To traverse complex three-dimensional terrain with large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize near-steady-state, single-mode locomotion (e.g. walk, run). We know little about how to use physical interaction to make robust locomotor transitions. Here, we review our progress towards filling this gap by discovering terradynamic principles of multi-legged locomotor transitions, using simplified model systems representing distinct challenges in complex three-dimensional terrain. Remarkably, general physical principles emerge across diverse model systems, by modelling locomotor–terrain interaction using a potential energy landscape approach. The animal and robots' stereotyped locomotor modes are constrained by physical interaction. Locomotor transitions are stochastic, destabilizing, barrier-crossing transitions on the landscape. They can be induced by feed-forward self-propulsion and are facilitated by feedback-controlled active adjustment. General physical principles and strategies from our systematic studies already advanced robot performance in simple model systems. Efforts remain to better understand the intelligence aspect of locomotor transitions and how to compose larger-scale potential energy landscapes of complex three-dimensional terrains from simple landscapes of abstracted challenges. This will elucidate how the neuromechanical control system mediates physical interaction to generate multi-pathway locomotor transitions and lead to advancements in biology, physics, robotics and dynamical systems theory.

Randomness is common in biological and artificial systems, resulting either from stochasticity of the environment or noise in organisms or devices themselves. In locomotor control, randomness is typically considered a nuisance. For example, during dynamic walking, randomness in stochastic terrain leads to metastable dynamics, which must be mitigated to stabilize the system around limit cycles. Here, we studied whether randomness in motion is beneficial for strenuous locomotor tasks. Our study used robotic simulation modeling of strenuous, leg-assisted, winged ground self-righting observed in cockroaches, in which unusually large randomness in wing and leg motions is present. We developed a simplified simulation robot capable of generating similar self-righting behavior and varied the randomness level in wing-leg coordination. During each wing opening attempt, the more randomness added to the time delay between wing opening and leg swinging, the more likely it was for the naive robot (which did not know what coordination is best) to self-right within a finite time. Wing-leg coordination, measured by the phase between wing and leg oscillations, had a crucial impact on self-righting outcome. Without randomness, periodic wing and leg oscillations often limited the system to visit a few bad phases, leading to failure to escape from the metastable state. With randomness, the system explored phases thoroughly and had a better chance of encountering good phases to self-right. Our study complements previous work by demonstrating that randomness helps destabilize locomotor systems from being trapped in undesired metastable states, a situation common in strenuous locomotion.

Animals and robots must right themselves after flipping over on the ground. The discoid cockroach pushes its wings against the ground in an attempt to dynamically self-right by a somersault. However, because this maneuver is strenuous, the animal often fails to overcome the potential energy barrier and makes continual attempts. In this process, the animal flails its legs, whose lateral perturbation eventually leads it to roll to the side to self-right. Our previous work developed a cockroachinspired robot capable of leg-assisted, winged self-righting, and a robot simulation study revealed that the outcome of this strategy depends sensitively on wing-leg coordination (measured by the phase between their motions). Here, we further elucidate why this is the case by developing a template to model the complex hybrid dynamics resulting from discontinuous contact and actuation. We used the template to calculate the potential energy barrier that the body must overcome to self-right, mechanical energy contribution by wing pushing and leg flailing, and mechanical energy dissipation due to wing-ground collision. The template revealed that wing-leg coordination (phase) strongly affects self-righting outcome by changing mechanical energy budget. Well-coordinated appendage motions (good phase) accumulate more mechanical energy than poorlycoordinated motions (bad phase), thereby better overcoming the potential energy barrier to self-right more successfully. Finally, we demonstrated practical use of the template for predicting a new control strategy to further increase self-righting performance and informing robot design.

Terrestrial animals must self-right when overturned on the ground. To do so, the discoid cockroach often pushes its wings against the ground to begin a somersault but rarely succeeds in completing it. As it repeatedly attempts this, it probabilistically rolls to the side to self-right. Here, we studied whether seemingly wasteful leg flailing in this process helps. Adding mass to increase hind leg flailing kinetic energy fluctuation increased the animal's self-righting probability. We then developed a robot with similar, strenuous self-righting behavior and used it as a physical model for systematic experiments. As legs flailed more vigorously and wings opened more, self-righting became more probable. A potential energy landscape model revealed that, although wing opening did not generate sufficient kinetic energy to overcome the high pitch potential energy barrier, it reduced barriers for rolling, facilitating the small kinetic energy fluctuation from leg flailing to probabilistically overcome roll barriers to self-right.

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