Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model

Educational Soft Underwater Robot with an Electromagnetic Actuation

As demonstrated by the Soft Robotics Toolkit Platform, compliant robotics pose an exciting educational opportunity. Underwater robotics using soft undulating fins is an expansive research topic with applications such as exploration of underwater life or replicating 3d swarm behavior. To make this research area accessible for education we developed Educational Soft Underwater Robot with Electromagnetic Actuation (ESURMA), a humanoid soft underwater robot. We achieved advances in simplicity, modularity, and performance by implementing electromagnetic actuation into the caudal fin. An electromagnet, including electronics, is placed in a waterproof housing, and permanent magnets are embedded in a soft silicone cast tail. The force from their magnetic interaction results in a bending movement of the tail. The magnetic actuation is simple to implement and requires no mechanical connection between the actuated component and the electrically controlled coil. This enables robust waterproofing and makes the device fully modular. Thanks to the direct and immediate transmission of force, experimental flapping frequencies of 14 Hz were achieved, an order of magnitude higher compared to pneumatically actuated tails. The completely silent actuation of the caudal fin enables a maximum swimming speed of 14.3 cm/s. With its humanoid shape, modular composition, and cost efficiency ESURMA represents an attractive platform for education and demonstrates an alternative method of actuating soft structures.

Recent progress on underwater soft robots: adhesion, grabbing, actuating, and sensing

The research on biomimetic robots, especially soft robots with flexible materials as the main structure, is constantly being explored. It integrates multi-disciplinary content, such as bionics, material science, mechatronics engineering, and control theory, and belongs to the cross-disciplinary field related to mechanical bionics and biological manufacturing. With the continuous development of various related disciplines, this area has become a hot research field. Particularly with the development of practical technologies such as 3D printing technology, shape memory alloy, piezoelectric materials, and hydrogels at the present stage, the functions and forms of soft robots are constantly being further developed, and a variety of new soft robots keep emerging. Soft robots, combined with their own materials or structural characteristics of large deformation, have almost unlimited degrees of freedom (DoF) compared with rigid robots, which also provide a more reliable structural basis for soft robots to adapt to the natural environment. Therefore, soft robots will have extremely strong adaptability in some special conditions. As a type of robot made of flexible materials, the changeable pose structure of soft robots is especially suitable for the large application environment of the ocean. Soft robots working underwater can better mimic the movement characteristics of marine life in the hope of achieving more complex underwater tasks. The main focus of this paper is to classify different types of underwater organisms according to their common motion modes, focusing on the achievements of some bionic mechanisms in different functional fields that have imitated various motion modes underwater in recent years (e.g., the underwater sucking glove, the underwater Gripper, and the self-powered soft robot). The development of various task types (e.g., grasping, adhesive, driving or swimming, and sensing functions) and mechanism realization forms of the underwater soft robot are described based on this article.

Computational Study of Stiffness-Tuning Strategies in Anguilliform Fish

Biological evidence demonstrates that fish can tune their body stiffness to improve thrust and efficiency during swimming locomotion. However, the stiffness-tuning strategies that maximize swimming speed or efficiency are still unclear. In the present study, a musculo-skeletal model of anguilliform fish is developed to study the properties of variable stiffness, in which the planar serial-parallel mechanism is used to model the body structure. The calcium ion model is adopted to simulate muscular activities and generate muscle force. Further, the relations among the forward speed, the swimming efficiency, and Young's modulus of the fish body are investigated. The results show that for certain body stiffness, the swimming speed and efficiency are increased with the tail-beat frequency until reaching the maximum value and then decreased. The peak speed and efficiency are also increased with the amplitude of muscle actuation. Anguilliform fish tend to vary their body stiffness to improve the swimming speed and efficiency at a high tail-beat frequency or small amplitude of muscle actuation. Furthermore, the midline motions of anguilliform fish are analyzed by the complex orthogonal decomposition (COD) method, and the discussions of fish motions associated with the variable body stiffness and the tail-beat frequency are also presented. Overall, the optimal swimming performance of anguilliform fish benefits from the matching relationships among the muscle actuation, the body stiffness, and the tail-beat frequency.

Experiment for Effect of Attack Angle and Environmental Condition on Hydrodynamics of Near-Surface Swimming Fish-Like Robot

Fish-like robot is a special autonomous underwater vehicle with broad application prospects. Some previous studies concentrated on the hydrodynamics of free-swimming fish-like robots. But the hydrodynamic performance of fish-like robot swimming with a tilt angle in constrained space has not been well studied, and the influence of environmental wave and current on its is also still unclear. In this paper, the experiment devices, including a physical fish-like robot, a hydrodynamics measurement platform, and a six-axis force sensor, are used to study the effect of attack angle and environmental condition on the hydrodynamics of near-surface swimming fish-like robot. Nine attack angles, five oscillating amplitudes, and three environmental conditions are analyzed in the experiments. It shows that thrust force decreases when caudal fin passes above water surface, but the increased difference between gravity force and buoyancy force will compensate the decreased force generated by caudal fin when fish-like robot swims with certain dive angle. The extra reaction force generated by solid bottom boundary will promote the thrust force and vertical force. The surface water wave condition or surface water current condition also has obvious effects on hydrodynamic performance. This paper provides a new perspective to the research on the hydrodynamic performance of fish-like robot and will do favor in the development of fish-like robot.

Tail-stiffness optimization for a flexible robotic fish

Undulation regulation in a robotic fish propelled by a passive flexible tail is more similar to that of a natural fish than with a rigid tail, owing to the smooth curvature of the flexible tail. Moreover, it has been observed that fish change the stiffness of their bodies to adapt to various swimming states. Inspired by this, a stiffness optimization scheme is explored for a novel elastic tail, which can improve the performance of the robotic fish. Spring steels are used as passive flexible joints of the fishtail; these can be easily expanded into multi-joint structures and the joint stiffness can be altered by changing the joint size. In this study, the Lagrangian dynamic method is employed to establish a dynamic model of the robotic fish in which passive flexible joints are simplified by a pseudo-rigid-body model. In addition, the hydrodynamics of the head and tail are analyzed using the simplified Morison equation and quasi-steady wing theory, respectively. Furthermore, to determine unknown hydrodynamic parameters in the dynamic model, a parameter identification method is applied. The results show that the identified simulation speeds fit the experimental speeds well within a wide range of stiffness values. Finally, to improve performance, the influence of joint stiffness and frequency on swimming speed is investigated based on the identified dynamic model. At each frequency, the optimal joint stiffness distribution is one that reduces the stiffness from the front to the rear. At the maximum driving frequency of 2.5 Hz, the optimal swimming speed is 0.3 body lengths per second, higher than that when rigid joints are used.

Thrust Improvement of a Biomimetic Robotic Fish by Using a Deformable Caudal Fin

In nature, live fish has various deformable fins which are capable to promote the swimming speed, efficiency, stability, and thrust generation. However, this feature is rarely possessed by current man-made biomimetic robotic fishes. In this paper, a novel deformable caudal fin platform is proposed to improve thrust generation of biomimetic robotic fish. First, the design of the deformable caudal fin is given, which includes a servo motor, a gear-based transmission mechanism, fin bones, and silica membrane. Second, an improved Central Pattern Generator (CPG) model was developed to coordinately control the flapping of the tail and the deformation of the caudal fin. More specifically, three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, instant mode, of the caudal fin are investigated. Third, extensive experiments are conducted to explore the effects of deformation of the caudal fin on the thrust generation of the biomimetic robotic fish. It was found that the instant mode of the caudal fin has the largest thrust, which sees a 27.5% improvement compared to the conventional nondeformable mode, followed by the sinusoidal-based mode, which also sees an 18.2% improvement. This work provides a novel way to design and control the deformation of the caudal fin, which sheds light on the development of high-performance biomimetic robotic fish.

A fish-like soft-robotic model generates a diversity of swimming patterns

Fish display a versatile array of swimming patterns, and frequently demonstrate the ability to switch between these patterns altering kinematics as necessary. Many hard and soft robotic systems have sought to understand a variety of aspects pertaining to undulatory swimming, but most have been built to focus solely on a subset of those swimming patterns. We have expanded upon a previous soft robotic model, the pneufish, so that it can now simulate a variety of swimming patterns, much like a real fish. We explore the performance space available for this longer soft robotic model, which we call the quad-pneufish, with particular attention to the effects on lateral forces and z-torques produced during locomotion. We show that the quad-pneufish is capable of achieving a variety of midline patterns - including more realistic, fish-like patterns - and introducing a slight amount of co-activation between the left and right sides maintains forward thrust while decreasing lateral forces, indicating an increase in swimming efficiency. Robotic systems that are capable of producing an array of swimming movement patterns hold promise as experimental platforms for studying the diversity of fish locomotor patterns.

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.

A Shift from Efficiency to Adaptability: Recent Progress in Biomimetic Interactive Soft Robotics in Wet Environments

Research field of soft robotics develops exponentially since it opens up many imaginations, such as human-interactive robot, wearable robots, and transformable robots in unpredictable environments. Wet environments such as sea and in vivo represent dynamic and unstructured environments that adaptive soft robots can reach their potentials. Recent progresses in soft hybridized robotics performing tasks underwater herald a diversity of interactive soft robotics in wet environments. Here, the development of soft robots in wet environments is reviewed. The authors recapitulate biomimetic inspirations, recent advances in soft matter materials, representative fabrication techniques, system integration, and exemplary functions for underwater soft robots. The authors consider the key challenges the field faces in engineering material, software, and hardware that can bring highly intelligent soft robots into real world.

A fluid-driven soft robotic fish inspired by fish muscle architecture

Artificial fish-like robots developed to date often focus on the external morphology of fish and have rarely addressed the contribution of the structure and morphology of biological muscle. However, biological studies have proven that fish utilize the contraction of muscle fibers to drive the protective flexible connective tissue to swim. This paper introduces a pneumatic silicone structure prototype inspired by the red muscle system of fish and applies it to the fish-like robot named Flexi-Tuna. The key innovation is to make the fluid-driven units simulate the red muscle fiber bundles of fish and embed them into a flexible tuna-like matrix. The driving units act as muscle fibers to generate active contraction force, and the flexible matrix as connective tissue to generate passive deformation. Applying alternant pressure to the driving units can produce a bending moment, causing the tail to swing. As a result, the structural design of Flexi-Tuna has excellent bearing capacity compared with the traditional cavity-type and keeps the body smooth. On this basis, a general method is proposed for modeling the fish-like robot based on the independent analysis of the active and passive body, providing a foundation for Flexi-Tuna's size design. Followed by the robot's static and underwater dynamic tests, we used finite element static analysis and fluid numerical simulation to compare the results. The experimental results showed that the maximum swing angle of the tuna-like robot reached 20°, and the maximum thrust reached 0.185 N at the optimum frequency of 3.5 Hz. In this study, we designed a unique system that matches the functional level of biological muscles. As a result, we realized the application of fluid-driven artificial muscle to bionic fish and expanded new ideas for the structural design of flexible bionic fish.

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.

Testing the effects of body depth on fish maneuverability via robophysical models

Fish show a wide diversity of body shapes which affect many aspects of their biology, including swimming and feeding performance, and defense from predators. Deep laterally compressed bodies are particularly common, and have evolved multiple times in different families. Functional hypotheses that explain these trends include predator defense and increased maneuverability. While there is strong evidence that increasing body depth helps fish avoid gape-limited predators, the evidence that body shape increases a fish's maneuverability is ambiguous. We used a two-pronged approach to explore the effects of body shape on the control of maneuvers using both live fish and a robotic model that allowed us to independently vary body shape. We captured ventral video of two tetra species (Gymnocorymbus ternetziandAphyocharax anisitsi) performing a wide range of maneuvers to confirm that both species of live fish utilize fundamentally similar body deformations to execute a turn, despite their different body depths. Both species use a propagating 'pulse' of midline curvature that is qualitatively similar to prior studies and displayed similar trends in the relationships between body kinematics and performance. We then tested the robotic model's maneuverability, defined as the total heading change and maximum centripetal acceleration generated during a single pulse, at a range of different input kinematics across three body shapes. We found that deepening bodies increase the robot's ability to change direction and centripetal acceleration, though centripetal acceleration exhibits diminishing returns beyond a certain body depth. By using a robotic model, we were able to isolate the effects of body shape on maneuverability and clarify this confounded relationship. Studying the functional morphology of complex traits such as body shape and their interaction with complex behavior like maneuverability benefits from both the broad view provided by comprehensive comparative studies, and the control of variables enabled by robophysical experiments.

A magnetically controlled soft miniature robotic fish with a flexible skeleton inspired by zebrafish

The untethered miniature swimming robot actuation and control is difficult as the robot size becomes smaller, due to limitations of feasible miniaturized on-board components. Nature provides much inspiration for developing miniature robot. Here, a new artificial untethered miniature robotic fish with a flexible magnetic skeleton and soft body that achieve controlled locomotion under the water through an external magnetic field is presented. The soft body of the shuttle-shaped structure microrobot was manufactured from pure Ecoflex, while the skeleton for magnetic actuation was manufactured from Ecoflex and NdFeB composites in a certain ratio and was endowed with a special magnetization profile. Microrobots that experience external magnetic fields are able to swim underwater and have environmental adaptations that include the flexibility to traverse aquatic plants area and crushed stone terrain. The robot also exhibits friendly interactivity and camouflage ability to get close to the zebrafish without scaring them. Moreover, the soft miniature robotic fish could be used to study the impacts of the morphology and kinematics changing in zebrafish populations.

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

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

Body Caudal Undulation measured by Soft Sensors and emulated by Soft Artificial Muscles

We propose the use of bio-inspired robotics equipped with soft sensor technologies to gain a better understanding of the mechanics and control of animal movement. Soft robotic systems can be used to generate new hypotheses and uncover fundamental principles underlying animal locomotion and sensory capabilities, which could subsequently be validated using living organisms. Physical models increasingly include lateral body movements, notably back and tail bending, which are necessary for horizontal plane undulation in model systems ranging from fish to amphibians and reptiles. We present a comparative study of the use of physical modeling in conjunction with soft robotics and integrated soft and hyperelastic sensors to monitor local pressures, enabling local feedback control, and discuss issues related to understanding the mechanics and control of undulatory locomotion. A parallel approach combining live animal data with biorobotic physical modeling promises to be beneficial for gaining a better understanding of systems in motion.

Emergence of robust self-organized undulatory swimming based on local hydrodynamic force sensing

Undulatory swimming represents an ideal behavior to investigate locomotion control and the role of the underlying central and peripheral components in the spinal cord. Many vertebrate swimmers have central pattern generators and local pressure-sensitive receptors that provide information about the surrounding fluid. However, it remains difficult to study experimentally how these sensors influence motor commands in these animals. Here, using a specifically designed robot that captures the essential components of the animal neuromechanical system and using simulations, we tested the hypothesis that sensed hydrodynamic pressure forces can entrain body actuation through local feedback loops. We found evidence that this peripheral mechanism leads to self-organized undulatory swimming by providing intersegmental coordination and body oscillations. Swimming can be redundantly induced by central mechanisms, and we show that, therefore, a combination of both central and peripheral mechanisms offers a higher robustness against neural disruptions than any of them alone, which potentially explains how some vertebrates retain locomotor capabilities after spinal cord lesions. These results broaden our understanding of animal locomotion and expand our knowledge for the design of robust and modular robots that physically interact with the environment.

Spider-Inspired Electrohydraulic Actuators for Fast, Soft-Actuated Joints

The impressive locomotion and manipulation capabilities of spiders have led to a host of bioinspired robotic designs aiming to reproduce their functionalities; however, current actuation mechanisms are deficient in either speed, force output, displacement, or efficiency. Here-using inspiration from the hydraulic mechanism used in spider legs-soft-actuated joints are developed that use electrostatic forces to locally pressurize a hydraulic fluid, and cause flexion of a segmented structure. The result is a lightweight, low-profile articulating mechanism capable of fast operation, high forces, and large displacement; these devices are termed spider-inspired electrohydraulic soft-actuated (SES) joints. SES joints with rotation angles up to 70°, blocked torques up to 70 mN m, and specific torques up to 21 N m kg-1 are demonstrated. SES joints demonstrate high speed operation, with measured roll-off frequencies up to 24 Hz and specific power as high as 230 W kg-1 -similar to human muscle. The versatility of these devices is illustrated by combining SES joints to create a bidirectional joint, an artificial limb with independently addressable joints, and a compliant gripper. The lightweight, low-profile design, and high performance of these devices, makes them well-suited toward the development of articulating robotic systems that can rapidly maneuver.

Mechanisms for mid-air reorientation using tail rotation in gliding geckos

Arboreal animals face numerous challenges when negotiating complex three-dimensional terrain. Directed aerial descent or gliding flight allows for rapid traversal of arboreal environments, but presents control challenges. Some animals, such as birds or gliding squirrels, have specialized structures to modulate aerodynamic forces while airborne. However, many arboreal animals do not possess these specializations but still control posture and orientation in mid-air. One of the largest inertial segments in lizards is their tail. Inertial reorientation can be used to attain postures appropriate for controlled aerial descent. Here, we discuss the role of tail inertia in a range of mid-air reorientation behaviors using experimental data from geckos in combination with mathematical and robotic models. Geckos can self-right in mid-air by tail rotation alone. Equilibrium glide behavior of geckos in a vertical wind tunnel show that they can steer toward a visual stimulus by using rapid, circular tail rotations to control pitch and yaw. Multiple coordinated tail responses appear to be required for the most effective terminal velocity gliding. A mathematical model allows us to explore the relationship between morphology and the capacity for inertial reorientation by conducting sensitivity analyses, and testing control approaches. Robotic models further define the limits of performance and generate new control hypotheses. Such comparative analysis allows predictions about the diversity of performance across lizard morphologies, relative limb proportions, and provides insights into the evolution of aerial behaviors.

Fish without Tail Fins-Exploring the Function of Tail Morphology of the First Vertebrates

We use a series of hydrodynamic experiments on abstracted models to explore whether primitive vertebrates may have swum under various conditions without a clearly-differentiated tail fin. Cambrian vertebrates had post-anal stubby tails, some had single dorsal and ventral fins, but none had yet evolved a clearly differentiated caudal fin typical of post-Cambrian fishes, and must have relied on their long and flexible laterally-compressed bodies for locomotion, i.e., by bending their bodies side-to-side in order to propagate waves from head to tail. We approach this problem experimentally based on an abstracted model of Metaspriggina walcotti from the 506-million-year old Burgess Shale by using oscillating thin flexible plates while varying the tail fin geometry from rectangular to uniform, and finally to a no tail-fin condition. Despite a missing tail fin, this study supports the observation that the abstracted Metaspriggina model can generate a strong propulsive force in cruise conditions, both away from, and near the sea bed (in ground effect). However, when the abstracted Metaspriggina model moves in ground effect, a weaker performance is observed, indicating that Metaspriggina may not necessarily have been optimized for swimming near the sea bed. When considering acceleration from rest, we find that the Metaspriggina model's performance is not significantly different from other morphological models (abstracted truncate tail and abstracted heterocercal tail). Statistical analysis shows that morphological parameters, swimming modes, and ground effect all play significant roles in thrust performance. While the exact relationships of Cambrian vertebrates are still debated, as agnathans, they share some general characteristics with modern cyclostomes, in particular an elongate body akin to lampreys. Lampreys, as anguilliform swimmers, are considered to be some of the most efficient swimmers using a particular type of suction thrust induced by the traveling body wave as it travels from head to tail. Our current experiments suggest that Metaspriggina's ability in acceleration from rest, through possibly a similar type of suction thrust, which is defined as the ability to generate low pressure on upstream facing sections of the body, might have evolved early in response to increasing predator pressure during the Cambrian Explosion.

Role of Electromechanical Coupling, Locomotion Type and Damping on the Effectiveness of Fish-Like Robot Energy Harvesters

In this work, an investigation into the influence of prescribed motion on a body caudal fin aquatic unmanned vehicle (AUV) energy harvester is carried out. The undulatory–oscillation locomotion inspired by fishes actuates a composite beam representative of a spinal column with a piezoelectric patch. Two patch configurations—one at the head and tail—are considered for the AUV energy harvester, with a length that would not activate a harmonic in the system. An electromechanical model which accounts for the strain of the prescribed motion and the induced relative strain is developed. Discretizing the relative strain using Galerkin’s method requires a convergence study in which the impacts of the prescribed motion, dependent on the undulation and envelope of the motion, are investigated. The combination of prescribed motion and structural terms leads to a coupling that requires multiple investigations. The removal of the undulation of the system produces a more consistent response. The performances of the two different patch configurations undergoing different prescribed motions are studied in terms of coupled damping and frequency effects. An uncoupled Gauss law-based model is adopted to compare the performance of our approach and that of the coupled electromechanical model harvester. It is demonstrated that there is a complex interaction of the phases of the prescribed and relative motions of the structure which can lead to the development or destruction of the response of the total motion or voltage for the system. The results show that the structural damping and type of locomotion are the most influential parameters on the validity of the uncoupled approach. It is also found that the optimal resistances for the coupled and uncoupled representations are the same for the two motions and patch configurations considered.