains as a switched dynamical system. Experimental results show that the learned switched system model can be used to predict gait trajectories on unknown terrain. Furthermore, we exploit the linearity of the Koopman operator to extract the complex leg-terrain interaction dynamics. Finally, we show that the Koopman generator has a unique spectrum associated with each terrain, making terrain classification possible without the need for foot force sensors.