An energy landscape approach to locomotor transitions in complex 3D terrain

Significance Effective locomotion in nature happens by transitioning across multiple modes (e.g., walk, run, climb). Using laboratory experiments on a model system, we demonstrate that an energy landscape approach helps understand how multipathway transitions across locomotor modes in complex 3D terrain statistically emerge from physical interaction. Animals’ and robots’ locomotor modes are attracted to basins of a potential energy landscape. They can use kinetic energy fluctuation from oscillatory self-propulsion to cross potential energy barriers, escaping from one basin and reaching another to make locomotor transitions. Our first-principle energy landscape approach is the beginning of a statistical physics theory of locomotor transitions in complex terrain. It will help understand and predict how animals, and how robots should, move through the real world. Effective locomotion in nature happens by transitioning across multiple modes (e.g., walk, run, climb). Despite this, far more mechanistic understanding of terrestrial locomotion has been on how to generate and stabilize around near–steady-state movement in a single mode. We still know little about how locomotor transitions emerge from physical interaction with complex terrain. Consequently, robots largely rely on geometric maps to avoid obstacles, not traverse them. Recent studies revealed that locomotor transitions in complex three-dimensional (3D) terrain occur probabilistically via multiple pathways. Here, we show that an energy landscape approach elucidates the underlying physical principles. We discovered that locomotor transitions of animals and robots self-propelled through complex 3D terrain correspond to barrier-crossing transitions on a potential energy landscape. Locomotor modes are attracted to landscape basins separated by potential energy barriers. Kinetic energy fluctuation from oscillatory self-propulsion helps the system stochastically escape from one basin and reach another to make transitions. Escape is more likely toward lower barrier direction. These principles are surprisingly similar to those of near-equilibrium, microscopic systems. Analogous to free-energy landscapes for multipathway protein folding transitions, our energy landscape approach from first principles is the beginning of a statistical physics theory of multipathway locomotor transitions in complex terrain. This will not only help understand how the organization of animal behavior emerges from multiscale interactions between their neural and mechanical systems and the physical environment, but also guide robot design, control, and planning over the large, intractable locomotor-terrain parameter space to generate robust locomotor transitions through the real world.