Swimming Gaits Research Articles

Terrain following and applications: Caenorhabditis elegans swims along the floor using a bump and undulate strategy.

Nematodes such as Caenorhabditis elegans are heavier than water. When submerged in water, they settle to the bottom surface. Observations reveal that the animals do not lie flat on the bottom surface, but remain substantially suspended above the surface through continuous collisions with the surface, while maintaining their swimming gaits. Consequently, the swimming animals follow the bottom surface topography. When the bottom surface is inclined, the animals swim up or down along the incline. As the magnitude of the gravitational force can be easily estimated, this behaviour provides a convenient means to estimate the animal's propulsive thrust. The animals' tendency to follow the surface topography provides a means to control the swimmers' trajectories and direction of motion, which we demonstrate with a saw tooth-like ratchet that biases the animals to swim in a selected direction. The animals can also serve as surface topography probes since their residence time as a function of position provides information on surface features. Finally, we take advantage of surface following to construct a simple motility-based sorter that can sort animals based on genotype and state of health.

Modeling and simulation of fish swimming with active muscles

Our goal is to reproduce the key features of carangiform swimming by modeling muscle functioning using the notion of active distortions, thus emphasizing the kinematical role of muscle, the generation of movement, rather than the dynamical one, the production of force. This approach, already proposed to model the action of muscles in different contexts, is here tested again for the problem of developing an effective and reliable framework to model and simulate swimming. A proper undulatory movement of a fish-like body is reproduced by defining a pattern of distortions, tuned in both space and time, meant to model the muscles activation which produce the flexural motion of body fish; eventually, interactions with the surrounding water yields the desired thrust. Carangiform swimmers have a relatively inflexible anterior body section and a generally flat, flexible posterior section. Because of this configuration, undulations sent rearward along the body attain a significant amplitude only in the posterior section. We compare the performances of different swimming gaits, and we are able to find some important relations between key parameters such as frequencies, wavelength, tail amplitude, and the achieved swim velocity, or the generated thrust, which summarize the swimming performance. In particular, an interesting relation is found between the Strouhal number and the wavelength of muscles activation. We highlight the muscle function during fish locomotion describing the activation of muscles and the relation between the force production and the shortening–lengthening cycle of muscle. We found a great accordance between results and empirical relations, giving an implicit validation of our models.

From cineradiography to biorobots: an approach for designing robots to emulate and study animal locomotion.

Robots are increasingly used as scientific tools to investigate animal locomotion. However, designing a robot that properly emulates the kinematic and dynamic properties of an animal is difficult because of the complexity of musculoskeletal systems and the limitations of current robotics technology. Here, we propose a design process that combines high-speed cineradiography, optimization, dynamic scaling, three-dimensional printing, high-end servomotors and a tailored dry-suit to construct Pleurobot: a salamander-like robot that closely mimics its biological counterpart, Pleurodeles waltl Our previous robots helped us test and confirm hypotheses on the interaction between the locomotor neuronal networks of the limbs and the spine to generate basic swimming and walking gaits. With Pleurobot, we demonstrate a design process that will enable studies of richer motor skills in salamanders. In particular, we are interested in how these richer motor skills can be obtained by extending our spinal cord models with the addition of more descending pathways and more detailed limb central pattern generator networks. Pleurobot is a dynamically scaled amphibious salamander robot with a large number of actuated degrees of freedom (DOFs: 27 in total). Because of our design process, the robot can capture most of the animal's DOFs and range of motion, especially at the limbs. We demonstrate the robot's abilities by imposing raw kinematic data, extracted from X-ray videos, to the robot's joints for basic locomotor behaviours in water and on land. The robot closely matches the behaviour of the animal in terms of relative forward speeds and lateral displacements. Ground reaction forces during walking also resemble those of the animal. Based on our results, we anticipate that future studies on richer motor skills in salamanders will highly benefit from Pleurobot's design.

Turtle mimetic soft robot with two swimming gaits

This paper presents a biomimetic turtle flipper actuator consisting of a shape memory alloy composite structure for implementation in a turtle-inspired autonomous underwater vehicle. Based on the analysis of the Chelonia mydas, the flipper actuator was divided into three segments containing a scaffold structure fabricated using a 3D printer. According to the filament stacking sequence of the scaffold structure in the actuator, different actuating motions can be realized and three different types of scaffold structures were proposed to replicate the motion of the different segments of the flipper of the Chelonia mydas. This flipper actuator can mimic the continuous deformation of the forelimb of Chelonia mydas which could not be realized in previous motor based robot. This actuator can also produce two distinct motions that correspond to the two different swimming gaits of the Chelonia mydas, which are the routine and vigorous swimming gaits, by changing the applied current sequence of the SMA wires embedded in the flipper actuator. The generated thrust and the swimming efficiency in each swimming gait of the flipper actuator were measured and the results show that the vigorous gait has a higher thrust but a relatively lower swimming efficiency than the routine gait. The flipper actuator was implemented in a biomimetic turtle robot, and its average swimming speed in the routine and vigorous gaits were measured with the vigorous gait being capable of reaching a maximum speed of 11.5 mm s−1.

Post-tagging behaviour and habitat use in shortnose sturgeon measured with high-frequency accelerometer and PSATs

External tagging of fish using pop-up satellite tags (PSATs) can cause trauma and stress associated with capture, handling, tagging injury and tag placement that impedes body function and mobility, and these can affect the behaviour of the fish. We measured short-term (days) post-release behavioural response of estuarine shortnose sturgeon to tagging with PSATs and high-frequency accelerometers. We developed a secure, low-noise attachment method for high-resolution (50 Hz) accelerometer PSATs in shortnose sturgeon. The archived time series of acceleration was used to determine sturgeon post-tagging activity, estimate swimming speed, erratic behaviour and behavioural clusters in relation to ambient light level and temperature, depth and tidal flow. Short-term (hours) post-release response was characterized by resting periods on the river bottom and decreased swimming activity that was associated with individual-specific modulations in the swimming gait and high-energy burst acceleration movements. Locomotion routines suggested a relation to tidal flow, yet the short-term time series did not allow for routine movements to be classified. The approach used provides a useful method of revealing behavioural modifications during the post-release recovery period of PSAT-tagged fish. We discuss how short-term (acute) effects on behaviour and potential longer-term (chronic) effects on survival are especially relevant in tagging studies.

The effect of gait on swimming in viscoelastic fluids

In this paper, we give formulas for the swimming of simplified two-dimensional bodies in complex fluids using the reciprocal theorem. By way of these formulas we calculate the swimming velocity due to small-amplitude deformations on the simplest of these bodies, a two-dimensional sheet, to explore general conditions on the swimming gait under which the sheet may move faster, or slower, in a viscoelastic fluid compared to a Newtonian fluid. We show that in general, for small amplitude deformations, a speed increase can only be realized by multiple deformation modes in contrast to slip flows. Additionally, we show that a change in swimming speed is directly due to a change in thrust generated by the swimmer.

Swimming Robots Have Scaling Laws, Too

Aquatic animals of vastly different size show a simple relationship between swimming speed and body kinematics. Swimming robots, whose morphology and gaits are inspired by those animals, are not an exception.

ITAG: an eco-sensor for fine-scale behavioral measurements of soft-bodied marine invertebrates

Soft-bodied marine invertebrates comprise a keystone component of ocean ecosystems; however, we know little of their behaviors and physiological responses within their natural habitat. Quantifying ocean conditions and measuring organismal responses to the physical environment is vital to understanding the species or ecosystem-level influences of a changing ocean. Here we describe a novel, soft-bodied invertebrate eco-sensor tag (the ITAG), its trial attachments to squid and jellyfish, and the fine-scale behavioral measurements recorded on captive animals. Tags were deployed on five jellyfish (Aurelia aurita) and eight squid (Loligo forbesi) in laboratory conditions for up to 24 h. Using concurrent video and tag data, movement signatures for specific behaviors were identified. These behaviors included straight swimming (for jellyfish), and finning, jetting, direction reversal and turning (for squid). Overall activity levels were quantified using the root-mean-squared magnitude of acceleration, and finning was found to be the dominant squid swimming gait during captive squid experiments. External light sensors on the ITAG were used to compare squid swimming activity relative to ambient light across a ca. 20-h trial. The deployments revealed that while swimming was continuous for captive squid, energetically costly swimming behaviors (i.e., jetting and rapid direction reversals) occurred infrequently. These data reflect the usefulness of the ITAG to study trade-offs between behavior and energy expenditure in captive and wild animals. These data demonstrate that eco-sensors with sufficiently high sampling rates can be applied to quantify behavior of soft-bodied taxa and changes in behavior due to interactions with the surrounding environment. The methods and tool described here open the door for substantial lab and field-based measurements of fine-scale behavior, physiology, and concurrent environmental parameters that will inform fisheries management, and elucidate the ecology of these important keystone taxa.

Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method

We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection (104–105) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.

Self-entrainment to optimal gaits of an underactuated biomimetic swimming robot using adaptive frequency oscillators.

Underactuated compliant swimming robots are characterized by a simple mechanical structure, capable to mimic the body undulation of many fish species. One of the design issue for these robots is the generation and control of best performing swimming gaits. In this paper we propose a new controller, based on AFO oscillators, to address this issue. After analyzing the effects of the motion on the robot natural frequencies, we show that the closed loop system is able to generate self-sustained oscillations, at a characteristic frequency, while maximizing swimming velocity.

A Data-driven Motion Control Approach for a Robotic Fish

In this paper we propose a data-driven motion control approach for a biomimetic robotic fish. The task of the motion control is to achieve desired motion by means of controlling the fish-like swimming gaits of the robot. Due to the complexity of hydrodynamics, it is impossible to derive an analytic model that can precisely describe the interaction between the robotic fish and surrounding water during motion. To address the lack of the robotic model, we explore data-based modeling and control design methods. First, through biomimetic learning from real fish motion data, a General Internal Model (GIM) is established. GIM translates fish undulatory body motion into robotic joint movement; associates the fish gait patterns, such as cruise and turning, with corresponding joint coordination; and adjusts the robotic velocity by GIM parameters. Second, by collecting robotic motion data at a set of operating points, we obtain the quantitative mapping from GIM tuning parameters to robotic speed. Third, applying the quantitative mapping and using GIM parameters as manipulating variables, a feedforward control is computed according to the desired speed, which greatly expedites the initial movement of the robotic fish. Fourth, Proportional-Integral-Derivative (PID) is employed as feedback control, together with an inverse mapping that compensates for the nonlinearity appeared in the quantitative mapping. Fifth, modified Iterative Feedback Tuning (IFT) is developed as an appropriate data-driven tuning approach to determine controller gains. By switching between feedforward and feedback, the motion performance is improved. Finally, real-time control of robotic fish is implemented on a two-joint platform, and two representative swimming gaits, namely “cruise” and “cruise in turning”, are achieved.

Predicting propulsive forces using distributed sensors in a compliant, high DOF, robotic fin

Engineered robotic fins have adapted principles of propulsion from bony-finned fish, using spatially-varying compliance and complex kinematics to produce and control the fin’s propulsive force through time. While methods of force production are well understood, few models exist to predict the propulsive forces of a compliant, high degree of freedom, robotic fin as it moves through fluid. Inspired by evidence that the bluegill sunfish (Lepomis macrochirus) has bending sensation in its pectoral fins, the objective of this study is to understand how sensors distributed within a compliant robotic fin can be used to estimate and predict the fin’s propulsive force. A biorobotic model of a bluegill sunfish pectoral fin was instrumented with pressure and bending sensors at multiple locations. Experiments with the robotic fin were executed that varied the swimming gait, flapping frequency, stroke phase, and fin stiffness to understand the forces and sensory measures that occur during swimming. A convolution-based, multi-input-single-output (MISO) model was selected to model and study the relationships between sensory data and propulsive force. Subsets of sensory data were studied to determine which sensor modalities and sensor placement locations resulted in the best force predictions. The propulsive forces of the fin were accurately predicted using the linear MISO model on intrinsic sensory data. Bending sensation was more effective than pressure sensation for predicting propulsive forces, and the importance of bending sensation was consistent with several results in biology and engineering studies. It was important to have a spatial distribution of sensors and multiple sensory modalities in order to predict forces across large changes to dynamics. The relationship between propulsive forces and intrinsic sensory measures is complex, and good models should allow for temporal lags between forces and sensory data, changes to the model within a fin stroke, and changes to the model through gait transitions.

Octopus-inspired multi-arm robotic swimming

The outstanding locomotor and manipulation characteristics of the octopus have recently inspired the development, by our group, of multi-functional robotic swimmers, featuring both manipulation and locomotion capabilities, which could be of significant engineering interest in underwater applications. During its little-studied arm-swimming behavior, as opposed to the better known jetting via the siphon, the animal appears to generate considerable propulsive thrust and rapid acceleration, predominantly employing movements of its arms. In this work, we capture the fundamental characteristics of the corresponding complex pattern of arm motion by a sculling profile, involving a fast power stroke and a slow recovery stroke. We investigate the propulsive capabilities of a multi-arm robotic system under various swimming gaits, namely patterns of arm coordination, which achieve the generation of forward, as well as backward, propulsion and turning. A lumped-element model of the robotic swimmer, which considers arm compliance and the interaction with the aquatic environment, was used to study the characteristics of these gaits, the effect of various kinematic parameters on propulsion, and the generation of complex trajectories. This investigation focuses on relatively high-stiffness arms. Experiments employing a compliant-body robotic prototype swimmer with eight compliant arms, all made of polyurethane, inside a water tank, successfully demonstrated this novel mode of underwater propulsion. Speeds of up to 0.26 body lengths per second (approximately 100 mm s−1), and propulsive forces of up to 3.5 N were achieved, with a non-dimensional cost of transport of 1.42 with all eight arms and of 0.9 with only two active arms. The experiments confirmed the computational results and verified the multi-arm maneuverability and simultaneous object grasping capability of such systems.

Gait switches in deep-diving beaked whales: biomechanical strategies for long-duration dives

Diving animals modulate their swimming gaits to promote locomotor efficiency and so enable longer, more productive dives. Beaked whales perform extremely long and deep foraging dives that probably exceed aerobic capacities for some species. Here, we use biomechanical data from suction-cup tags attached to three species of beaked whales (Mesoplodon densirostris, N=10; Ziphius cavirostris, N=9; and Hyperoodon ampullatus, N=2) to characterize their swimming gaits. In addition to continuous stroking and stroke-and-glide gaits described for other diving mammals, all whales produced occasional fluke-strokes with distinctly larger dorso-ventral acceleration, which we termed 'type-B' strokes. These high-power strokes occurred almost exclusively during deep dive ascents as part of a novel mixed gait. To quantify body rotations and specific acceleration generated during strokes we adapted a kinematic method combining data from two sensors in the tag. Body rotations estimated with high-rate magnetometer data were subtracted from accelerometer data to estimate the resulting surge and heave accelerations. Using this method, we show that stroke duration, rotation angle and acceleration were bi-modal for these species, with B-strokes having 76% of the duration, 52% larger body rotation and four times more surge than normal strokes. The additional acceleration of B-strokes did not lead to faster ascents, but rather enabled brief glides, which may improve the overall efficiency of this gait. Their occurrence towards the end of long dives leads us to propose that B-strokes may recruit fast-twitch fibres that comprise ∼80% of swimming muscles in Blainville's beaked whales, thus prolonging foraging time at depth.

Gait and speed selection in slender inertial swimmers.

Inertial swimmers use flexural movements to push water and generate thrust. We quantify this dynamical process for a slender body in a fluid by accounting for passive elasticity and hydrodynamics and active muscular force generation and proprioception. Our coupled elastohydrodynamic model takes the form of a nonlinear eigenvalue problem for the swimming speed and locomotion gait. The solution of this problem shows that swimmers use quantized resonant interactions with the fluid environment to enhance speed and efficiency. Thus, a fish is like an optimized diode that converts a prescribed alternating transverse motion to forward motion. Our results also allow for a broad comparative view of swimming locomotion and provide a mechanistic basis for the empirical relation linking the swimmer's speed U, length L, and tail beat frequency f, given by U/L ~ f [Bainbridge R (1958) J Exp Biol 35:109-133]. Furthermore, we show that a simple form of proprioceptive sensory feedback, wherein local muscle activation is function of body curvature, suffices to drive elastic instabilities associated with thrust production and leads to a spontaneous swimming gait without the need for a central pattern generator. Taken together, our results provide a simple mechanistic view of swimming consistent with natural observations and suggest ways to engineer artificial swimmers for optimal performance.

Design and Construction of a Specialised Biomimetic Robot in Multiple Swimming Gaits

Efficient cruising, manoeuvrability and noiseless performance of fish robots have been attracting people in various scientific realms. Accordingly, a number of fish robots are designed and fabricated so far. However, the existing robots are only capable of one gait of locomotion. This deficiency is addressed by UC-Ika 2 with multiple gaits of locomotion including cruising and manoeuvring that are inspired from two different fishes. This paper aims at presenting the design and fabrication process of UC-Ika 2. The swimming performance of the robot is tested and compared with its previous version UC-Ika 1.

Free-swimming northern elephant seals have low field metabolic rates that are sensitive to an increased cost of transport.

Widely ranging marine predators often adopt stereotyped, energy-saving behaviours to minimize the energetic cost of transport while maximizing energy gain. Environmental and anthropogenic disturbances can disrupt energy balance by prompting avoidance behaviours that increase transport costs, thereby decreasing foraging efficiency. We examined the ability of 12 free-ranging, juvenile northern elephant seals (Mirounga angustirostris) to mitigate the effects of experimentally increased transport costs by modifying their behaviour and/or energy use in a compensatory manner. Under normal locomotion, elephant seals had low energy requirements (106.5±28.2 kJ kg(-1) day(-1)), approaching or even falling below predictions of basal requirements. Seals responded to a small increase in locomotion costs by spending more time resting between dives (149±44 s) compared with matched control treatments (102±11 s; P<0.01). Despite incurred costs, most other dive and transit behaviours were conserved across treatments, including fixed, rhythmic swimming gaits. Because of this, and because each flipper stroke had a predictable effect on total costs (P<0.001), total energy expenditure was strongly correlated with time spent at sea under both treatments (P<0.0001). These results suggest that transiting elephant seals have a limited capacity to modify their locomotory behaviour without increasing their transport costs. Based on this, we conclude that elephant seals and other ocean predators occupying similar niches may be particularly sensitive to increased transport costs incurred when avoiding unanticipated disturbances.

Gait synchronization in Caenorhabditis elegans.

Collective motion is observed in swarms of swimmers of various sizes, ranging from self-propelled nanoparticles to fish. The mechanisms that govern interactions among individuals are debated, and vary from one species to another. Although the interactions among relatively large animals, such as fish, are controlled by their nervous systems, the interactions among microorganisms, which lack nervous systems, are controlled through physical and chemical pathways. Little is known, however, regarding the mechanism of collective movements in microscopic organisms with nervous systems. To attempt to remedy this, we studied collective swimming behavior in the nematode Caenorhabditis elegans, a microorganism with a compact nervous system. We evaluated the contributions of hydrodynamic forces, contact forces, and mechanosensory input to the interactions among individuals. We devised an experiment to examine pair interactions as a function of the distance between the animals and observed that gait synchronization occurred only when the animals were in close proximity, independent of genes required for mechanosensation. Our measurements and simulations indicate that steric hindrance is the dominant factor responsible for motion synchronization in C. elegans, and that hydrodynamic interactions and genotype do not play a significant role. We infer that a similar mechanism may apply to other microscopic swimming organisms and self-propelled particles.

On-line Optimization of Biomimetic Undulatory Swimming by an Experiment-based Approach

AbstractAn experiment-based approach is proposed to improve the performance of biomimetic undulatory locomotion through on-line optimization. The approach is implemented through two steps: (1) the generation of coordinated swimming gaits by artificial Central Pattern Generators (CPGs); (2) an on-line searching of optimal parameter sets for the CPG model using Genetic Algorithm (GA). The effectiveness of the approach is demonstrated in the optimization of swimming speed and energy efficiency for a biomimetic fin propulsor. To evaluate how well the input energy is converted into the kinetic energy of the propulsor, an energy-efficiency index is presented and utilized as a feedback to regulate the on-line searching with a closed-loop swimming control. Experiments were conducted on propulsor prototypes with different fin segments and the optimal swimming patterns were found separately. Comparisons of results show that the optimal curvature of undulatory propulsor, which might have different shapes depending on the actual prototype design and control scheme. It is also found that the propulsor with six fin segments, is preferable because of higher speed and lower energy efficiency.

CPG-based Sensory Feedback Control for Bio-inspired Multimodal Swimming

Sensory feedback plays a very significant role in the generation of diverse and stable movements for animals. In this paper we describe our effort to develop a Central Pattern Generator (CPG)-based sensory feedback control for the creation of multimodal swimming for a multi-articulated robotic fish in the context of neurocomputing. The proposed control strategy is composed of two phases: the upper decision-making and the automatic adjustment. According to the upper control commands and the sensory inputs, different swimming gaits are determined by a finite state machine algorithm. At the same time, the sensory feedback is exploited to shape the CPG coupling forms and control parameters. In the automatic adjustment phase, the CPG model with sensory feedback will adapt the environment autonomously. Simulation and underwater tests are further conducted to verify the presented control scheme. It is found that the CPG-based sensory feedback control method can effectively improve the manoeuvrability and adaptability of the robotic fish in water.