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.

To discover principles of flipper-based terrestrial locomotion we study the mechanics of a hatchling sea turtle-inspired robot, FlipperBot (FBot), during quasi-static movement on granular media. FBot implements a symmetric gait using two servo-motor-driven front limbs with flat-plate flippers and either freely rotating or fixed wrist joints. For a range of gaits, FBot moves with a constant step length. However, for gaits with sufficiently shallow flipper penetration or sufficiently large stroke, per step displacement decreases with each successive step resulting in failure (zero forward displacement) within a few steps. For the fixed wrist, failure occurs when FBot interacts with ground disturbed during previous steps, and measurements reveal that flipper generated forces decrease as per step displacement decreases. The biologically inspired free wrist is less prone to failure, but slip-induced failure can still occur if FBot pitches forward and drives its leading edge into the substrate. In the constant step length regime, kinematic and force-based models accurately predict FBot's motion for free and fixed wrist configurations, respectively. When combined with independent force measurements, models and experiments provide insight into how disturbed ground leads to locomotory failure and help explain differences in hatchling sea turtle performance.

Biological terrestrial locomotion occurs on substrate materials with a range of rheological behaviour, which can affect limb-ground interaction, locomotor mode and performance. Surfaces like sand, a granular medium, can display solid or fluid-like behaviour in response to stress. Based on our previous experiments and models of a robot moving on granular media, we hypothesize that solidification properties of granular media allow organisms to achieve performance on sand comparable to that on hard ground. We test this hypothesis by performing a field study examining locomotor performance (average speed) of an animal that can both swim aquatically and move on land, the hatchling Loggerhead sea turtle (Caretta caretta). Hatchlings were challenged to traverse a trackway with two surface treatments: hard ground (sandpaper) and loosely packed sand. On hard ground, the claw use enables no-slip locomotion. Comparable performance on sand was achieved by creation of a solid region behind the flipper that prevents slipping. Yielding forces measured in laboratory drag experiments were sufficient to support the inertial forces at each step, consistent with our solidification hypothesis.

Social insects work together to complete tasks. However, different individuals within a colony may vary in task proficiency. We investigated if fire ant (Solenopsis invicta) worker body size influenced the ability to construct tunnels-a key component of subterranean nests. We monitored excavation by worker groups in a substrate of small wetted glass particles in quasi-two-dimensional arenas. Morphological and network features of the tunnel system were measured. Total tunnel area did not differ significantly between groups of large and small workers, although the tunnel area of control sized workers was significantly larger than that of large workers. Moreover, large workers created wider but shorter tunnels, with slower growth rate of tunnel number. However, edge -vertex scaling and degree distribution of the tunnel network were similar across all treatments. In all cases, the amount of excavated material was correlated with the number of active workers. Our study reveals that morphological features of excavated tunnels show modest variation when constructed by workers of varying sizes, but topological features associated with the tunnel network are conserved. These results suggest that important behavioural aspects of tunnel construction-and thus nest building-are similar among morphologically distinct members of fire ant societies.

Terrestrial locomotion can take place on complex substrates such as leaf litter, debris, and soil that flow or solidify in response to stress. While principles of movement in air and water are revealed through study of the hydrodynamic equations of fluid motion, discovery of principles of movement in complex terrestrial environments is less advanced in part because describing the physics of limb and body interaction with such environments remains challenging. We report progress our group has made in discovering principles of movement of organisms and models of organisms (robots) on and within granular materials (GM) like sand. We review current understanding of localized intrusion in GM relevant to foot and body interactions. We discuss the limb-ground interactions of a desert lizard, a hatchling sea turtle, and various robots and reveal that control of granular solidification can generate effective movement. We describe the sensitivity of movement on GM to gait parameters and discuss how changes in material state can strongly affect locomotor performance. We examine subsurface movement, common in desert animals like the sandfish lizard. High speed x-ray imaging resolves subsurface kinematics, while electromyography (EMG) allows muscle activation patterns to be studied. Our resistive force theory, numerical, and robotic models of sand-swimming reveal that subsurface swimming occurs in a "frictional fluid" whose properties differ from Newtonian fluids.