Inertial Tail Effects during Righting of Squirrels in unexpected Falls: From Behavior to Robotics

Arboreal mammals navigate a highly three dimensional and discontinuous habitat. Among arboreal mammals, squirrels demonstrate impressive agility. In a recent ‘viral’ YouTube video, unsuspecting squirrels were mechanically catapulted off of a track, inducing an initially uncontrolled rotation of the body. Interestingly, they skillfully stabilized themselves using tail motion, which ultimately allowed the squirrels to land successfully. Here we analyze the mechanism by which the squirrels recover from large body angular rates. We analyzed from the video that squirrels first use their tail to help stabilizing their head to visually fix a landing site. Then the tail starts to rotate to help stabilizing the body, preparing themselves for landing. To analyze further the mechanism of this tail use during mid-air, we built a multibody squirrel model and showed the righting strategy based on body inertia moment changes and active angular momentum transfer between axes. To validate the hypothesized strategy, we made a squirrel-like robot and demonstrated a fall-stabilizing experiment. Our results demonstrate squirrel’s long tail, despite comprising just 3% of body mass, can inertially stabilize a rapidly rotating body. This research contributes to better understanding the importance of long tails for righting mechanisms in animals living in complex environments such as trees.

Mitigating memory effects during undulatory locomotion on hysteretic materials

While terrestrial locomotors often contend with permanently deformable substrates like sand, soil, and mud, principles of motion on such materials are lacking. We study the desert-specialist shovel-nosed snake traversing a model sand and find body inertia is negligible despite rapid transit and speed dependent granular reaction forces. New surface resistive force theory (RFT) calculation reveals how wave shape in these snakes minimizes material memory effects and optimizes escape performance given physiological power limitations. RFT explains the morphology and waveform-dependent performance of a diversity of non-sand-specialist snakes but overestimates the capability of those snakes which suffer high lateral slipping of the body. Robophysical experiments recapitulate aspects of these failure-prone snakes and elucidate how re-encountering previously deformed material hinders performance. This study reveals how memory effects stymied the locomotion of a diversity of snakes in our previous studies (Marvi et al., 2014) and indicates avenues to improve all-terrain robots.

Mitigating memory effects during undulatory locomotion on hysteretic materials

Undulatory swimming in flowing media like water is well-studied, but little is known about loco-motion in environments that are permanently deformed by body–substrate interactions like snakes in sand, eels in mud, and nematode worms in rotting fruit. We study the desert-specialist snake Chion-actis occipitalis traversing granular matter and find body inertia is negligible despite rapid transit and speed dependent granular reaction forces. New surface resistive force theory (RFT) calculation reveals how this snakes wave shape minimizes memory effects and optimizes escape performance given physiological limitations (power). RFT explains the morphology and waveform dependent performance of a diversity of non-sand-specialist, but overpredicts the capability of snakes with high slip. Robophysical experiments recapitulate aspects of these failure-prone snakes and elucidate how reencountering previously remodeled material hinders performance. This study reveals how memory effects stymied the locomotion of a diversity of snakes in our previous studies [Marvi et al, Science, 2014] and suggests the existence of a predictive model for history-dependent granular physics.

Scaling of inertial delays in terrestrial mammals

As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose motion, delaying the completion of the movement—we refer to this additional elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Here, we quantify it using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes—larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.

Note on a ball rolling over a sphere: Integrable Chaplygin system with an invariant measure without Chaplygin hamiltonization

In this note we consider the nonholonomic problem of rolling without slipping and twisting of an ??-dimensional balanced ball over a fixed sphere. This is a ????(??)?Chaplygin system with an invariant measure that reduces to the cotangent bundle ??*?????1. For the rigid body inertia operator r I? = I? + ?I, I = diag(I1,...,In) with a symmetry I1 = I2 = ... =Ir ? Ir+1 = Ir+2 = ... = In, we prove that the reduced system is integrable, general trajectories are quasi-periodic, while for ?? ? 1, ?? ? 1 the Chaplygin reducing multiplier method does not apply.

Passive Pitch Mechanics of Elastic Flapping Wings

Many flapping wing micro air vehicles (FWMAVs) utilize a flexible joint that allows the wing to passively rotate about the pitching axis. Generally, simple rigid body models are used to estimate the passive pitching dynamics. However, evidence suggests elastic wings increase aerodynamic force generation and expend less energy relative to rigid wings. As a result, elastic wings are becoming an integral part of FWMAV design. But, the effect of wing elasticity on passive pitching mechanics is unclear. To explore this, we develop a coupled model of an elastic wing attached to a flexible pitching joint. Aerodynamic moments are included through a simple blade element approach. The model is applied to an idealized insect forewing subject to prescribed roll rotation. The simulation results suggest (1) aerodynamic moments, not rigid body inertia or elastic forces, are primarily responsible for lift-generating passive pitch, (2) joint stiffness influences pitching mechanics more than wing elasticity does, and (3) flexible wings can increase net lift by as much as 20% if the pitching joint is mistuned. The framework developed in this paper can be used to design and optimize FWMAV systems in terms of both elastic wings and flexible passive pitch joints.

Hydrodynamic schooling of multiple self-propelled flapping plates

While hydrodynamic interactions for aggregates of swimmers have received significant attention in the low Reynolds number realm ($Re\ll 1$), there has been far less work at higher Reynolds numbers, in which fluid and body inertia are involved. Here we study the collective behaviour of multiple self-propelled plates in tandem configurations, which are driven by harmonic flapping motions of identical frequency and amplitude. Both fast modes with compact configurations and slow modes with sparse configurations were observed. The Lighthill conjecture that orderly configurations may emerge passively from hydrodynamic interactions was verified on a larger scale with up to eight plates. The whole group may consist of subgroups and individuals with regular separations. Hydrodynamic forces experienced by the plates near their multiple equilibrium locations are all springlike restoring forces, which stabilize the orderly formation and maintain group cohesion. For the cruising speed of the whole group, the leading subgroup or individual plays the role of ‘leading goose’.