Biomimetic evolutionary analysis: testing the adaptive value of vertebrate tail stiffness in autonomous swimming robots

Paleomimetics: A Conceptual Framework for a Biomimetic Design Inspired by Fossils and Evolutionary Processes

In biomimetic design, functional systems, principles, and processes observed in nature are used for the development of innovative technical systems. The research on functional features is often carried out without giving importance to the generative mechanism behind them: evolution. To deeply understand and evaluate the meaning of functional morphologies, integrative structures, and processes, it is imperative to not only describe, analyse, and test their behaviour, but also to understand the evolutionary history, constraints, and interactions that led to these features. The discipline of palaeontology and its approach can considerably improve the efficiency of biomimetic transfer by analogy of function; additionally, this discipline, as well as biology, can contribute to the development of new shapes, textures, structures, and functional models for productive and generative processes useful in the improvement of designs. Based on the available literature, the present review aims to exhibit the potential contribution that palaeontology can offer to biomimetic processes, integrating specific methodologies and knowledge in a typical biomimetic design approach, as well as laying the foundation for a biomimetic design inspired by extinct species and evolutionary processes: Paleomimetics. A state of the art, definition, method, and tools are provided, and fossil entities are presented as potential role models for technical transfer solutions.

Robotics as a Comparative Method in Ecology and Evolutionary Biology

Comparative biologists have typically used one or more of the following methods to assist in evaluating the proposed functional and performance significance of individual traits: comparative phylogenetic analysis, direct interspecific comparison among species, genetic modification, experimental alteration of morphology (for example by surgically modifying traits), and ecological manipulation where individual organisms are transplanted to a different environment. But comparing organisms as the endpoints of an evolutionary process involves the ceteris paribus assumption: that all traits other than the one(s) of interest are held constant. In a properly controlled experimental study, only the variable of interest changes among the groups being compared. The theme of this paper is that the use of robotic or mechanical models offers an additional tool in comparative biology that helps to minimize the effect of uncontrolled variables by allowing direct manipulation of the trait of interest against a constant background. The structure and movement pattern of mechanical devices can be altered in ways not possible in studies of living animals, facilitating testing hypotheses of the functional and performance significant of individual traits. Robotic models of organismal design are particularly useful in three arenas: (1) controlling variation to allow modification only of the trait of interest, (2) the direct measurement of energetic costs of individual traits, and (3) quantification of the performance landscape. Obtaining data in these three areas is extremely difficult through the study of living organisms alone, and the use of robotic models can reveal unexpected effects. Controlling for all variables except for the length of a swimming flexible object reveals substantial non-linear effects that vary with stiffness. Quantification of the swimming performance surface reveals that there are two peaks with comparable efficiency, greatly complicating the inference of performance from morphology alone. Organisms and their ecological interactions are complex, and dissecting this complexity to understand the effects of individual traits is a grand challenge in ecology and evolutionary biology. Robotics has great promise as a "comparative method," allowing better-controlled comparative studies to analyze the many interacting elements that make up complex behaviors, ecological interactions, and evolutionary histories.

Connecting materials, performance and evolution: a case study of the glue of moth-catching spiders (Cyrtarachninae)

Morphological structures and extended phenotypes are made possible by materials that are encoded by the genome. Nearly all biomaterials are viscoelastic, which means that to understand performance, one must understand the strain rate-dependent properties of these materials in relevant ecological interactions, as the behavior of a material can vary dramatically and rapidly. Spider silks are an example of materials whose properties vary substantially intra- and inter-specifically. Here, we focus on aggregate silk, which functions as a biological adhesive. As a case study to understand how a material manifests from genome through organism to ecology, we highlight moth-specialist spiders, the Cyrtarachninae, and their glues as an ideal experimental system to investigate the relationship between genomics and ecologically variable performance of a biological material. There is a clear eco-evolutionary innovation that Cyrtarachne akirai and related species have evolved, a unique trait not found in other spiders, a glue which overcomes the scales of moths. By examining traditional orb-weavers, C. akirai and other subfamily members using biomechanical testing and genomic analysis, we argue that we can track the evolution of this novel bioadhesive and comment on the selection pressures influencing prey specialization. The importance of the ecological context of materials testing is exemplified by the poor performance of C. akirai glue on glass and the exceptional spreading ability and adhesive strength on moths. The genetic basis for these performance properties is experimentally tractable because spider silk genes are minimally pleiotropic and advances in genomic technologies now make possible the discovery of complete silk gene sequences.

Tunable stiffness in fish robotics: mechanisms and advantages

One of the emerging themes of fish-inspired robotics is flexibility. Adding flexibility to the body, joints, or fins of fish-inspired robots can significantly improve thrust and/or efficiency during locomotion. However, the optimal stiffness depends on variables such as swimming speed, so there is no one 'best' stiffness that maximizes efficiency in all conditions. Fish are thought to solve this problem by using muscular activity to tune their body and fin stiffness in real-time. Inspired by fish, some recent robots sport polymer actuators, adjustable leaf springs, or artificial tendons that tune stiffness mechanically. Models and water channel tests are providing a theoretical framework for stiffness-tuning strategies that devices can implement. The strategies can be thought of as analogous to car transmissions, which allow users to improve efficiency by tuning gear ratio with driving speed. We provide an overview of the latest discoveries about (1) the propulsive benefits of flexibility, particularlytunableflexibility, and (2) the mechanisms and strategies that fish and fish-inspired robots use to tune stiffness while swimming.

Future Tail Tales: A Forward-Looking, Integrative Perspective on Tail Research

Synopsis Tails are a defining characteristic of chordates and show enormous diversity in function and shape. Although chordate tails share a common evolutionary and genetic-developmental origin, tails are extremely versatile in morphology and function. For example, tails can be short or long, thin or thick, and feathered or spiked, and they can be used for propulsion, communication, or balancing, and they mediate in predator-prey outcomes. Depending on the species of animal the tail is attached to, it can have extraordinarily multi-functional purposes. Despite its morphological diversity and broad functional roles, tails have not received similar scientific attention as, for example, the paired appendages such as legs or fins. This forward-looking review article is a first step toward interdisciplinary scientific synthesis in tail research. We discuss the importance of tail research in relation to five topics: (1) evolution and development, (2) regeneration, (3) functional morphology, (4) sensorimotor control, and (5) computational and physical models. Within each of these areas, we highlight areas of research and combinations of long-standing and new experimental approaches to move the field of tail research forward. To best advance a holistic understanding of tail evolution and function, it is imperative to embrace an interdisciplinary approach, re-integrating traditionally siloed fields around discussions on tail-related research.

Tunable stiffness enables fast and efficient swimming in fish-like robots

Fish maintain high swimming efficiencies over a wide range of speeds. A key to this achievement is their flexibility, yet even flexible robotic fish trail real fish in terms of performance. Here, we explore how fish leverage tunable flexibility by using their muscles to modulate the stiffness of their tails to achieve efficient swimming. We derived a model that explains how and why tuning stiffness affects performance. We show that to maximize efficiency, muscle tension should scale with swimming speed squared, offering a simple tuning strategy for fish-like robots. Tuning stiffness can double swimming efficiency at tuna-like frequencies and speeds (0 to 6 hertz; 0 to 2 body lengths per second). Energy savings increase with frequency, suggesting that high-frequency fish-like robots have the most to gain from tuning stiffness.

Automatic segmentation of fish midlines for optimizing robot design

While fish use continuous and flexible bodies to propel themselves, fish robots are often made from interconnected segments. How many segments do robots need to represent fish movements accurately? We propose a new method to automatically determine parsimonious robot models from actual fish data. We first identify key bending points (i.e., joint positions) along the body and then study the concerted movement of the segments so that the difference between actual fish and modelled bending kinematics is minimized. To demonstrate the utility of our method, we analyse the steady swimming kinematics of 10 morphologically distinct fish species. Broadly classified as sub-carangiform (e.g., rainbow trout) and carangiform (e.g., crevalle jack) swimmers, these species exhibit variations in the way they undulate when traditional parameters (including head and tail beat amplitudes, body wavelength and maximum curvature along the body) are considered. We show that five segments are sufficient to describe the kinematics with at least 99% accuracy. For optimal performance, segments should progressively get shorter towards the tail. We also show that locations where bending moments are applied vary among species, possibly because of differences in morphology. More specifically, we find that wider fish have shorter head segments. We discover that once bending points are factored in, the kinematics differences observed in these species collapse into a single undulatory pattern. The amplitude and timing of how body segments move entirely depend on their respective joint positions along the body. Head and body segments are also coupled in a timely manner, which depends on the position of the most anterior joint. Our findings provide a mechanistic understanding of how morphology relates to kinematics and highlight the importance of head control, which is often overlooked in current robot designs.

Tunabot Flex: a tuna-inspired robot with body flexibility improves high-performance swimming

Tunas are flexible, high-performance open ocean swimmers that operate at high frequencies to achieve high swimming speeds. Most fish-like robotic systems operate at low frequencies (≤3 Hz) resulting in low swim speeds (≤1.5 body lengths per second), and the cost of transport (COT) is often one to four orders of magnitude higher than that of tunas. Furthermore, the impact of body flexibility on high-performance fish swimming remains unknown. Here we design and test a research platform based on yellowfin tuna (Thunnus albacares) to investigate the role of body flexibility and to close the performance gap between robotic and biological systems. This single-motor platform, termed Tunabot Flex, measures 25.5 cm in length. Flexibility is varied through joints in the tail to produce three tested configurations. We find that increasing body flexibility improves self-propelled swimming speeds on average by 0.5 body lengths per second while reducing the minimum COT by 53%. The most flexible configuration swims 4.60 body lengths per second with a tail beat frequency of 8.0 Hz and a COT measuring 18.4 J kg^-1m^-1. We then compare these results in addition to the midline kinematics, stride length, and Strouhal number with yellowfin tuna data. The COT of Tunabot Flex's most flexible configuration is less than a half-order of magnitude greater than that of yellowfin tuna across all tested speeds. Tunabot Flex provides a new baseline for the development of future bio-inspired underwater vehicles that aim to explore a fish-like, high-performance space and close the gap between engineered robotic systems and fish swimming ability.

Fish-like three-dimensional swimming with an autonomous, multi-fin, and biomimetic robot

Fish migrate across considerable distances and exhibit remarkable agility to avoid predators and feed. Fish swimming performance and maneuverability remain unparalleled when compared to robotic systems, partly because previous work has focused on robots and flapping foil systems that are either big and complex, or tethered to external actuators and power sources. By contrast, we present a robot-the Finbot-that combines high degrees of autonomy, maneuverability, and biomimicry with miniature size (160 cm³). Thus, it is well-suited for controlled three-dimensional experiments on fish swimming in confined laboratory test beds. Finbot uses four independently controllable fins and sensory feedback for precise closed-loop underwater locomotion. Different caudal fins can be attached magnetically to reconfigure Finbot for swimming at top speed (122 mm s^-1≡ 1 BL s^-1) or minimal cost of transport (CoT = 8.2) at Strouhal numbers as low as 0.53. We conducted more than 150 experiments with 12 different caudal fins to measure three key characteristics of swimming fish: (i) linear speed-frequency relationships, (ii) U-shaped CoT, and (iii) reverse Kármán wakes (visualized with particle image velocimetry). More fish-like wakes appeared where the CoT was low. By replicating autonomous multi-fin fish-like swimming, Finbot narrows the gap between fish and fish-like robots and can address open questions in aquatic locomotion, such as optimized propulsion for new fish robots, or the hydrodynamic principles governing the energy savings in fish schools.

A Survey on Mechanical Solutions for Hybrid Mobile Robots

This paper presents a survey on mobile robots as systems that can move in different environments with walking, flying and swimming up to solutions that combine those capabilities. The peculiarities of these mobile robots are analyzed with significant examples as references and a specific case study is presented as from the direct experiences of the authors for the robotic platform HeritageBot, in applications within the frame of Cultural Heritage. The hybrid design of mobile robots is explained as integration of different technologies to achieve robotic systems with full mobility.

Advantages of aquatic animals as models for bio-inspired drones over present AUV technology

Robotic systems are becoming more ubiquitous, whether on land, in the air, or in water. In the aquatic realm, aquatic drones including ROVs (remotely operated vehicles) and AUVs (autonomous underwater vehicles) have opened new opportunities to investigate the ocean depths. However, these technologies have limitations related to shipboard support, programing, and functionality in complex marine environments. A new form of AUV is being developed to become operational. These drones are based on animal designs and capabilities. Biological AUVs (BAUVs) promise to improve performance in the varied environments of the ocean. Comparison of animal swimming performance with conventional AUVs and BAUVs demonstrates that natural systems still have swimming capabilities beyond the current state of AUV technology. However, the performances of aquatic animals with respect to swimming speed, efficiency, maneuverability, and stealth can serve as benchmarks to direct the development of bio-inspired AUV technology with enhanced capabilities.

Tuna robotics: A high-frequency experimental platform exploring the performance space of swimming fishes

Tuna and related scombrid fishes are high-performance swimmers that often operate at high frequencies, especially during behaviors such as escaping from predators or catching prey. This contrasts with most fish-like robotic systems that typically operate at low frequencies (< 2 hertz). To explore the high-frequency fish swimming performance space, we designed and tested a new platform based on yellowfin tuna (Thunnus albacares) and Atlantic mackerel (Scomber scombrus). Body kinematics, speed, and power were measured at increasing tail beat frequencies to quantify swimming performance and to study flow fields generated by the tail. Experimental analyses of freely swimming tuna and mackerel allow comparison with the tuna-like robotic system. The Tunabot (255 millimeters long) can achieve a maximum tail beat frequency of 15 hertz, which corresponds to a swimming speed of 4.0 body lengths per second. Comparison of midline kinematics between scombrid fish and the Tunabot shows good agreement over a wide range of frequencies, with the biggest discrepancy occurring at the caudal fin, primarily due to the rigid propulsor used in the robotic model. As frequency increases, cost of transport (COT) follows a fish-like U-shaped response with a minimum at ~1.6 body lengths per second. The Tunabot has a range of ~9.1 kilometers if it swims at 0.4 meter per second or ~4.2 kilometers at 1.0 meter per second, assuming a 10-watt-hour battery pack. These results highlight the capabilities of high-frequency biological swimming and lay the foundation to explore a fish-like performance space for bio-inspired underwater vehicles.

Swimming performance of a bio-inspired robotic vessel with undulating fin propulsion

Undulatory fin propulsion exhibits a high degree of maneuver control-an ideal feature for underwater vessels exploring complex environments. In this work, we developed and tested a self-contained, free-swimming robot with a single undulating fin running along the length of the robot, which controls both forward motion and directional maneuvers. We successfully replicated several maneuvers including forward swimming, reversed motion, diving, station-keeping and vertical swimming. For each maneuver, a series of experiments was performed as a function of fin frequency, wavelength and traveling wave direction to measure swimming velocities, orientation angles and mean power consumption. In addition, 3D flow fields were measured during forward swimming and station-keeping using volumetric particle image velocimetry (PIV). The efficiency for forward swimming was compared using three metrics: cost of transport, wave efficiency and Strouhal number (St). The results indicate that the cost of transport exhibits a V-shape trend with the minimum value at low swimming velocity. The robot reaches optimal wave efficiency and locomotor performance at a range of 0.2-0.4 St. Volumetric PIV data reveal the shed of vortex tubes generated by the fin during forward swimming and station keeping. For forward swimming, a series of vortex tubes are shed off the fin edge with a lateral and downward direction with respect to the longitudinal axis of the fin. For station keeping, flow measurements suggest that the vortex tubes are shed at the mid-section of the fin while the posterior and anterior segment of the vortex stay attached to the fin. These results agree with the previous vortex structures based on simulations and 2D PIV. The development of this vessel with high maneuverability and station keeping performance has applications for oceanography, coastal exploration, defense, the oil industry and other marine industries where operations are unsafe or impractical for divers or human-piloted vessels.

Robotics-inspired biology

For centuries, designers and engineers have looked to biology for inspiration. Biologically inspired robots are just one example of the application of knowledge of the natural world to engineering problems. However, recent work by biologists and interdisciplinary teams have flipped this approach, using robots and physical models to set the course for experiments on biological systems and to generate new hypotheses for biological research. We call this approach robotics-inspired biology; it involves performing experiments on robotic systems aimed at the discovery of new biological phenomena or generation of new hypotheses about how organisms function that can then be tested on living organisms. This new and exciting direction has emerged from the extensive use of physical models by biologists and is already making significant advances in the areas of biomechanics, locomotion, neuromechanics and sensorimotor control. Here, we provide an introduction and overview of robotics-inspired biology, describe two case studies and suggest several directions for the future of this exciting new research area.

The notochord in Atlantic salmon (Salmo salar L.) undergoes profound morphological and mechanical changes during development

We present the development of the notochord of the Atlantic salmon (Salmo salar L.), from early embryo to sexually mature fish. Over the salmon's lifespan, profound morphological changes occur. Cells and gross structures of the notochord reorganize twice. In the embryo, the volume of the notochord is dominated by large, vacuolated chordocytes; each cell can be modeled as a hydrostat organized into a larger cellular-hydrostat network, structurally bound together with desmosomes. After the embryo hatches and grows into a fry, vacuolated chordocytes disappear, replaced by extracellular lacunae. The formation of mineralized, segmental chordacentra stiffens the notochord and creates intervertebral joints, where tissue strain during lateral bending is now focused. As development proceeds towards the parr stage, a process of devacuolization and intracellular filament accumulation occur, forming highly dense, non-vacuolated chordocytes. As extracellular lacunae enlarge, they are enclosed by dense filamentous chordocytes that form transverse intervertebral septa, which are connected to the intervertebral ligaments, and a longitudinal notochordal strand. In the vertebral column of pelagic adults, large vacuolated chordocytes reappear; cells of this secondary population have a volume up to 19 000 times larger than the primary vacuolated chordocytes of the early notochord. In adults the lacunae have diminished in relative size. Hydrostatic pressure within the notochord increases significantly during growth, from 525 Pa in the alevins to 11 500 Pa in adults, at a rate of increase with total body length greater than that expected by static stress similarity. Pressure and morphometric measurements were combined to estimate the stress in the extracellular material of the notochordal sheath and intervertebral ligaments and the flexural stiffness of the axial skeleton. The functional significance of the morphological changes in the axial skeleton is discussed in relation to the different developmental stages and locomotor behavior changes over the lifespan of the fish.

Propulsive performance of an under-actuated robotic ribbon fin

Many aquatic animals propelled by elongated undulatory fins can perform complex maneuvers and swim with high efficiency at low speeds. In this propulsion, one or multiple waves travel along an elastic fin composed of flexible rays. In this study, we explore the potential benefits or disadvantages of passive fin motion based on the coupling of fluid-structure interactions and elasto-mechanical responses of the undulatory fin. The motivation is to understand how an under-actuated undulating fin can modify its active and passive fin motion to effectively control the hydrodynamic force and propulsive efficiency. We study the kinematics and propulsive performance of an under-actuated ribbon fin using a robotic device. During two experimental sets for fully-actuated fin and under-actuated fin respectively, we measured fin kinematics, surge forces and power consumption. Our results show that under-actuated fin can generate smaller thrust but consume less power comparing to a fully-actuated counterpart. The thrust generated by an under-actuated fin scales similarly to a fully-actuated fin-linear with the enclosed area and quadratic with the relative velocity. Power consumption scales with cube of lateral tangential velocity. Furthermore, we find that the under-actuated fin can keep the same propulsive efficiency as the fully-actuated fin at low relative velocities. This finding has profound implications to both natural swimmers and underwater vehicles using undulating fin-based propulsion, as it suggests that they can potentially exploit passive fin motion without decrementing propulsive efficiency. For underwater vehicles with undulatory fins, an under-actuated design can greatly simplify the mechanical design and control complexity of a versatile propulsion system.

On Design Mining: Coevolution and Surrogate Models

Design mining is the use of computational intelligence techniques to iteratively search and model the attribute space of physical objects evaluated directly through rapid prototyping to meet given objectives. It enables the exploitation of novel materials and processes without formal models or complex simulation. In this article, we focus upon the coevolutionary nature of the design process when it is decomposed into concurrent sub-design-threads due to the overall complexity of the task. Using an abstract, tunable model of coevolution, we consider strategies to sample subthread designs for whole-system testing and how best to construct and use surrogate models within the coevolutionary scenario. Drawing on our findings, we then describe the effective design of an array of six heterogeneous vertical-axis wind turbines.

Development of a vortex generator to perturb fish locomotion

Knowledge about the stiffness of fish fins, and whether stiffness is modulated during swimming, is important for understanding the mechanics of a fin's force production. However, the mechanical properties of fins have not been studied during natural swimming, in part because of a lack of instrumentation. To remedy this, a vortex generator was developed that produces traveling vortices of adjustable strength which can be used to perturb the fins of swimming fish. Experiments were conducted to understand how the generator's settings affected the resulting vortex rings. A variety of vortices (14-32 mm diameter traveling at 371-2155 mm s^-1) were produced that elicited adequate responses from the fish fins to help us to understand the fin's mechanical properties at various swimming speeds (0-350 mm s^-1).

Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions

During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m−1. Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion.

Surface microstructural features of scales in relation to toxic stress of Basic Violet-1

The present work deals with scanning electron microscopic (SEM) studies of the scales of Labeo rohita on exposure to lethal and sublethal doses of Basic Violet-1 (an important textile and hair colorant). The dye induced loosening of the scales and caused breakage and disorganization of lepidonts. Erosion of lepidonts occurred mostly in the fish exposed to 0.20 and 0.40 mg/L dye, during acute exposure and to 0.0225 and 0.045 mg/L dye, during the subchronic exposure. However, lepidonts were sloughed off from their sockets in 0.60 and 0.80 mg/L dye during acute exposure and in 0.09 mg/L dye during the subchronic exposure. Circuli, the base that provides anchorage to the lepidonts, got damaged, and tubercles responsible for coloration of a fish became atrophied with an increase in the duration of exposure. The results of the present investigation clearly indicated that exposure to Basic Violet-1 (BV-1) even at a concentration as low as 0.0225 mg was responsible for deleterious changes in the scale morphology of the test fish after 150 days of exposure. Similar changes were observed in the scales of the dead fish also. It can thus be suggested that this noninvasive technique is very helpful for evaluating the health status of an aquatic body. At the same time, the changes in ultramorphology of scales can act as an early indicator of the stress of very minute doses of dyes and even the scales of a dead fish can act as indicators of the untoward changes that would have occurred in the environment of the fish before death.

Evolutionary multiobjective design of a flexible caudal fin for robotic fish

Robotic fish accomplish swimming by deforming their bodies or other fin-like appendages. As an emerging class of embedded computing system, robotic fish are anticipated to play an important role in environmental monitoring, inspection of underwater structures, tracking of hazardous wastes and oil spills, and the study of live fish behaviors. While integration of flexible materials (into the fins and/or body) holds the promise of improved swimming performance (in terms of both speed and maneuverability) for these robots, such components also introduce significant design challenges due to the complex material mechanics and hydrodynamic interactions. The problem is further exacerbated by the need for the robots to meet multiple objectives (e.g., both speed and energy efficiency). In this paper, we propose an evolutionary multiobjective optimization approach to the design and control of a robotic fish with a flexible caudal fin. Specifically, we use the NSGA-II algorithm to investigate morphological and control parameter values that optimize swimming speed and power usage. Several evolved fin designs are validated experimentally with a small robotic fish, where fins of different stiffness values and sizes are printed with a multi-material 3D printer. Experimental results confirm the effectiveness of the proposed design approach in balancing the two competing objectives.

The effect of unmeasured confounders on the ability to estimate a true performance or selection gradient (and other partial regression coefficients)

Multiple regression of observational data is frequently used to infer causal effects. Partial regression coefficients are biased estimates of causal effects if unmeasured confounders are not in the regression model. The sensitivity of partial regression coefficients to omitted confounders is investigated with a Monte-Carlo simulation. A subset of causal traits is "measured" and their effects are estimated using ordinary least squares regression and compared to their expected values. Three major results are: (1) the error due to confounding is much larger than that due to sampling, especially with large samples, (2) confounding error shrinks trivially with sample size, and (3) small true effects are frequently estimated as large effects. Consequently, confidence intervals from regression are poor guides to the true intervals, especially with large sample sizes. The addition of a confounder to the model improves estimates only 55% of the time. Results are improved with complete knowledge of the rank order of causal effects but even with this omniscience, measured intervals are poor proxies for true intervals if there are many unmeasured confounders. The results suggest that only under very limited conditions can we have much confidence in the magnitude of partial regression coefficients as estimates of causal effects.

Metabolic and embryonic responses to terrestrial incubation of Fundulus grandis embryos across a temperature gradient

This study simulated terrestrial incubation and measured rates of embryogenesis, nitrogen elimination, heart rate, lactate production, maximum length of time a hatch could be delayed and developmental responses of terrestrially incubated Gulf killifish Fundulus grandis embryos at temperatures ranging from 20 to 30° C. Temperature had a positive relationship with rate of embryogenesis, but a negative relationship with extent of extended incubation. The 30° C treatment reached embryonic maturity 6 days before the 20° C treatment. Embryos hatched between intervals of 240 and 336, 144 and 288, 96 and 240 and 96 and 192 h after reaching developmental maturity for the 20, 23, 26 and 30° C treatments. Significantly higher concentrations of total nitrogen, in the form of ammonia and urea, were recorded in the 20 and 30° C treatments. While temperature significantly influenced lactate and ATP concentrations, no significant influence of time of incubation was detected. Terrestrial embryos displayed an ability to develop quickly during embryogenesis and prolong incubation for an extended period of time after reaching embryonic maturity. This adaptation may be a life-history trait used to minimize asynchronous hatching, cannibalism and cohort size heterogeneity.

Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion

An undulatory pattern of body bending in which waves pass along the body from head to tail is a major means of creating thrust in many fish species during steady locomotion. Analyses of live fish swimming have provided the foundation of our current understanding of undulatory locomotion, but our inability to experimentally manipulate key variables such as body length, flexural stiffness, and tailbeat frequency in freely-swimming fish has limited our ability to investigate a number of important features of undulatory propulsion. In this paper we use a robotic apparatus to create an undulatory wave in swimming passive flexible foils by creating a heave motion at their leading edge, and compare this motion to body bending patterns of bluegill sunfish (Lepomis macrochirus) and clown knifefish (Notopterus chitala). We found similar swimming speeds, Reynolds and Strouhal numbers, and patterns of curvature and shape between these fish and foils suggesting that passive flexible foils provide a useful model for understanding fish undulatory locomotion. We swam foils with different lengths, stiffnesses, and heave frequencies while measuring forces, torques, and hydrodynamics. From measured forces and torques we calculated thrust and power coefficients, work, and cost of transport for each foil. We found that increasing frequency and stiffness produced faster swimming speeds and more thrust. Increasing length had minimal impact on swimming speed, but had a large impact on Strouhal number, cost of transport, and thrust coefficient. Foils that were both stiff and long had the lowest cost of transport (in mJ m-1 g-1) at low cycle frequencies, and the ability to reach the highest speed at high cycle frequencies.

Robots in the service of animal behavior

As reading fiction can challenge us to better understand fact, using fake animals can sometimes serve as our best solution to understanding the behavior of real animals. The use of dummies, doppelgangers, fakes, and physical models have served to elicit behaviors in animal experiments since the early history of behavior studies, and, more recently, robotic animals have been employed by researchers to further coax behaviors from their study subjects. Here, we review the use of robots in the service of animal behavior, and describe in detail the production and use of one type of robot - "faux" frogs - to test female responses to multisensory courtship signals. The túngara frog (Physalaemus pustulosus) has been a study subject for investigating multimodal signaling, and we discuss the benefits and drawbacks of using the faux frogs we have designed, with the larger aim of inspiring other scientists to consider the appropriate application of physical models and robots in their research.

A robotic fish caudal fin: effects of stiffness and motor program on locomotor performance

We designed a robotic fish caudal fin with six individually moveable fin rays based on the tail of the bluegill sunfish, Lepomis macrochirus. Previous fish robotic tail designs have loosely resembled the caudal fin of fishes, but have not incorporated key biomechanical components such as fin rays that can be controlled to generate complex tail conformations and motion programs similar to those seen in the locomotor repertoire of live fishes. We used this robotic caudal fin to test for the effects of fin ray stiffness, frequency and motion program on the generation of thrust and lift forces. Five different sets of fin rays were constructed to be from 150 to 2000 times the stiffness of biological fin rays, appropriately scaled for the robotic caudal fin, which had linear dimensions approximately four times larger than those of adult bluegill sunfish. Five caudal fin motion programs were identified as kinematic features of swimming behaviors in live bluegill sunfish, and were used to program the kinematic repertoire: flat movement of the entire fin, cupping of the fin, W-shaped fin motion, fin undulation and rolling movements. The robotic fin was flapped at frequencies ranging from 0.5 to 2.4 Hz. All fin motions produced force in the thrust direction, and the cupping motion produced the most thrust in almost all cases. Only the undulatory motion produced lift force of similar magnitude to the thrust force. More compliant fin rays produced lower peak magnitude forces than the stiffer fin rays at the same frequency. Thrust and lift forces increased with increasing flapping frequency; thrust was maximized by the 500× stiffness fin rays and lift was maximized by the 1000× stiffness fin rays.

Bioinspirations: cell-inspired small-scale systems for enabling studies in experimental biomechanics

Biomechanical forces govern the behaviors of organisms and their environment and examining these behaviors to understand the underlying phenomena is an important challenge. One experimental approach for probing these interactions between organisms and their biomechanical environment uses biologically-inspired, artificial surrogates that reproduce organic mechanical systems. For the case of complex, multicellular organisms, robot surrogates have been particularly effective, such as in the analysis of the fins of fish and insects' wings. This biologically-inspired approach is also exciting when examining cell-scale responses as multicellular organisms' behavior is directly influenced by the integrated interactions of smaller-scale components (i.e., cells). In this review, we introduce the burgeoning field of engineering of artificial cells, which focuses on developing cell-scale entities replicating cellular behaviors. We describe both a bottom-up approach to constructing artificial cells, using molecular components to directly assemble artificial cells, as well as a top-down approach, in which living cells are encapsulated in a single entity whose behavior is determined by its constituent members. In particular, we discuss the potential role of these artificial cells as implantable controllers, designed to alter the mechanical behavior of a host organism. Eventually, artificial cells designed to function as small-scale controllers may help alter organisms' phenotypes.

Mechanical properties of a bio-inspired robotic knifefish with an undulatory propulsor

South American electric knifefish are a leading model system within neurobiology. Recent efforts have focused on understanding their biomechanics and relating this to their neural processing strategies. Knifefish swim by means of an undulatory fin that runs most of the length of their body, affixed to the belly. Propelling themselves with this fin enables them to keep their body relatively straight while swimming, enabling straightforward robotic implementation with a rigid hull. In this study, we examined the basic properties of undulatory swimming through use of a robot that was similar in some key respects to the knifefish. As we varied critical fin kinematic variables such as frequency, amplitude, and wavelength of sinusoidal traveling waves, we measured the force generated by the robot when it swam against a stationary sensor, and its velocity while swimming freely within a flow tunnel system. Our results show that there is an optimal operational region in the fin's kinematic parameter space. The optimal actuation parameters found for the robotic knifefish are similar to previously observed parameters for the black ghost knifefish, Apteronotus albifrons. Finally, we used our experimental results to show how the force generated by the robotic fin can be decomposed into thrust and drag terms. Our findings are useful for future bio-inspired underwater vehicles as well as for understanding the mechanics of knifefish swimming.

Go reconfigure: how fish change shape as they swim and evolve

The bodies of fish change shape over propulsive, behavioral, developmental, and evolutionary time scales, a general phenomenon that we call "reconfiguration". Undulatory, postural, and form-reconfiguration can be distinguished, studied independently, and examined in terms of mechanical interactions and evolutionary importance. Using a combination of live, swimming fishes and digital robotic fish that are autonomous and self-propelled, we examined the functional relation between undulatory and postural reconfiguration in forward swimming, backward swimming, and yaw turning. To probe how postural and form reconfiguration interact, the yaw turning of leopard sharks was examined using morphometric and kinematic analyses. To test how undulatory reconfiguration might evolve, the digital robotic fish were subjected to selection for enhanced performance in a simulated ecology in which each individual had to detect and move towards a food source. In addition to the general issue of reconfiguration, these investigations are united by the fact that the dynamics of undulatory and postural reconfigurations are predicted to be determined, in part, by the structural stiffness of the fish's body. Our method defines undulatory reconfiguration as the combined, point-by-point periodic motion of the body, leaving postural reconfiguration as the combined deviations from undulatory reconfiguration. While undulatory reconfiguration appears to be the sole or primary propulsive driver, postural reconfiguration may contribute to propulsion in hagfish and it is correlated with differences in forward, and backward, swimming in lamprey. Form reconfigures over developmental time in leopard sharks in a manner that is consistent with an allometric scaling theory in which structural stiffness of the body is held constant. However, correlation of a form proxy for structural stiffness of the body suggests that body stiffness may scale in order to limit maximum postural reconfiguration during routine yaw turns. When structural stiffness and undulatory frequency are modeled as determining the tail's undulatory wave speed, both factors evolve under selection for enhanced foraging behavior in the digital fish-like robots. The methods used in making these distinctions between kinds of reconfiguration have broad applicability in fish biology, especially for quantifying complex motor behaviors in the wild and for simulating selection on behavior that leads to directional evolution of functional phenotypes.

Vertebrae in compression: Mechanical behavior of arches and centra in the gray smooth-hound shark (Mustelus californicus)

In swimming sharks, vertebrae are subjected, in part, to compressive loads as axial muscles contract. We currently have no information about which vertebral elements, centra, arch cartilages, or both, actually bear compressive loads in cartilaginous vertebrae. To address this issue, the goal of this experiment was to determine the load-bearing ability of arch and centrum cartilages in compression, to determine the material properties of shark vertebrae, and to document fracture patterns in the centra with and without the arches. Intact vertebrae and vertebrae with the arch cartilages experimentally removed (centra alone) were subjected to compressive loading to failure at a single strain rate. The maximum compressive forces sustained by the vertebrae and the centra are statistically indistinguishable. Thus we conclude that under these testing conditions the arch does not bear appreciable loads. Independent evidence for this conclusion comes from the fact that vertebrae fail in compression at the centra, and not at the arches. Overall, the results of these mechanical tests suggest that the neural arches are not the primary load-bearing structure during axial compression.

Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems

Researchers studying aspects of locomotion or movement in biological and biomimetic systems commonly use video or stereo video recordings to quantify the behaviour of the system in question, often with an emphasis on measures of position, velocity and acceleration. However, despite the apparent simplicity of video analysis, it can require substantial investment of time and effort, even when performed with adequate software tools. This paper reviews the underlying principles of video and stereo video analysis as well as its automation and is accompanied by fully functional and freely available software implementation.

Fish biorobotics: kinematics and hydrodynamics of self-propulsion

As a result of years of research on the comparative biomechanics and physiology of moving through water, biologists and engineers have made considerable progress in understanding how animals moving underwater use their muscles to power movement, in describing body and appendage motion during propulsion, and in conducting experimental and computational analyses of fluid movement and attendant forces. But it is clear that substantial future progress in understanding aquatic propulsion will require new lines of attack. Recent years have seen the advent of one such new avenue that promises to greatly broaden the scope of intellectual opportunity available to researchers: the use of biorobotic models. In this paper we discuss, using aquatic propulsion in fishes as our focal example, how using robotic models can lead to new insights in the study of aquatic propulsion. We use two examples: (1) pectoral fin function, and (2) hydrodynamic interactions between dorsal and caudal fins. Pectoral fin function is characterized by considerable deformation of individual fin rays, as well as spanwise (along the length) and chordwise (across the fin) deformation and area change. The pectoral fin can generate thrust on both the outstroke and instroke. A robotic model of the pectoral fin replicates this result, and demonstrates the effect of altering stroke kinematics on the pattern of force production. The soft dorsal fin of fishes sheds a distinct vortex wake that dramatically alters incoming flow to the tail: the dorsal fin and caudal fin act as dual flapping foils in series. This design can be replicated with a dual-foil flapping robotic device that demonstrates this phenomenon and allows examination of regions of the flapping performance space not available to fishes. We show how the robotic flapping foil device can also be used to better understand the significance of flexible propulsive surfaces for locomotor performance. Finally we emphasize the utility of self-propelled robotic devices as a means of understanding how locomotor forces are generated, and review different conceptual designs for robotic models of aquatic propulsion.