A potential energy landscape based dynamic model of locomotion in complex 3-D terrain

It is challenging to model locomotion in complex terrain. Recently, our lab successfully used a quasi-static potential energy landscape approach (Othayoth, Thoms, Li, 2020, PNAS) to model locomotor transitions in complex 3-D terrain. To add dynamics, here we developed an energy landscape based dynamic model and tested it using an ellipsoid body traversing beam obstacle. The model simplifies traversal as a self-propelled particle moving on a potential energy landscape in 3-D position and 3-D orientation space, whose dynamics follows a Langevin equation. The model contains conservative forces (weight and elastic forces) described by the potential energy landscape, plus propulsive forces, viscous forces, and random forces, which model self-propulsion, damping, and stochasticity, respectively. Because it is challenging to calculate torques of conservative forces from energy landscape gradient using Euler angles, we used virtual rotation to calculate them. Although our dynamic model neglected collisional dynamics and used simple non-conservative forces, it well simulated locomotion in complex terrain and matched experimental observations. Our model is useful not only for understanding dynamic locomotor transitions but also for robot control during locomotion in complex 3-D terrain.