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

Abstract

<jats:p>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.</jats:p>

Propelling and perturbing appendages together facilitate strenuous ground self-righting

“…It was recently suggested that there is an "energy landscape-dominated" regime of locomotion (Othayoth et al, 2020)-when there are large potential energy barriers comparable to or exceeding kinetic energy and/or mechanical work generated by each propulsive cycle or motion, an energy landscape approach is useful for understanding probabilistic locomotor transitions. Our findings supported this notion and expanded the range of this regime of from locomotor transitions in complex 3-D terrain to strenuous self-righting transitions.…”

“…We note that, unlike the simplistic, rigid body model for calculating potential energy barriers in the previous study (Li et al, 2019), our potential energy landscape takes into account how wing opening affects potential energy and thus barriers. Our energy landscape modeling analysis is also different from that in complex 3-D terrain (Othayoth et al, 2020) because here two types of appendages work together to generate locomotor transitions. Because wing opening (primary propulsion) and leg flailing (secondary perturbation) induce different levels of kinetic energy and face different levels of potential energy barriers, their effects must be considered separately to understand the physical mechanism (see discussion of new insight this offers).…”

“…Finally, we modeled the self-righting transition from the pitch to the roll mode as a probabilistic barrier-crossing transition on a potential energy landscape facilitated by kinetic energy fluctuation. Such an energy landscape approach was recently demonstrated to be useful in understanding locomotor transitions in complex 3-D terrain (Othayoth et al, 2020), but it was not clear whether it applies to strenuous self-righting transitions. To test this, we used the potential energy landscape to quantify the potential energy barrier that must be overcome to transition from the pitch to the roll mode, and we evaluated whether it is comparable to kinetic energy fluctuation from leg flailing.…”

Randomness in appendage coordination facilitates strenuous ground self-righting

“…Bioinspiration & Biomimetics (2020), 10.1088/1748-3190/abac47; https://li.me.jhu.edu/ 25 with large obstacles, animals and robots must often dynamically transition across distinct locomotor modes (Li et al, 2015;Othayoth et al, 2020). Our group's recent work demonstrated that, in different modes, their states are strongly attracted to different basins of an underlying potential energy landscape Han et al, 2017;Othayoth et al, 2020). Our study suggested that body and appendage coordination is crucial for quickly escaping from these attractive landscape basins and having large randomness in coordination is beneficial.…”

“…We speculate that randomness in coordination could also improve the performance of robots in other strenuous locomotor tasks. When robots are trapped in undesirable metastable states, such as in complex terrain Li et al, 2015;Othayoth et al, 2020), their normal gait (walking, running, etc.) may no longer work.…”