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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 10 − 1  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. 

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. 

Numerous worm and arthropod species form physically-connected aggregations in which interactions among individuals give rise to emergent macroscale dynamics and functionalities that enhance collective survival. In particular, some aquatic worms such as the California blackworm ( Lumbriculus variegatus ) entangle their bodies into dense blobs to shield themselves against external stressors and preserve moisture in dry conditions. Motivated by recent experiments revealing emergent locomotion in blackworm blobs, we investigate the collective worm dynamics by modeling each worm as a self-propelled Brownian polymer. Though our model is two-dimensional, compared to real three-dimensional worm blobs, we demonstrate how a simulated blob can collectively traverse temperature gradients via the coupling between the active motion and the environment. By performing a systematic parameter sweep over the strength of attractive forces between worms, and the magnitude of their directed self-propulsion, we obtain a rich phase diagram which reveals that effective collective locomotion emerges as a result of finely balancing a tradeoff between these two parameters. Our model brings the physics of active filaments into a new meso- and macroscale context and invites further theoretical investigation into the collective behavior of long, slender, semi-flexible organisms. 

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. 

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 geneOryza sativahistidine kinase-1 (HK1) as well as the auxin influx carrier geneOsAUX1as 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. 

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.