Thomas Libby

Tail-assisted pitch control in lizards, robots and dinosaurs

In 1969, a palaeontologist proposed that theropod dinosaurs used their tails as dynamic stabilizers during rapid or irregular movements, contributing to their depiction as active and agile predators. Since then the inertia of swinging appendages has been implicated in stabilizing human walking, aiding acrobatic manoeuvres by primates and rodents, and enabling cats to balance on branches. Recent studies on geckos suggest that active tail stabilization occurs during climbing, righting and gliding. By contrast, studies on the effect of lizard tail loss show evidence of a decrease, an increase or no change in performance. Application of a control-theoretic framework could advance our general understanding of inertial appendage use in locomotion. Here we report that lizards control the swing of their tails in a measured manner to redirect angular momentum from their bodies to their tails, stabilizing body attitude in the sagittal plane. We video-recorded Red-Headed Agama lizards (Agama agama) leaping towards a vertical surface by first vaulting onto an obstacle with variable traction to induce a range of perturbations in body angular momentum. To examine a known controlled tail response, we built a lizard-sized robot with an active tail that used sensory feedback to stabilize pitch as it drove off a ramp. Our dynamics model revealed that a body swinging its tail experienced less rotation than a body with a rigid tail, a passively compliant tail or no tail. To compare a range of tails, we calculated tail effectiveness as the amount of tailless body rotation a tail could stabilize. A model Velociraptor mongoliensis supported the initial tail stabilization hypothesis, showing as it did a greater tail effectiveness than the Agama lizards. Leaping lizards show that inertial control of body attitude can advance our understanding of appendage evolution and provide biological inspiration for the next generation of manoeuvrable search-and-rescue robots.

A lizard-inspired active tail enables rapid maneuvers and dynamic stabilization in a terrestrial robot

We present a novel approach to stabilizing rapid locomotion in mobile terrestrial robots inspired by the tail function of lizards. We built a 177 (g) robot with inertial sensors and a single degree-of-freedom active tail. By utilizing both contact forces and zero net angular momentum maneuvering, our tailed robot can rapidly right itself in a fall, avoid flipping over after a large perturbation, and smoothly transition between surfaces of different slopes. We also use a modeling approach to show that a tail-like design offers significant advantages to other alternatives, including reaction wheels, when the speed of response is important.

Righting and turning in mid-air using appendage inertia: reptile tails, analytical models and bio-inspired robots

Unlike the falling cat, lizards can right themselves in mid-air by a swing of their large tails in one direction causing the body to rotate in the other. Here, we developed a new three-dimensional analytical model to investigate the effectiveness of tails as inertial appendages that change body orientation. We anchored our model using the morphological parameters of the flat-tailed house gecko Hemidactylus platyurus. The degree of roll in air righting and the amount of yaw in mid-air turning directly measured in house geckos matched the models results. Our model predicted an increase in body roll and turning as tails increase in length relative to the body. Tails that swung from a near orthogonal plane relative to the body (i.e. 0-30° from vertical) were the most effective at generating body roll, whereas tails operating at steeper angles (i.e. 45-60°) produced only half the rotation. To further test our analytical models predictions, we built a bio-inspired robot prototype. The robot reinforced how effective attitude control can be attained with simple movements of an inertial appendage.

A nonlinear feedback controller for aerial self-righting by a tailed robot

In this work, we propose a control scheme for attitude control of a falling, two link active tailed robot with only two degrees of freedom of actuation. We derive a simplified expression for the robots angular momentum and invert this expression to solve for the shape velocities that drive the bodys angular momentum to a desired value. By choosing a body angular velocity vector parallel to the axis of error rotation, the controller steers the robot towards its desired orientation. The proposed scheme is accomplished through feedback laws as opposed to feedforward trajectory generation, is fairly robust to model uncertainties, and is simple enough to implement on a miniature microcontroller. We verify our approach by implementing the controller on a small (175 g) robot platform, enabling rapid maneuvers approaching the spectacular capability of animals.

Shifts in a single muscle's control potential of body dynamics are determined by mechanical feedback

Muscles are multi-functional structures that interface neural and mechanical systems. Muscle work depends on a large multi-dimensional space of stimulus (neural) and strain (mechanical) parameters. In our companion paper, we rewrote activation to individual muscles in intact, behaving cockroaches (Blaberus discoidalis L.), revealing a specific muscles potential to control body dynamics in different behaviours. Here, we use those results to provide the biologically relevant parameters for in situ work measurements. We test four hypotheses about how muscle function changes to provide mechanisms for the observed control responses. Under isometric conditions, a graded increase in muscle stress underlies its linear actuation during standing behaviours. Despite typically absorbing energy, this muscle can recruit two separate periods of positive work when controlling running. This functional change arises from mechanical feedback filtering a linear increase in neural activation into nonlinear work output. Changing activation phase again led to positive work recruitment, but at different times, consistent with the muscles ability to also produce a turn. Changes in muscle work required considering the natural sequence of strides and separating swing and stance contributions of work. Both in vivo control potentials and in situ work loops were necessary to discover the neuromechanical coupling enabling control.

Stress distribution and contact area measurements of a gecko toe using a high-resolution tactile sensor

The adhesive systems of geckos have been widely studied and have been a great source of bioinspiration. Load-sharing (i.e. preventing stress concentrations through equal distribution of loads) is necessary to maximize the performance of an adhesive system, but it is not known to what extent load-sharing occurs in gecko toes. In this paper, we present in vivo measurements of the stress distribution and contact area on the toes of a tokay gecko (Gekko gecko) using a custom tactile sensor with 100 μm spatial resolution. We found that the stress distributions were nonuniform, with large variations in stress between and within lamellae, suggesting that load-sharing in the tokay gecko is uneven. These results may be relevant to the understanding of gecko morphology and the design of improved synthetic adhesive systems.

Gliding saves time but not energy in Malayan colugos.

SUMMARY Gliding is thought to be an economical form of locomotion. However, few data on the climbing and gliding of free-ranging gliding mammals are available. This study employed an animal-borne three-dimensional acceleration data-logging system to collect continuous data on the climbing and gliding of free-ranging Malayan colugos, Galeopterus variegatus. We combined these movement data with empirical estimates of the metabolic costs to move horizontally or vertically to test this long-standing hypothesis by determining whether the metabolic cost to climb to sufficient height to glide a given distance was less than the cost to move an equivalent distance horizontally through the canopy. On average, colugos climb a short distance to initiate glides. However, due to the high energetic cost of climbing, gliding is more energetically costly to move a given horizontal distance than would be predicted for an animal travelling the same distance through the canopy. Furthermore, because colugos spend a small fraction of their time engaged in locomotor activity, the high costs have little effect on their overall energy budget. As a result, the energetic economy hypothesis for the origins of gliding is not supported. It is likely that other ecologically relevant factors have played a greater role in the origins of gliding in colugos and other mammals.

Comparative Design, Scaling, and Control of Appendages for Inertial Reorientation

This paper develops a comparative framework for the design of actuated inertial appendages for planar aerial reorientation. We define the inertial reorientation template, the simplest model of this behavior, and leverage its linear dynamics to reveal the design constraints linking a task with the body designs capable of completing it. As practicable inertial appendage designs lead to morphology that is generally more complex, we advance a notion of “anchoring,” whereby a judicious choice of physical design in concert with an appropriate control policy yields a system whose closed-loop dynamics are sufficiently captured by the template to permit all further designs to take place in its far simpler parameter space. This approach is effective and accurate over the diverse design spaces afforded by existing platforms, enabling a performance comparison through the shared task space. We analyze examples from the literature and find advantages to each body type, but conclude that tails provide the highest potential performance for reasonable designs. Thus motivated, we build a physical example by retrofitting a tail to a RHex robot and present empirical evidence of its efficacy.