Locomotor transitions in the potential energy landscape-dominated regime

Using Pose Estimation and 3D Rendered Models to Study Leg-Mediated Self-righting by Lanternflies

The ability to upright quickly and efficiently when overturned on the ground (terrestrial self-righting) is crucial for living organisms and robots. Previous studies have mapped the diverse behaviors used by various animals to self-right on different substrates, and proposed physical models to explain how body morphology can favor specific self-righting methods. However, to our knowledge, no studies have quantified and modeled all of an animal's limb motions during these complicated behaviors. Here, we studied terrestrial self-righting by immature invasive spotted lanternflies (Lycorma delicatula), an insect species that must frequently recover from being overturned after jumping and falling in its native habitat. These nymphs self-righted successfully in 92-100% of trials on three substrates with different friction and roughness, with no significant difference in the time or number of attempts required. They accomplished this using three stereotypic sequences of movements. To understand these motions, we combined 3D poses tracked on multi-view high-speed video with articulated 3D models created using photogrammetry and Blender rendering software. The results were used to calculate the mechanical properties (e.g., potential and kinetic energy, angular speed, stability margin, torque, force, etc.) of these insects during righting trials. We used an inverted physical pendulum model (a "template") to estimate the kinetic energy available in comparison to the increase in potential energy required to flip over. While these insects began righting using primarily quasistatic motions, they also used dynamic leg motions to achieve final tip-over. However, this template did not describe important features of the insect's center of mass trajectory and rotational dynamics, necessitating the use of an "anchor" model comprising the 3D rendered body model and six articulated two-segment legs to model the body's internal degrees of freedom and capture the role of the legs' contribution to inertial reorientation. This anchor elucidated the sequence of highly coordinated leg movements these insects used for propulsion, adhesion, and inertial reorientation during righting, and how they frequently pivot about a body contact point on the ground to flip upright. In the most frequently used method, diagonal rotation, these motions allowed nymphs to spin their bodies to upright with lower force with a greater stability margin compared to the other less frequently used methods. We provide a concise overview of necessary background on 3D orientation and rotational dynamics, and the resources required to apply these low-cost modeling methods to other problems in biomechanics.

Maneuverable and Efficient Locomotion of a Myriapod Robot with Variable Body-Axis Flexibility via Instability and Bifurcation

Legged robots have remarkable terrestrial mobility, but are susceptible to falling and leg malfunction during locomotion. The use of a large number of legs, as in centipedes, can overcome these problems, but it makes the body long and leads to many legs being constrained to contact with the ground to support the long body, which impedes maneuverability. A mechanism for maneuverable locomotion using a large number legs is thus desirable. However, controlling a long body with a large number of legs requires huge computational and energy costs. Inspired by agile locomotion in biological systems, this study proposes a control strategy for maneuverable and efficient locomotion of a myriapod robot based on dynamic instability. Specifically, our previous study made the body axis of a 12-legged robot flexible and showed that changing the body-axis flexibility produces pitchfork bifurcation. The bifurcation not only induces the dynamic instability of a straight walk but also a transition to a curved walk, whose curvature is controllable by the body-axis flexibility. This study incorporated a variable stiffness mechanism into the body axis and developed a simple control strategy based on the bifurcation characteristics. With this strategy, maneuverable and autonomous locomotion was achieved, as demonstrated by multiple robot experiments. Our approach does not directly control the movement of the body axis; instead, it controls body-axis flexibility, which significantly reduces computational and energy costs. This study provides a new design principle for maneuverable and efficient locomotion of myriapod robots.

The bumpy road ahead: the role of substrate roughness on animal walking and a proposed comparative metric

Outside laboratory conditions and human-made structures, animals rarely encounter flat surfaces. Instead, natural substrates are uneven surfaces with height variation that ranges from the microscopic scale to the macroscopic scale. For walking animals (which we define as encompassing any form of legged movement across the ground, such as walking, running, galloping, etc.), such substrate 'roughness' influences locomotion in a multitude of ways across scales, from roughness that influences how each toe or foot contacts the ground, to larger obstacles that animals must move over or navigate around. Historically, the unpredictability and variability of natural environments has limited the ability to collect data on animal walking biomechanics. However, recent technical advances, such as more sensitive and portable cameras, biologgers, laboratory tools to fabricate rough terrain, as well as the ability to efficiently store and analyze large variable datasets, have expanded the opportunity to study how animals move under naturalistic conditions. As more researchers endeavor to assess walking over rough terrain, we lack a consistent approach to quantifying roughness and contextualizing these findings. This Review summarizes existing literature that examines non-human animals walking on rough terrain and presents a metric for characterizing the relative substrate roughness compared with animal size. This framework can be applied across terrain and body scales, facilitating direct comparisons of walking over rough surfaces in animals ranging in size from ants to elephants.

A Step Forward: Functional Diversity and Emerging Themes of Slow-Speed Locomotion in Vertebrates

Walking can be defined broadly as a slow-speed movement produced when appendages interact with the ground to generate forward propulsion. Until recently, most studies of walking have focused on humans and a handful of domesticated vertebrates moving at a steady rate over highly simplified, static surfaces, which may bias our understanding of the unifying principles that underlie vertebrate locomotion. In the last few decades, studies have expanded to include a range of environmental contexts (e.g., uneven terrain, perturbations, deformable substrates) and greater phylogenetic breadth (e.g., non-domesticated species, small and/or ectothermic tetrapods and fishes); these studies have revealed that even a gait as superficially simple as walking is far more complex than previously thought. In addition, technological advances and accessibility of imaging systems and computational power have recently expanded our capabilities to test hypotheses about the locomotor movements of extant and extinct organisms in silico. In this symposium, scientists showcased diverse taxa (from extant fishes to extinct dinosaurs) moving through a range of variable conditions (speed perturbations, inclines, and deformable substrates) to address the causes and consequences of functional diversity in locomotor systems and discuss nascent research areas and techniques. From the symposium contributions, several themes emerged: (1) slow-speed, appendage-based movements in fishes are best described as walking-like movements rather than true walking gaits, (2) environmental variation (e.g., deformable substrates) and dynamic stimuli (e.g., perturbations) trigger kinematic and neuromuscular changes in animals that make defining a single gait or the transition between gaits more complicated than originally thought, and (3) computational advances have increased the ability to process large data sets, emulate the 3D motions of extant and extinct taxa, and even model species interactions in ancient ecosystems. Although this symposium allowed us to make great strides forward in our understanding of vertebrate walking, much ground remains to be covered. First, there is a much greater range of vertebrate appendage-based locomotor behaviors than has been previously recognized and existing terminology fails to accurately capture and describe this diversity. Second, despite recent efforts, the mechanisms that vertebrates use modify locomotor behaviors in response to predictable and unpredictable locomotor challenges are still poorly understood. Third, while computer-based models and simulations facilitate a greater understanding of the kinetics and kinematics of movement in both extant and extinct animals, a universal, one-size-fits-all, predictive model of appendage-based movement in vertebrates remains elusive.

A terrain treadmill to study animal locomotion through large obstacles

A challenge to understanding locomotion in complex 3-D terrain with large obstacles is to create tools for controlled, systematic experiments. Recent terrain arenas allow observations at small spatiotemporal scales (∼10 body length or cycles). Here, we create 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 atop. During sustained locomotion, a discoid cockroach moved through pillar obstacles for up to 25 minutes (2500 cycles) over 67 m (1500 body lengths). Over 12 trials totaling∼1 hour, 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 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 discovered that locomotor transitions in complex 3-D 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 to using a less strenuous roll mode rolling into and through the gaps, and this transition requires overcoming a potential energy barrier. 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 hind leg sprawl, and depressed one hind leg and elevated the other during the pitch-to-roll transition, 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, whereas leg sprawl reduction did so dramatically. 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.