The effect of tail stiffness on a sprawling quadruped locomotion.

A distinctive feature of quadrupeds that is integral to their locomotion is the tail. Tails serve many purposes in biological systems, including propulsion, counterbalance, and stabilization while walking, running, climbing, or jumping. Similarly, tails in legged robots may augment the stability and maneuverability of legged robots by providing an additional point of contact with the ground. However, in the field of terrestrial bio-inspired legged robotics, the tail is often ignored because of the difficulties in design and control. In this study, we test the hypothesis that a variable stiffness robotic tail can improve the performance of a sprawling quadruped robot by enhancing its stability and maneuverability in various environments. In order to validate our hypothesis, we integrated a cable-driven, flexible tail with multiple segments into the underactuated sprawling quadruped robot, where a single servo motor working alongside a reel and cable mechanism regulates the tail's stiffness. Our results demonstrated that by controlling the stiffness of the tail, the stability of locomotion on rough terrain and the climbing ability of the robot are improved compared to the movement with a rigid tail and no tail. Our findings highlight that constant ground support provided by the flexible tail is key to maintaining stable locomotion. This ensured a predictable gait cycle, eliminating unexpected turning and slipping, resulting in an increase in locomotion speed and efficiency. Additionally, we observed the robot's enhanced climbing ability on surfaces inclined up to 20°. The flexibility of the tail enabled the robot to overcome obstacles without external sensing, exhibiting significant adaptability across various terrains.

Robotic swimming in curved space via geometric phase.

Locomotion by shape changes or gas expulsion is assumed to require environmental interaction, due to conservation of momentum. However, as first noted in [J. Wisdom, Science 299, 1865-1869 (2003)] and later in [E. Guéron, Sci. Am. 301, 38-45 (2009)] and [J. Avron, O. Kenneth, New J. Phys, 8, 68 (2006)], the noncommutativity of translations permits translation without momentum exchange in either gravitationally curved spacetime or the curved surfaces encountered by locomotors in real-world environments. To realize this idea which remained unvalidated in experiments for almost 20 y, we show that a precision robophysical apparatus consisting of motors driven on curved tracks (and thereby confined to a spherical surface without a solid substrate) can self-propel without environmental momentum exchange. It produces shape changes comparable to the environment's inverse curvatures and generates movement of [Formula: see text] cm per gait. While this simple geometric effect predominates over short time, eventually the dissipative (frictional) and conservative forces, ubiquitous in real systems, couple to it to generate an emergent dynamics in which the swimming motion produces a force that is counter-balanced against residual gravitational forces. In this way, the robot both swims forward without momentum and becomes fixed in place with a finite momentum that can be released by ceasing the swimming motion. We envision that our work will be of use in a broad variety of contexts, such as active matter in curved space and robots navigating real-world environments with curved surfaces.

Field-mediated locomotor dynamics on highly deformable surfaces.

Studies of active matter-systems consisting of individuals or ensembles of internally driven and damped locomotors-are of interest to physicists studying nonequilibrium dynamics, biologists interested in individuals and swarm locomotion, and engineers designing robot controllers. While principles governing active systems on hard ground or within fluids are well studied, another class of systems exists at deformable interfaces. Such environments can display mixes of fluid-like and elastic features, leading to locomotor dynamics that are strongly influenced by the geometry of the surface, which, in itself, can be a dynamical entity. To gain insight into principles by which locomotors are influenced via a deformation field alone (and can influence other locomotors), we study robot locomotion on an elastic membrane, which we propose as a model of active systems on highly deformable interfaces. As our active agent, we use a differential driven wheeled robotic vehicle which drives straight on flat homogeneous surfaces, but reorients in response to environmental curvature. We monitor the curvature field-mediated dynamics of a single vehicle interacting with a fixed deformation as well as multiple vehicles interacting with each other via local deformations. Single vehicles display precessing orbits in centrally deformed environments, while multiple vehicles influence each other by local deformation fields. The active nature of the system facilitates a differential geometry-inspired mathematical mapping from the vehicle dynamics to those of test particles in a fictitious "spacetime," allowing further understanding of the dynamics and how to control agent interactions to facilitate or avoid multivehicle membrane-induced cohesion.

Lateral bending and buckling aids biological and robotic earthworm anchoring and locomotion.

Earthworms (Lumbricus terrestris) are characterized by soft, highly flexible and extensible bodies, and are capable of locomoting in most terrestrial environments. Previous studies of earthworm movement focused on the use of retrograde peristaltic gaits in which controlled contraction of longitudinal and circular muscles results in waves of shortening/thickening and thinning/lengthening of the hydrostatic skeleton. These waves can propel the animal across ground as well as into soil. However, worms benefit from axial body bends during locomotion. Such lateral bending and buckling dynamics can aid locomotor function via hooking/anchoring (to provide propulsion), modify travel orientation (to avoid obstacles and generate turns) and even generate snake-like undulatory locomotion in environments where peristaltic locomotion results in poor performance. To the best of our knowledge, lateral bending and buckling of an earthworm's body has not yet been systematically investigated. In this study, we observed that within confined environments, worms use lateral bending and buckling to anchor their body to the walls of their burrows and tip (anterior end) bending to search the environment. This locomotion strategy improved the performance of our soft-bodied robophysical model of the earthworm both in a confined (in an acrylic tube) and above-ground heterogeneous environment (rigid pegs), where present peristaltic robots are relatively limited in terradynamic capabilities. In summary, lateral bending and buckling facilitates the mobility of earthworm locomotion in diverse terrain and can play an important role in the creation of low cost soft robotic devices capable of traversing a variety of environments.

Self-reconfigurable multilegged robot swarms collectively accomplish challenging terradynamic tasks.

Swarms of ground-based robots are presently limited to relatively simple environments, which we attribute in part to the lack of locomotor capabilities needed to traverse complex terrain. To advance the field of terradynamically capable swarming robotics, inspired by the capabilities of multilegged organisms, we hypothesize that legged robots consisting of reversibly chainable modular units with appropriate passive perturbation management mechanisms can perform diverse tasks in variable terrain without complex control and sensing. Here, we report a reconfigurable swarm of identical low-cost quadruped robots (with directionally flexible legs and tail) that can be linked on demand and autonomously. When tasks become terradynamically challenging for individuals to perform alone, the individuals suffer performance degradation. A systematic study of performance of linked units leads to new discoveries of the emergent obstacle navigation capabilities of multilegged robots. We also demonstrate the swarm capabilities through multirobot object transport. In summary, we argue that improvement capabilities of terrestrial swarms of robots can be achieved via the judicious interaction of relatively simple units.

Controlling subterranean forces enables a fast, steerable, burrowing soft robot.

Robotic navigation on land, through air, and in water is well researched; numerous robots have successfully demonstrated motion in these environments. However, one frontier for robotic locomotion remains largely unexplored-below ground. Subterranean navigation is simply hard to do, in part because the interaction forces of underground motion are higher than in air or water by orders of magnitude and because we lack for these interactions a robust fundamental physics understanding. We present and test three hypotheses, derived from biological observation and the physics of granular intrusion, and use the results to inform the design of our burrowing robot. These results reveal that (i) tip extension reduces total drag by an amount equal to the skin drag of the body, (ii) granular aeration via tip-based airflow reduces drag with a nonlinear dependence on depth and flow angle, and (iii) variation of the angle of the tip-based flow has a nonmonotonic effect on lift in granular media. Informed by these results, we realize a steerable, root-like soft robot that controls subterranean lift and drag forces to burrow faster than previous approaches by over an order of magnitude and does so through real sand. We also demonstrate that the robot can modulate its pullout force by an order of magnitude and control its direction of motion in both the horizontal and vertical planes to navigate around subterranean obstacles. Our results advance the understanding and capabilities of robotic subterranean locomotion.

Mechanism and function of root circumnutation.

Early root growth is critical for plant establishment and survival. We have identified a molecular pathway required for helical root tip movement known as circumnutation. Here, we report a multiscale investigation of the regulation and function of this phenomenon. We identify key cell signaling events comprising interaction of the ethylene, cytokinin, and auxin hormone signaling pathways. We identify the gene Oryza sativa histidine kinase-1 (HK1) as well as the auxin influx carrier gene OsAUX1 as essential regulators of this process in rice. Robophysical modeling and growth challenge experiments indicate circumnutation is critical for seedling establishment in rocky soil, consistent with the long-standing hypothesis that root circumnutation facilitates growth past obstacles. Thus, the integration of robotics, physics, and biology has elucidated the functional importance of root circumnutation and uncovered the molecular mechanisms underlying its regulation.

Collective dynamics in entangled worm and robot blobs.

Living systems at all scales aggregate in large numbers for a variety of functions including mating, predation, and survival. The majority of such systems consist of unconnected individuals that collectively flock, school, or swarm. However, some aggregations involve physically entangled individuals, which can confer emergent mechanofunctional material properties to the collective. Here, we study in laboratory experiments and rationalize in theoretical and robophysical models the dynamics of physically entangled and motile self-assemblies of 1-cm-long California blackworms (Lumbriculus variegatus, Annelida: Clitellata: Lumbriculidae). Thousands of individual worms form braids with their long, slender, and flexible bodies to make a three-dimensional, soft, and shape-shifting "blob." The blob behaves as a living material capable of mitigating damage and assault from environmental stresses through dynamic shape transformations, including minimizing surface area for survival against desiccation and enabling transport (negative thermotaxis) from hazardous environments (like heat). We specifically focus on the locomotion of the blob to understand how an amorphous entangled ball of worms can break symmetry to move across a substrate. We hypothesize that the collective blob displays rudimentary differentiation of function across itself, which when combined with entanglement dynamics facilitates directed persistent blob locomotion. To test this, we develop a robophysical model of the worm blobs, which displays emergent locomotion in the collective without sophisticated control or programming of any individual robot. The emergent dynamics of the living functional blob and robophysical model can inform the design of additional classes of adaptive mechanofunctional living materials and emergent robotics.

Stretchable Nanocomposite Sensors, Nanomembrane Interconnectors, and Wireless Electronics toward Feedback-Loop Control of a Soft Earthworm Robot.

Sensors that can detect external stimuli and perceive the surrounding areas could offer an ability for soft biomimetic robots to use the sensory feedback for closed-loop control of locomotion. Although various types of biomimetic robots have been developed, few systems have included integrated stretchable sensors and interconnectors with miniaturized electronics. Here, we introduce a soft, stretchable nanocomposite system with built-in wireless electronics with an aim for feedback-loop motion control of a robotic earthworm. The nanostructured strain sensor, based on a carbon nanomaterial and a low-modulus silicone elastomer, allows for seamless integration with the body of the soft robot that can accommodate large strains caused by bending, stretching, and physical interactions with obstacles. A scalable, cost-effective, and screen-printing method manufactures an array of the strain sensors that are conductive and stretchable over 100% with a gauge factor over 38. An array of nanomembrane interconnectors enables a reliable connection between soft sensors and wireless electronics while tolerating the robot's multimodal movements. A set of computational and experimental studies of soft materials, stretchable mechanics, and hybrid packaging provides the key design factors for a reliable, nanocomposite sensor system. The miniaturized wireless circuit, embedded in the robot joint, offers real-time monitoring of strain changes during the motions of a robotic segment. Collectively, the soft sensor system presented in this work shows great potential to be integrated with other flexible, stretchable electronics for applications in soft robotics, wearable devices, and human-machine interfaces.