A terrain treadmill to study animal locomotion through large obstacles.

A challenge to understanding locomotion in complex three-dimensional terrain with large obstacles is to create tools for controlled, systematic experiments. Recent terrain arenas allow observations at small spatiotemporal scales (∼10 body lengths or cycles). Here, we created a terrain treadmill to enable high-resolution observation of animal locomotion through large obstacles over large spatiotemporal scales. An animal moves through modular obstacles on an inner sphere, while a rigidly attached, concentric, transparent outer sphere rotates with the opposite velocity via closed-loop feedback to keep the animal on top. During sustained locomotion, a discoid cockroach moved through pillar obstacles for up to 25 min (2500 cycles) over 67 m (1500 body lengths). Over 12 trials totaling ∼1 h, the animal was maintained within a radius of 1 body length (4.5 cm) on top of the sphere 90% of the time. The high-resolution observation enables the study of diverse locomotor behaviors and quantification of animal-obstacle interaction.

Cockroaches adjust body and appendages to traverse cluttered large obstacles.

To traverse complex terrain, animals often transition between locomotor modes. It is well known that locomotor transitions can be induced by switching in neural control circuits or driven by a need to minimize metabolic energetic cost. Recent work revealed that locomotor transitions in complex 3D terrain cluttered with large obstacles can emerge from physical interaction with the environment controlled by the nervous system. For example, to traverse cluttered, stiff grass-like beams, the discoid cockroach often transitions from using a strenuous pitch mode pushing across the beams to using a less strenuous roll mode rolling into and through the gaps. This transition can save mechanical energetic cost substantially (∼100-101 mJ) but requires overcoming a potential energy barrier (∼10-3-10-2 mJ). Previous robotic physical modeling demonstrated that kinetic energy fluctuation of body oscillation from self-propulsion can help overcome the barrier and facilitate this transition. However, the animal was observed to transition even when the barrier still exceeded kinetic energy fluctuation. Here, we further studied whether and how the cockroach makes active adjustments to facilitate this transition to traverse cluttered beams. The animal repeatedly flexed its head and abdomen, reduced hindleg sprawl, and depressed one hindleg and elevated the other during the pitch-to-roll transition, adjustments which were absent when running on a flat ground. Using a refined potential energy landscape with additional degrees of freedom to model these adjustments, we found that head flexion did not substantially reduce the transition barrier (by ∼10-3 mJ), whereas leg sprawl reduction did so dramatically (by ∼10-2 mJ). We speculate that head flexion is for sensing the terrain to guide the transition via sensory feedback control.

Propelling and perturbing appendages together facilitate strenuous ground self-righting.

Terrestrial animals must self-right when overturned on the ground, but this locomotor task is strenuous. To do so, the discoid cockroach often pushes its wings against the ground to begin a somersault which rarely succeeds. As it repeatedly attempts this, the animal probabilistically rolls to the side to self-right. During winged self-righting, the animal flails its legs vigorously. Here, we studied whether wing opening and leg flailing together facilitate strenuous ground self-righting. Adding mass to increase hind leg flailing kinetic energy 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. The robot's self-righting probability increased with wing opening and leg flailing amplitudes. A potential energy landscape model revealed that, although wing opening did not generate sufficient kinetic energy to overcome the high pitch potential energy barrier to somersault, it reduced the barrier for rolling, facilitating the small kinetic energy from leg flailing to probabilistically overcome it to self-right. The model also revealed that the stereotyped body motion during self-righting emerged from physical interaction of the body and appendages with the ground. Our work demonstrated the usefulness of potential energy landscape for modeling self-righting transitions.

Locomotor transitions in the potential energy landscape-dominated regime.

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.

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

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.

Dynamic traversal of large gaps by insects and legged robots reveals a template.

It is well known that animals can use neural and sensory feedback via vision, tactile sensing, and echolocation to negotiate obstacles. Similarly, most robots use deliberate or reactive planning to avoid obstacles, which relies on prior knowledge or high-fidelity sensing of the environment. However, during dynamic locomotion in complex, novel, 3D terrains, such as a forest floor and building rubble, sensing and planning suffer bandwidth limitation and large noise and are sometimes even impossible. Here, we study rapid locomotion over a large gap-a simple, ubiquitous obstacle-to begin to discover the general principles of the dynamic traversal of large 3D obstacles. We challenged the discoid cockroach and an open-loop six-legged robot to traverse a large gap of varying length. Both the animal and the robot could dynamically traverse a gap as large as one body length by bridging the gap with its head, but traversal probability decreased with gap length. Based on these observations, we developed a template that accurately captured body dynamics and quantitatively predicted traversal performance. Our template revealed that a high approach speed, initial body pitch, and initial body pitch angular velocity facilitated dynamic traversal, and successfully predicted a new strategy for using body pitch control that increased the robot's maximal traversal gap length by 50%. Our study established the first template of dynamic locomotion beyond planar surfaces, and is an important step in expanding terradynamics into complex 3D terrains.