[Show abstract][Hide abstract] ABSTRACT: The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a "granular frictional fluid" and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.
Full-text · Article · Dec 2012 · PLoS Computational Biology
[Show abstract][Hide abstract] ABSTRACT: Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM.
[Show abstract][Hide abstract] ABSTRACT: Many animals move within in granular media such as desert sand. Recent
biological experiments have revealed that the sandfish lizard uses an
undulatory gait to swim within sand. Models reveal that swimming occurs
in a frictional fluid in which inertial effects are small and kinematics
dominate. To understand the fundamental mechanics of swimming in
granular media (GM), we examine a model system that has been
well-studied in Newtonian fluids: the three-link swimmer. We create a
physical model driven by two servo-motors, and a discrete element
simulation of the swimmer. To predict optimal gaits we use a recent
geometric mechanics theory combined with empirically determined
resistive force laws for GM. We develop a kinematic relationship between
the swimmer's shape and position velocities and construct connection
vector field and constraint curvature function visualizations of the
system dynamics. From these we predict optimal gaits for forward,
lateral and rotational motion. Experiment and simulation are in accord
with the theoretical predictions; thus geometric tools can be used to
study locomotion in GM.
[Show abstract][Hide abstract] ABSTRACT: Previously we modeled the undulatory subsurface locomotion of the sandfish lizard with a sand-swimming robot which displayed performance comparable to the organism. In this work we control the lift forces on the robot by varying its head shape and demonstrate that these granular forces predict the vertical motion of the robot. Inspired by the tapered head of the sandfish lizard, we drag a wedge shaped object horizontally and parallel to its lower face through a granular medium and show that by varying the angle of the upper leading surface of the wedge, α, the lift force can be varied from positive to negative. Testing the robot with these wedges as heads results in vertical motion in the same direction as the lift force in the drag experiments. As the robot moves forward, the force on its head normal to the body plane results in a net torque imbalance which pitches the robot causing it to rise or sink within the medium. Since repeatedly varying α for a wedge head to achieve a desired lift is impractical, we test robot heads that approximate a wedge head inclined at varying angles by changing the angle of the bottom and top surfaces of the wedge, and show that similar lift control is achieved. Our results provide principles for the construction of robots that will be able to follow arbitrary trajectories within complex substrates like sand, and also lend support to hypotheses that morphological adaptations of desert-dwelling organisms aid in their subsurface locomotion.