STATEMENTComparative study of cockroach self-righting reveals performance advantages of using rotational kinetic energy to overcome potential energy barrier and rolling more to lower it, while maintaining diverse strategies. ABSTRACTTerrestrial animals often must self-right from an upside-down orientation on the ground to survive. Here, we compared self-righting strategies of the Madagascar hissing, American, and discoid cockroaches on a challenging flat, rigid, low-friction surface to quantify the mechanical principles. All three species almost always self-righted (97% probability) when given time (30 seconds), frequently self-righted (63%) on the first attempt, and on that attempt did so in one second or less. When successful, two of the three species gained and used pitch and/or roll rotational kinetic energy to overcome potential energy barriers (American 63% of all attempts and discoid 78%). By contrast, the largest, heaviest, wingless cockroach (Madagascar hissing) relied far less on the energy of motion and was the slowest to self-right. Two of the three species used rolling strategies to overcome low potential energy barriers. Successful righting attempts had greater rolling rotation than failed attempts as the center of mass rose to the highest position. Madagascar hissing cockroaches rolled using body deformation (98% of all trials) and the American cockroach relied on leg forces (93%). By contrast, the discoid cockroach overcame higher and a wider range of potential energy barriers with simultaneous pitching and rolling using wings (46% of all trials) and legs (49%) equally to self-right. Our quantification revealed the performance advantages of using Journal of Experimental Biology (2019), 222, jeb186080; https://li.me.jhu.edu 2 rotational kinetic energy to overcome the potential energy barrier and rolling more to lower it, while maintaining diverse strategies for ground-based self-righting.

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.

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.

STATEMENTGeneralist snakes divide their body into sections, each using distinct movement patterns, to get over large step-like obstacles. Such body partitioning may be generally useful for diverse, complex 3-D terrain. ABSTRACTMany snakes live in deserts, forests, and river valleys and traverse challenging 3-D terrain like rocks, felled trees, and rubble, with obstacles as large as themselves and variable surface properties. By contrast, apart from branch cantilevering, burrowing, swimming, and gliding, laboratory studies of snake locomotion focused on that on simple flat surfaces. Here, to begin to understand snake locomotion in complex 3-D terrain, we study how the variable kingsnake, a terrestrial generalist, traversed a large step of variable surface friction and step height (up to 30% snout-vent length). The snake traversed by partitioning its body into three sections with distinct functions. Body sections below and above the step oscillated laterally on horizontal surfaces for propulsion, while the body section in between cantilevered in a vertical plane to bridge the large height increase. As the animal progressed, these three sections traveled down its body, †

Small animals and robots must often rapidly traverse large bump-like obstacles when moving through complex 3D terrains, during which, in addition to leg-ground contact, their body inevitably comes into physical contact with the obstacles. However, we know little about the performance limits of large bump traversal and how body-terrain interaction affects traversal. To address these, we challenged the discoid cockroach and an open-loop six-legged robot to dynamically run into a large bump of varying height to discover the maximal traversal performance, and studied how locomotor modes and traversal performance are affected by body-terrain interaction. Remarkably, during rapid running, both the animal and the robot were capable of dynamically traversing a bump much higher than its hip height (up to 4 times the hip height for the animal and 3 times for the robot, respectively) at traversal speeds typical of running, with decreasing traversal probability with increasing bump height. A stability analysis using a novel locomotion energy landscape model explained why traversal was more likely when the animal or robot approached the bump with a low initial body yaw and a high initial body pitch, and why deflection was more likely otherwise. Inspired by these principles, we demonstrated a novel control strategy of active body pitching that increased the robot's maximal traversable bump height by 75%. Our study is a major step in establishing the framework of locomotion energy landscapes to understand locomotion in complex 3D terrains.