Major Research Efforts
The goal of the CIBER-IGERT research effort is to discover general principles that define and explain the motion of biological and bio-inspired human-built systems that operate effectively in spatially complex and temporally varying environments. We contend that the study of motion from an integrative systems approach  is uniquely positioned to serve as an exemplar of the synergy between using quantitative engineering approaches to study biological systems, and using biological inspiration for engineering design. Four focus areas that explore different aspects of how motion systems function in variable environments will provide the research opportunities for our IGERT Trainees.
Focus Area 1 – Mechanics of systems that locomote and maneuver in complex, changing habitats
Focus Area 2 – Control of motion systems in variable environments
Focus Area 3 – Structure and function of bio- and bio-inspired materials, actuators and sensors that enable motion in complex settings
Focus Area 4 – Evolution of motion systems in the natural world
In part, these focus areas have emerged from our student’s increasing realization of common principles among disciplines and frustration when they find out too late that other disciplines had useful solutions, approaches or techniques. We are entering an era of integration that is simply unprecedented. Training the next generation of biologists and engineers demands that we go beyond traditional approaches that consider the areas of mechanics, controls, materials and their evolution separately. We must directly address how these areas relate to an integrated whole. Our leaders of the future will not see biology as distinct from engineering, but will see a mutually beneficial path towards knowledge and innovation.
Focus area 1 – Mechanics of systems that locomote and maneuver in complex, changing habitats: Dudley, Fearing, Fletcher, Full, Kazerooni, Keaveny, Koehl, Liepmann, McGuire, O’Brien, Oster, Pruitt, Stacey, Variano
This research effort will determine the principles by which organisms maintain course and maneuver while swimming or flying in turbulent ambient wind or water flow, how they find, capture, and manipulate diverse and moving objects and how they walk, run, and climb over complex terrains. By collaborating on these projects, both engineering and biology trainees will learn how to measure variation in environments, how to re-create such variation in the laboratory using wind tunnels, water flumes, wave tanks and arenas with surfaces and obstacles of different orientations and properties, and how to quantify the kinematics and kinetics of organismal and robotic motion systems operating in both laboratory and real-world sites.
An important underlying theme is how the size and speed of a motion system determine its interaction with the different spatial and temporal scales of environmental variation. The scaling principles that emerge from our proposed studies will improve our mechanistic understanding of the ecological functions of diverse types of organisms, and will also provide a conceptual framework for designing and testing devices of different sizes to operate in complex, real-word settings. A feature common to all these projects is the use of both living organisms and engineered devices (robots, physical models) to explore parameter spaces and to test our hypotheses about function.
Effect of size on navigating and feeding in turbulent aquatic environments. Aquatic organisms are exposed to moving water as they swim in the water column or walk on the substratum, and they must find and capture prey in this turbulent environment. Trainees will use state-or-the-art aquatic instrumentation to make detailed measurements of the structure and variability of turbulent water motions and turbulent fluxes of water-borne materials (e.g., odors, particles) in the field. Environmental variability will be mimicked in our flumes and wave tanks (Fig. 1), where detailed mechanistic studies can be conducted to examine how patchy distributions of particles, chemicals, or plankton form in the water, and how organisms of different sizes walk or swim, and navigate through such patchy moving aquatic environments .
At the micron scale, protozoans and bacteria are so small that they swim within the smallest eddies, experiencing turbulence as local shear and encountering patchily distributed nutrients and particulate food. By working with laboratories from several disciplines, trainees can study the environmental conditions under which different forms of marine protozoans have a feeding performance advantage. Trainees can compare the ability of protozoans to aggregate in patches of bacterial prey that form in turbulent flow, and to catch bacteria. Trainees will investigate the underlying mechanisms by analyzing the physics of protozoan swimming and feeding, utilizing advanced optical approaches to quantify kinematics of cells and their flagella, mathematically modeling cell motility, and conducting biofluiddynamic experiments using dynamically-scaled physical models with undulating flagella.
At the millimeter scale, trainees can study the mechanisms of how marine zooplankton and larvae (0.1-1mm body length) swim, feed, and navigate by olfaction in turbulent water flow. On this size scale, turbulent odor plumes are made up of filaments of high concentration swirling in odor-free water (Fig. 1). Animals are transported by the ambient flow, but also are able to swim across eddies and thus encounter rapidly-changing shears and odor concentrations. Trainees also will investigate how the fine-scale topography of benthic communities of organisms affects the fluctuating velocity structure of the flow, and how that, in turn, affects the hydrodynamic forces that buffet larvae recruiting into benthic communities and that wash small organisms off surfaces in different microhabitats.
At the meter scale, macroscopic, long-lived organisms (e.g., lobsters, fish, coral, giant kelp) experience a greater range of scales of environmental variation than do micro-organisms. Trainees studying macroscopic organisms or bio-inspired devices will be trained to distinguish the spatial and temporal scales of environmental variation that affect different aspects of their performance. For example, the scale at which a lobster’s olfactory antennule samples a turbulent odor plume (mm; < 0.1s; see Materials Focus) is different from the scales (m, s) at which the animal walks to the odor source and is pushed off course by waves.
Maneuverability of gliding and flying in windy, variable density habitats. Flying animals negotiate complex natural environments characterized by variable turbulence and numerous obstacles. Using hummingbirds and bumblebees as model fliers (both are routinely available throughout the Berkeley year from on-campus sources), trainees will investigate wing kinematics and aerodynamics as animals fly in a wind tunnel at different airspeeds and variable turbulence levels. Maneuvers through cluttered terrain will be investigated for the same birds and insects using learned behavioral protocols (e.g., flight to a nectar source through experimental simulations of both static and dynamic vegetational canopies). Trainees will use multiple-camera, synchronized high-speed video tracking of attached infrared markers.
In field contexts, trainees will study spatial and temporal distributions of turbulent wind and physical obstructions in natural canopies, and will investigate associated effects on flight performance for both wingless insects that maneuver to tree trunks when falling and for three-dimensional trajectories of winged insects in natural free flight obtained with multiple synchronized cameras. Ants without wings, for example, fall backward from the forest canopy at 4 m/sec, but manage to return to the same tree trunk 80% of the time . Trainees will determine how a variety of wingless insects directs their aerial descent with minimal structures for gliding. Future research will evaluate the roles of controlled gliding and descent in wing evolution, a pathway that may be general to origins of flight in animals (See Evolution Focus). Current students have begun to design bio-inspired, minimal gliding vehicles.
To complement these studies of natural performance, aerodynamic and physiological limits to flight performance will be assessed in the laboratory using variable-density gas mixtures and altitudinal simulations [4, 5]. Ongoing work with low-density heliox and hypobaric chambers has elicited extraordinary energetic and aerodynamic capacity in bumblebees as they fly at effective elevations of -1500 to 8000 meters, the equivalent of flying to the summit of Mt. Everest. Similarly, novel extremes of lift and power production have been demonstrated by hummingbirds lifting attached loads . Trainees will use these methods to elicit maximum performance from flying animals, and to understand the underlying aerodynamics of maneuvers and power transients in turbulent and otherwise demanding aerial environments. In aggregate, these studies will enable identification of animal flight features essential to flight in natural environments, and that will be translational into the design of micro-air vehicles, such as the Micromechanical Flying Insect (MFI) .
Traversing spatially and temporally variable terrain. No human-engineered robot can negotiate terrain like an animal. The challenges of discovering the mechanisms that terrestrial animals use to scramble over irregularly distributed, flowing debris with a low probability of foot contact are as great as those of discovering the mechanisms used by animals that fly and swim. Many terrestrial substrata display properties of both solids and fluids in response to a foot, toe, or claw interaction, yet we have no equivalent of Navier-Stokes for such “terradynamics”. The interaction of bodies with such materials can be even more complex than flow over a wing or water around a fin as such materials can undergo a solid/fluid phase transition, and during flow their transport properties can vary by orders of magnitude. To meet this challenge, we propose a new collaboration of participants studying terrestrial locomotion with hydrodynamicists from biology and civil engineering to develop a theory of terradynamics.
Trainees can study the limb mechanics that lizards and crabs use when running on sand, a penetrable flowing complex material. Lizards appear to paddle through the complex fluid with large drag on the power stroke created by long spread toes followed by collapse of the toes to decrease drag on the recovery stroke. Trainees can determine how animals negotiate substrata with a low probability of contact, such as a mesh-like array of plant needles . Leg spines on rapidly running spiders catch when thrusting against complex debris, but collapse when swinging forward. Placing simple collapsible spines on the leg of a running robot allows it to negotiate a mesh substratum that was otherwise impassible.
Most animals use an assortment of attachment devices to climb challenging vertical surfaces. Footforces in insects and lizards change from pushing out during level running to pulling in during climbing which load attachment structures. Geckos use millions of toe hairs with nano-size tips to stick to smooth surfaces, but rely on claws for interlocking when running up rough surfaces. Should geckos racing up a tree at a meter per second slip, they use their tail to contact the surface, thus preventing them from pitching backwards and falling head-over-heels (Fig. 2; ). This newly discovered neural reflex permits the active tail to function as an emergency fifth leg. Surprisingly, geckos also swing these active tails as inertial control devices if they lose their grip. Geckos that fall upside-down from the underside of a leaf swing their tails around producing the fastest zero-angular momentum righting response yet observed to position themselves in a gliding posture. Tail movements during gliding appear to steer and translate the gecko. Trainees will have the opportunity to use this inspiration to design an active tail on mobile climbing robots.
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This research effort is aimed at understanding the control principles that are used in robust natural motion systems which range from insect running to human arm movement, and applying those principles to robust control of legged robots, micro-fliers and prostheses. Trainees will focus on defining principles of stable and robust performance that integrate neurobiological (or electrical) and mechanical systems. Control issues will be considered broadly by combining behavior at all levels, from passive mechanical responses to perturbations dominated by material and geometric properties, to higher level reactive sensor-controlled reflexes and explicit sensor-based planning. Identification of robust control policies and optimal structural parameters will take advantage of current adaptive learning hypotheses in animal and human movement. Knowledge of these strategies will guide the hypotheses trainees test to explore how animals move effectively in variable natural habitats, as well as the design of moving robots and devices with better performance in unpredictable, complex environments.
Trainees will address three major challenges in the control of biological and engineered motion systems. First, they will determine how systems with far more degrees of freedom than necessary perform particular tasks so effectively. Second, they will explore how the passive structures that provide zero order mechanical feedback are integrated with active feedback from sensors. Third, trainees will test hypotheses that explain how motion systems learn to negotiate complex, variable environments.
Reduced order models. How low-level activation of multiple muscles translates into high-level task commands remains a fundamental issue in motion systems. Our trainees will research dimensionally reduced models from data that describe mechanical synergies for running, climbing, flying and primate/human arm movement. Surprisingly, trotting eight-legged crabs, six-legged insects, four-legged dogs and even running humans all collapse their degrees of freedom down to a bouncing pogo-stick. Termed a template, this represents the simplest model with the least number of variables and parameters that exhibits a targeted behavior of a system (Fig. 3; ). The presence of a template suggests that a system can restrict itself to a low-dimensional subset of its high dimensional morphology in the space of possible motions. More generally, trainees will create reduced order models where control effort is expended only along directions relevant to the control objective. This approach can lead to a low-dimensional representation that resolves redundancy according to optimality principles, and whose foundation is a bio-inspired model . Reduced models have inspired the design of robots that run, climb and fly and of robot arms that reach with simple, but effective controllers.
The integration of passive dynamic self-stabilization with active feedback. Despite general recognition of the role of the mechanical system in control, few neural control theories start with the body or plant as a source of mechanical feedback – passive viscoelastic properties that tend to stabilize a structure, sometimes referred to as a preflex. Likewise, many robot and device controllers are designed to remove kinetic energy and fight against the natural dynamics of the plant. Trainees will bring together approaches, algorithms and experimental methodologies to design the next generation of controllers that integrate passive dynamics with active sensing and inspire the design of new human-made devices and robots.
Trainees will take a dynamical systems approach to create hierarchical control models that couple mechanical and neural oscillators . Simple piecewise-holonomic, spring-mass models of legged locomotion mechanically self-stabilize when bumped or tripped during running with minimal neural feedback. Key leg control muscles in insects do not change their feedforward activation pattern even when running over rough terrain until large perturbations exceed the recovery capability of an animal’s passive, stabilizing mechanical feedback. To test these control hypotheses, trainees can rewrite the neural motor code to muscles in rapidly running insects by adding discrete spikes in a phase-locked manner to muscles, while measuring body dynamics with accelerometer backpacks and videography. These discoveries are inspiring the design of a new 2.4g robotic, autonomous, running hexapod . For flying insects and bio-inspired flapping wing robots, trainees will integrate wing-thorax passive dynamics, low Reynolds number aerodynamics, and biomimetic sensory feedback. To test these models, trainees will use a miniaturized, thorax-mounted system housing neural and muscular stimulators and a micro-controller capable of tetherless flight initiation, cessation and elevation control in flying beetles (Fig. 4; ). For higher center feedback integration with mechanics, trainees will study rapid reaching movement of humans in a 3D virtual reality system with force feedback . Research on bimanual coordination has highlighted a number of fundamental constraints that are manifest in both the temporal and spatial domain.
Role of learning in response to environmental uncertainty. One of motion control’s next frontiers is learning, both in bio- and bio-inspired systems. Learning is central to motor control in humans and other animals, yet we have very little idea how it works. Trainees will research how motor skills are learned in primates/humans, as well as how machine learning can model animal and robot control systems.
Current machine learning methods often require hundreds or thousands of trials to learn relatively simple motions that humans can acquire with a few minutes’ practice. Trainees will research new reinforcement learning methods that incorporate the sensory data obtained during the trial . This information is important because it can explain away perturbations in the reward signal; it provably reduces the variance of the gradient estimate and speeds up learning dramatically.
For tasks such as navigating a quadruped robot over irregular terrain (Fig. 5), the dimensionality of the state space for finding cost functions is prohibitively large, however hierarchical apprenticeship learning algorithms can infer such cost functions from observed behavior by giving advice independently at each level of the hierarchy . Lower levels of the control hierarchy require that the expert demonstrate good local behavior, rather than behavior that is optimal for the entire task. Trainees will use apprenticeship learning to automatically learn cost functions from observations of animal locomotion in difficult terrain, potentially leading to new robust control strategies. Trainees will apply iterative learning strategies that can teach flying vehicles, like helicopters, to fly as if they had expert human pilots.
A fundamental understanding of motor learning and memory promises to enable skilled direct neural control of a prosthetic device through brain-machine interfaces . Consolidation experiments using primates trained to perform a two-dimensional center-out reaching task by a brain-controlled computer cursor under visual feedback demonstrate a rapid increase in the accuracy and speed of performance, culminating in long-term consolidation of skill. Trainees will have the opportunity to research direct learning interactions between motor cortex neurons and prosthetic motor performance.
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Focus Area 3 — Structure and function of bio- and bio-inspired materials, actuators and sensors that enable motion in complex settings: Bajcsy, Caldwell, Dharan, Fearing, Fletcher, Full, Healy, Kazerooni, Keaveny, Koehl, Lee, Lehman, Malik, O’Brien, Oster, Pister, Pruitt
This research effort is focused on the principles by which materials, actuators and sensors function to give biological and bio-inspired motion systems robust performance in complex environments. Trainees will discover these principles through the integrated study of skeletal systems, the muscles that drive and control motion and the sensors that provide information about the environment. Biological discoveries will inspire the design of prosthetic devices, exoskeletal assist suits, synthetic self-cleaning dry adhesives, artificial muscles, antennae, and compounds eyes.
Rate-dependent performance of skeletal material. Material properties affected by the performance of motion systems in variable, complex environments include elastic energy storage, damping, functional deformation range, adhesive strength, resistance to wear and fracture, and rate-, temperature-, and load-dependent stiffness. Capitalizing on our diverse strengths, trainees will search for common principles by dynamically testing and modeling bone, cartilage, exoskeletons and fibrillar adhesives from the microscale to their effects on the motion of organisms, devices and robots.
Trainees can discover the importance of rate effects at different temporal scales by studying bone and cartilage. Our research on bone’s response to dynamic mechanical loads seeks to relate failure mechanisms at the scale of collagen chains and their interface with the mineral component of bone to those at the organ level scale. Studies will address rate effects associated with habitual loading, such as cyclic fatigue and creep loading , as well as traumatic loading at higher stress levels, typical of a spurious overload. Rate effects of loading on bone tissue will be integrated via high-fidelity computational models with trabecular micro-architecture, the spatial variation of bone density, and the 3D geometry of whole bones. This basic science will elucidate mechanisms of bone deformation and failure in response to locomotion, injury, aging and osteoporosis. A comparable approach examining the control of cartilage matrix material properties will reveal how changes in stiffness and time dependent properties are linked specifically to biological markers .
By studying the exoskeletons of insects and crustaceans, our trainees can compare the advantages and disadvantages relative to endoskeletal bone and cartilage. We have strong expertise in quantifying how the passive properties of arthropod exoskeletons contribute to self-stabilization, energy storage and fail resistance during locomotion. We place our dynamic material test results in the context of animals responding to environmental perturbations . Insights from these biological material studies will guide design of engineered systems. Trainees can apply a new technique using laser micro-machined composite fiber elements (Smart Composite Manufacturing) to build articulated robotic structures for millimeter-sized robots with tunable compliance properties . Entire structures such as limbs consisting of flexible and rigid joints can be fabricated from a single flat structure and then folded into a 3D shape. A new rapid prototyping process will allow trainees to quickly and inexpensively test designs using environmentally friendly materials. Engineered structures can be used as physical models to test our biological hypotheses. Trainees can examine the effects of scaling on exoskeletons by assisting in the design of human-sized exoskeletons .
Trainees will discover principles by which novel properties emerge from skeletal material with changes in geometry by exploring fibrillar adhesives. Geckos, spiders and insects evolved stiff structures made from keratin and chitin that when split into hairy arrays result in a compliance comparable to tacky materials.
During locomotion, these directional adhesive arrays permit attachment and detachment in milliseconds. Trainees will study how the micro-architecture of gecko feet affect their sticking performance as they run on diverse, changing surfaces. The self-cleaning, dry adhesive properties emerge from the millions of micron-scale hairs or setae that can have as many as 1000 tips per hair that stick by van der Waals forces . New discoveries in hair function and their evolution (see Evolution Focus) will further guide development of human-made fibrillar adhesives that have gecko-like properties (Fig. 6; ).
Actuators role in control at different scales. Fundamental to motion systems are the actuators that drive and control skeletal structures. Trainees will have an opportunity to discover the fundamental principles of actuators across a wide range of spatial scales. The biological principles discovered will inspire the design of artificial muscles and human-engineered electrostatic and piezo-electric motors.
On the smallest scale, Trainees will study protein motors that are mechano-chemical machines operating in a size regime where the dominant force is Brownian motion. They will create quantitative mechano-chemical models to study proteins such as ATPase that consist of an ATP driven rotary motor coupled by an elastic shaft to a counter-rotating ion-driven motor (Fig. 7; )By using a new instrument that measuresforce-velocity relationships and viscoelastic properties, Trainees will determine how external loads influence the dynamic assembly of actin filament networks during crawling, motility, and shape change to describe how cells adapt to their physical environment .
Muscles in vivo act as springs, brakes and dampers as often as they act as motors . On a cellular scale, trainees will stretch single, isolated mammalian muscle fibers at rates found in vivo to test hypotheses of the molecular motor’s response and their energetic consequences . At the organ level, trainees will perturb whole insect muscles during cyclic tests using the conditions observed in running. They will input stretch perturbations during sinusoidal oscillations that match conditions during locomotion when a leg is struck in its swing phase as an animal runs over debris. Trainees will then model the control aspects of muscle’s energy management.
Trainees’ biological discoveries will inspire the next design of electrostatic inchworm motors  that allow energy storage and return to drive millimeter-sized legs of microrobots that crawl and jump, and of milligram piezoelectric bending actuators that operate at frequencies from 10 to 300 Hz to drive the flapping wings of microrobot fliers and electroactive polymers operating by elecrostatic forces squeezing polymer sheets .
Sensor function is inseparable from the environment. Sensors give motion systems the information needed to navigate and communicate in complex environments. Trainees will study biological sensors involved in olfaction, vision and tactile sensing and will develop bio-inspired sensors that include artificial antennae derived from lobsters and insects, and microlenses inspired by arthropod eyes.
Determining the spatiotemporal pattern of stimuli in the environment is essential to understanding the function of biological sensors. Many animals capture odors from turbulent water currents or wind using antennae that bear chemosensory hairs (see Mechanics Focus). Whether animals can use the fine-scale patterns of concentration in a turbulent plume to locate an odor source depends not only on neural filtering of that information, but also on the fluid dynamics of their olfactory organs. For example, lobster antennules capture order structure on the fast downstroke . Trainees will have an opportunity to determine which aspects of plume information that lobsters actually use. Future robotic motion system sensors must consider a sensor’s interaction with the environment.
Extreme designs in nature can sense broad spectra. For instance, stomatopod crustaceans have the most complex eyes in the animal kingdom. Their eyes are organized as specialized rows of ommatidia with each row serving a distinct set of visual functions that include tunable, eight-channel color vision, the ability to see into the ultraviolet, complex linear polarization vision, monocular stereopsis, as well as luminance and form vision (Fig. 8; ). Trainees can study how multiple channels of information are integrated. Using this inspiration, they will have the chance to design artificial compound eyes by soft lithography and three-dimensional micro-scale processing techniques .
Effective biological sensors work with the natural dynamics of the body to which they are attached. Trainees can test a mechanosensory model for wall-following in rapid running insects that couples the body’s passive self-stabilization with active antennal sensing . They will determine the type of feedback used by neurophysiological recordings of the antennal nerves during simulated wall-following.
Data on insect antennae will inspire the design of both legged and wheeled wall-following robots.
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This unique research emphasis is focused on the evolution of biological motion systems in complex environments and the engineering-based capabilities that facilitate their elucidation. Trainees will use phylogenetic techniques to distinguish constraints of past history from the adaptations that can effectively inspire engineering designs. Engineering trainees will bring quantitative models, novel instrumentation, and engineered physical models, such as robots and manufactured materials, to make new discoveries possible in evolution.
Distinguishing historical constraints from adaptations to provide bio-inspiration.Evolutionary and comparative perspectives provide powerful insights into the nature of organismal design because all functional outcomes in biology must reflect genetic ancestry, and typically represent compromise among conflicting demands. The statistical nature of natural selection, combined with innumerable populations evolving over millions of years, provide an invaluable sorting process for effective design endpoints and a diversity of suboptimal outcomes that are nonetheless sufficient to persist. The choice of an appropriate taxon for bio-inspired design is accordingly critical to avoid potential pitfalls associated with biological compromises deriving from historical constraints, developmental canalization, selection for purposes other than immediate utility (e.g., sexual selection on exaggerated structures), and temporally variable and context-specific selection regimes. This methodology enhances the likelihood of discovering key innovations and of identifying useful extremes in biological design. Knowledge of the evolutionary process is thus essential for an integrative understanding of design and its technological emulation.
Our internationally recognized program in comparative biomechanics, coupled with the phylogenetic expertise in our Natural History Museums, gives trainees the opportunity to investigate the evolution of bone in humans and dinosaurs, sensors such as compound eyes, adhesive hairs of geckos and spiders, running in arthropods, reptiles, humans and their ancestors, and flight in insects, bats, birds and dinosaurs.
In particular, our trainees will benefitfrom our integrated perspectives on flying animals, ranging from phylogenetic and paleontological  approaches to the underlying biomechanics and physiology of flight. By comparing the limits of aerodynamic force and power generation in extant fliers with the functional utility of transitionally winged forms, trainees will more clearly see the biomechanical constraints of flight. Trainees will dissect an adaptation into its necessary (as distinct from ancillary) structural and functional components, and then use independent phylogenetic evidence to reconstruct the order in which these features appeared. For example, novel pre-flight behaviors in numerous wingless insects have established the behavioral origins of directed descent from trees as preceding the origins of wings proper . Trainees could integrate these approaches using gliders with partial wings and other ancillary, but aerodynamically useful structures, for which relevant morphologies can be fabricated readily using molded polymers and composite parts with distributed flexural components . Such prototypes will not only lead to effective physical models of extant organisms for flow quantification and direct force measurements, but also will be used to reconstruct ancestral forms for subsequent biomechanical study, as well as for the analysis of morphologies known only from fossils.
Using capabilities from engineering to study evolution.Engineering approaches based on mathematical and physical models can inform the understanding of biological function and evolution . Engineering trainees will be able to apply fluid dynamic, solid mechanic and control theory models to evolutionary biology’s most challenging questions concerning motion systems. Often bio-inspired human-engineered materials, sensors, devices and robots can serve as physical models to study organismal function and evolution. Our study of fibrillar adhesives exemplifies this approach.
By using a uniquely engineered MEMS force sensor, we discovered that fibrillar hairs on gecko toesstick by van der Waals forces. Quantitative models using beam and adhesive theory suggested a number of important parameters such as the density of fibrillar attachment points or tips, hair angle, and its curvature. Researchers not considering evolution scaled only the density of fibrillar attachment points in a few diverse species (Fig. 9A; ). Density of attachment points increased with body mass, suggesting the need to manufacture very high-density attachment points for high adhesion. By contrast, our subsequent phylogenetic analysis showed that hair tip density remains constant across related groups of taxa, and instead pointed to the other parameters critical for adhesion and also simpler to manufacture (Fig. 9B; .) However, even hairs with a single tip can provide effective directional adhesion when sufficiently compliant, a result that considerably reduces manufacturing difficulty. Still, the enormous variation in gecko hair length width, branching patterns and the number of tips an individual hair possesses remains to be explained. As the capability of manufacturing a fibrillar adhesive develops, trainees will be able to use these human-engineered fibrillar adhesives as physical models to test the hypotheses of the morphological variation we see in gecko hairs . Ultimately, IGERT Trainees will synthesize ancestral hairs, measure their performance, and test hypotheses of their evolutionary origin.
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