Limbless organisms like snakes can navigate nearly all terrain. In particular, desert-dwelling sidewinder rattlesnakes (C. cerastes) operate effectively on inclined granular media (like sand dunes) that induce failure in field-tested limbless robots through slipping and pitching. Our laboratory experiments reveal that as granular incline angle increases, sidewinder rattlesnakes increase the length of their body in contact with the sand. Implementing this strategy in a physical robot model of the snake enables the device to ascend sandy slopes close to the angle of maximum slope stability. Plate drag experiments demonstrate that granular yield stresses decrease with increasing incline angle. Together these three approaches demonstrate how sidewinding 1 arXiv:1410.2945v1 [physics.bio-ph] 11 Oct 2014 with contact-length control mitigates failure on granular media.The majority of terrestrial mobile robots are restricted to laboratory environments, in part because such robots are designed to roll on hard flat surfaces. It is difficult to systematically improve such terrestrial robots because we lack understanding of the physics of interaction with complex natural substrates like sand, dirt and tree bark. We are thus limited in our ability to computationally explore designs for potential all-terrain vehicles; in contrast, many of the recent developments in aerial and aquatic vehicles have been enabled by sophisticated computationaldynamics tools that allow such systems to be designed in silico (1).Compared with human-made devices, organisms such as snakes, lizards, and insects move effectively in nearly all natural environments. In recent years, scientists and engineers have sought to systematically discover biological principles of movement and implement these in robots (2). This "bioinspired robotics" approach (3) has proved fruitful to design laboratory robots with new capabilities (new gaits, morphologies, control schemes) including rapid running (2, 4), slithering (5), flying (6), and swimming in sand (7). Fewer studies have transferred biological principles into robust field-ready devices (4, 8) capable of operating in, and interacting with, natural terrain.Limbless locomotors like snakes are excellent systems to study to advance real-world allterrain mobility. Snakes are masters of most terrains: they can move rapidly on land (9, 10) and through water (11), burrow and swim through sand and soil (12), slither through tiny spaces (13), climb complex surfaces (14), and even glide through the air (15). Relative to legged locomotion, limbless locomotion is less studied, and thus broad principles which govern multi-environment movement are lacking. Recently developed limbless robotic platforms (5), based generally on the snake body plan, are appealing for multi-functional robotics study because they are also capable of a variety of modes of locomotion. These robots can traverse confined spaces, climb trees and pipes, and potentially dive through loose material. However, 2 the gaits that carry these robots across fir...

Discovery of fundamental principles which govern and limit effective locomotion (self-propulsion) is of intellectual interest and practical importance. Human technology has created robotic moving systems that excel in movement on and within environments of societal interest: paved roads, open air and water. However, such devices cannot yet robustly and efficiently navigate (as animals do) the enormous diversity of natural environments which might be of future interest for autonomous robots; examples include vertical surfaces like trees and cliffs, heterogeneous ground like desert rubble and brush, turbulent flows found near seashores, and deformable/flowable substrates like sand, mud and soil. In this review we argue for the creation of a physics of moving systems-a 'locomotion robophysics'-which we define as the pursuit of principles of self-generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement the study of complex robots in complex situations with systematic study of simplified robotic devices in controlled laboratory settings and in simplified theoretical models. We must thus use the methods of physics to examine both locomotor successes and failures using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and others' research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that have begun to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

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The locomotion of articulated mechanical systems is often complex and unintuitive, even when considered with the aid of reduction principles from geometric mechanics. In this paper, we present two tools for gaining insights into the underlying principles of locomotion: connection vector fields and connection height functions . Connection vector fields illustrate the geometric structure of the relationship between internal shape changes and the system body velocities they produce. Connection height functions measure the curvature of their respective vector fields and capture the net displacement over any cyclic shape change, or gait , allowing for the intuitive selection of gaits to produce desired displacements. Height function approaches have been previously attempted, but such techniques have been severely limited by their basis in a rotating body frame, and have only been useful for calculating planar rotations and infinitesimal translations. We circumvent this limitation by introducing a notion of optimal coordinates defining a body frame that rotates very little in response to shape changes, while still meeting the requirements of the geometric mechanics theory on which the vector fields and height functions are based. In these optimal coordinates, the height functions provide close approximations of the net displacement resulting from a broad selection of possible gaits.