Table of contents

The bend propagation involved in the stereotypical reaching movement of the octopus arm has been extensively studied. While these studies have analyzed the kinematics of bend propagation along the arm during its extension, possible length changes have been ignored. Here, the elongation profiles of the reaching movements of Octopus vulgaris were assessed using three-dimensional reconstructions. The analysis revealed that, in addition to bend propagation, arm extension movements involve elongation of the proximal part of the arm, i.e., the section from the base of the arm to the propagating bend. The elongations are quite substantial and highly variable, ranging from an average strain along the arm of −0.12 (i.e. shortening) up to 1.8 at the end of the movement (0.57 ± 0.41, n = 64 movements, four animals). Less variability was discovered in an additional set of experiments on reaching movements (0.64 ± 0.28, n = 30 movements, two animals), where target and octopus positions were kept more stationary. Visual observation and subsequent kinematic analysis suggest that the reaching movements can be broadly segregated into two groups. The first group involves bend propagation beginning at the base of the arm and propagating towards the arm tip. In the second, the bend is formed or present more distally and reaching is achieved mainly by elongation and straightening of the segment proximal to the bend. Only in the second type of movements is elongation significantly positively correlated with the distance of the bend from the target. We suggest that reaching towards a target is generated by a combination of both propagation of a bend along the arm and arm elongation. These two motor primitives may be combined to create a broad spectrum of reaching movements. The dynamical model, which recapitulates the biomechanics of the octopus muscular hydrostatic arm, suggests that achieving the observed elongation requires an extremely low ratio of longitudinal to transverse muscle force (<0.0016 for an average strain along the arm of around 0.5). This was not observed and moreover such extremely low value does not seem to be physiologically possible. Hence the assumptions made in applying the dynamic model to behaviors such as static arm stiffening that leads to arm extension through bend propagation and the patterns of activation used to simulate such behaviors should be modified to account for movements combining bend propagation and arm elongation.

This paper presents a novel spatial kinematic model for multisection continuum arms based on mode shape functions (MSF). Modal methods have been used in many disciplines from finite element methods to structural analysis to approximate complex and nonlinear parametric variations with simple mathematical functions. Given certain constraints and required accuracy, this helps to simplify complex phenomena with numerically efficient implementations leading to fast computations. A successful application of the modal approximation techniques to develop a new modal kinematic model for general variable length multisection continuum arms is discussed. The proposed method solves the limitations associated with previous models and introduces a new approach for readily deriving exact, singularity-free and unique MSF's that simplifies the approach and avoids mode switching. The model is able to simulate spatial bending as well as straight arm motions (i.e., pure elongation/contraction), and introduces inverse position and orientation kinematics for multisection continuum arms. A kinematic decoupling feature, splitting position and orientation inverse kinematics is introduced. This type of decoupling has not been presented for these types of robotic arms before. The model also carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics and impose actuator mechanical limitations onto the kinematics thus generating fully realizable results. The proposed method is easily applicable to a broad spectrum of continuum arm designs.

The octopus is an interesting model for the development of soft robotics, due to its high deformability, dexterity and rich behavioural repertoire. To investigate the principles of octopus dexterity, we designed an eight-arm soft robot and evaluated its performance with focused experiments. The OCTOPUS robot presented here is a completely soft robot, which integrates eight arms extending in radial direction and a central body which contains the main processing units. The front arms are mainly used for elongation and grasping, while the others are mainly used for locomotion. The robotic octopus works in water and its buoyancy is close to neutral. The experimental results show that the octopus-inspired robot can walk in water using the same strategy as the animal model, with good performance over different surfaces, including walking through physical constraints. It can grasp objects of different sizes and shapes, thanks to its soft arm materials and conical shape.

Octopus suckers are able to attach to all nonporous surfaces and generate a very strong attachment force. The well-known attachment features of this animal result from the softness of the sucker tissues and the surface morphology of the portion of the sucker that is in contact with objects or substrates. Unlike artificial suction cups, octopus suckers are characterized by a series of radial grooves that increase the area subjected to pressure reduction during attachment. In this study, we constructed artificial suction cups with different surface geometries and tested their attachment performances using a pull-off setup. First, smooth suction cups were obtained for casting; then, sucker surfaces were engraved with a laser cutter. As expected, for all the tested cases, the engraving treatment enhanced the attachment performance of the elastomeric suction cups compared with that of the smooth versions. Moreover, the results indicated that the surface geometry with the best attachment performance was the geometry most similar to octopus sucker morphology. The results obtained in this work can be utilized to design artificial suction cups with higher wet attachment performance.

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.

This work addresses the inverse kinematics problem of a bioinspired octopus-like manipulator moving in three-dimensional space. The bioinspired manipulator has a conical soft structure that confers the ability of twirling around objects as a real octopus arm does. Despite the simple design, the soft conical shape manipulator driven by cables is described by nonlinear differential equations, which are difficult to solve analytically. Since exact solutions of the equations are not available, the Jacobian matrix cannot be calculated analytically and the classical iterative methods cannot be used. To overcome the intrinsic problems of methods based on the Jacobian matrix, this paper proposes a neural network learning the inverse kinematics of a soft octopus-like manipulator driven by cables. After the learning phase, a feed-forward neural network is able to represent the relation between manipulator tip positions and forces applied to the cables. Experimental results show that a desired tip position can be achieved in a short time, since heavy computations are avoided, with a degree of accuracy of 8% relative average error with respect to the total arm length.

Soft robots can exhibit diverse behaviors with simple types of actuation by partially outsourcing control to the morphological and material properties of their soft bodies, which is made possible by the tight coupling between control, body, and environment. In this paper, we present a method that will quantitatively characterize these diverse spatiotemporal dynamics of a soft body based on the information-theoretic approach. In particular, soft bodies have the ability to propagate the effect of actuation through the entire body, with a certain time delay, due to their elasticity. Our goal is to capture this delayed interaction in a quantitative manner based on a measure called momentary information transfer. We extend this measure to soft robotic applications and demonstrate its power using a physical soft robotic platform inspired by the octopus. Our approach is illustrated in two ways. First, we statistically characterize the delayed actuation propagation through the body as a strength of information transfer. Second, we capture this information propagation directly as local information dynamics. As a result, we show that our approach can successfully characterize the spatiotemporal dynamics of the soft robotic platform, explicitly visualizing how information transfers through the entire body with delays. Further extension scenarios of our approach are discussed for soft robotic applications in general.

This paper introduces a novel, bioinspired manipulator for minimally invasive surgery (MIS). The manipulator is entirely composed of soft materials, and it has been designed to provide similar motion capabilities as the octopus's arm in order to reach the surgical target while exploiting its whole length to actively interact with the biological structures. The manipulator is composed of two identical modules (each of them can be controlled independently) with multi-directional bending and stiffening capabilities, like an octopus arm. In the authors' previous works, the design of the single module has been addressed. Here a two-module manipulator is presented, with the final aim of demonstrating the enhanced capabilities that such a structure can have in comparison with rigid surgical tools currently employed in MIS. The performances in terms of workspace, stiffening capabilities, and generated forces are characterized through experimental tests. The combination of stiffening capabilities and manipulation tasks is also addressed to confirm the manipulator potential employment in a real surgical scenario.

In the area of biomimetics, engineers use inspiration from natural systems to develop technical devices, such as sensors. One example is the lateral line system of fish. It is a mechanoreceptive system consisting of up to several thousand individual sensors called neuromasts, which enable fish to sense prey, predators, or conspecifics. So far, the small size and high sensitivity of the lateral line is unmatched by man-made sensor devices. Here, we describe an artificial lateral line system based on an optical detection principle. We developed artificial canal neuromasts using MEMS technology including thick film techniques. In this work, we describe the MEMS fabrication and characterize a sensor prototype. Our sensor consists of a silicon chip, a housing, and an electronic circuit. We demonstrate the functionality of our $\mu$-biomimetic flow sensor by analyzing its response to constant water flow and flow fluctuations. Furthermore, we discuss the sensor robustness and sensitivity of our sensor and its suitability for industrial and medical applications. In sum, our sensor can be used for many tasks, e.g. for monitoring fluid flow in medical applications, for detecting leakages in tap water systems or for air and gas flow measurements. Finally, our flow sensor can even be used to improve current knowledge about the functional significance of the fish lateral line.

Fishes are found in a great variety of body forms with tail shapes that vary from forked tuna-like tails to the square-shaped tails found in some deep-bodied species. Hydrodynamic theory suggests that a fish's body and tail shape affects undulatory swimming performance. For example, a narrow caudal peduncle is believed to reduce drag, and a tuna-like tail to increase thrust. Despite the prevalence of these assertions, there is no experimental verification of the hydrodynamic mechanisms that may confer advantages on specific forms. Here, we use a mechanically-actuated flapping foil model to study how two aspects of shape, caudal peduncle depth and presence or absence of a forked caudal fin, may affect different aspects of swimming performance. Four different foil shapes were each made of plastics of three different flexural stiffnesses, permitting us to study how shape might interact with stiffness to produce swimming performance. For each foil, we measured the self-propelling swimming speed. In addition, we measured the forces, torques, cost of transport and power coefficient of each foil swimming at its self-propelling speed. There was no single 'optimal' foil exhibiting the highest performance in all metrics, and for almost all measures of swimming performance, foil shape and flexural stiffness interacted in complicated ways. Particle image velocimetry of several foils suggested that stiffness might affect the relative phasing of the body trailing edge and the caudal fin leading edge, changing the flow incident to the tail, and affecting hydrodynamics of the entire foil. The results of this study of a simplified model of fish body and tail morphology suggest that considerable caution should be used when inferring a swimming performance advantage from body and tail shape alone.

Biologically, the vestibular feedback is critical to the ability of human body to balance in different conditions. This balancing ability inspires analysis of the reference equilibrium position in dynamic environments. The research proposes and experimentally validates the concept of equilibrium for the human body modeled as an inverted pendulum, which is instrumental in explaining why we align the body along the surface normal when standing on a surface but not on an incline, and tend to lean backward or forward on non-static surfaces e.g. accelerating or decelerating bus. This equilibrium position—the dynamic equilibrium axis—is dependent only on the acceleration of surface of contact (e.g. gravity) and acts as the reference to the orientation measurements. The research also draws design inspiration from the two human ears—symmetry and plurality of inertial sensors. The vestibular dynamic inclinometer and planar vestibular dynamic inclinometer consist of multiple (two or four) symmetrically placed accelerometers and a gyroscope. The sensors measure the angular acceleration and absolute orientation, not the change in orientation, from the reference equilibrium position and are successful in separating gravity from motion for objects moving on ground. The measurement algorithm is an analytical solution that is not time-recursive, independent of body dynamics and devoid of integration errors. The experimental results for the two sensor combinations validate the theoretically (kinematics) derived analytical solution of the measurement algorithm.

The highly flexible and stretchable wing skin of bats, together with the skeletal structure and musculature, enables large changes in wing shape during flight. Such compliance distinguishes bat wings from those of all other flying animals. Although several studies have investigated the aerodynamics and kinematics of bats, few have examined the complex histology and mechanical response of the wing skin. This work presents the first biaxial characterization of the local deformation, mechanical properties, and fiber kinematics of bat wing skin. Analysis of these data has provided insight into the relationships among the structural morphology, mechanical properties, and functionality of wing skin. Large spatial variations in tissue deformation and non-negligible fiber strains in the cross-fiber direction for both chordwise and spanwise fibers indicate fibers should be modeled as two-dimensional elements. The macroscopic constitutive behavior was anisotropic and nonlinear, with very low spanwise and chordwise stiffness (hundreds of kilopascals) in the toe region of the stress–strain curve. The structural arrangement of the fibers and matrix facilitates a low energy mechanism for wing deployment and extension, and we fabricate examples of skins capturing this mechanism. We propose a comprehensive deformation map for the entire loading regime. The results of this work underscore the importance of biaxial field approaches for soft heterogeneous tissue, and provide a foundation for development of bio-inspired skins to probe the effects of the wing skin properties on aerodynamic performance.

Four species of cacti were chosen for this study: Copiapoa cinerea var. haseltoniana, Ferocactus wislizenii, Mammillaria columbiana subsp. yucatanensis and Parodia mammulosa. It has been reported that dew condenses on the spines of C. cinerea and that it does not on the spines of F. wislizenii, and our preliminary observations of M. columbiana and P. mammulosa revealed a potential for collecting dew water. This study found all four cacti to harvest dew on their stems and spines (albeit rarely on the spines of F. wislizenii). Dew harvesting experiments were carried out in the UK, recording an increase in cacti mass on dewy nights. By applying a ranking relative to a polymethyl methacrylate (Plexiglas) reference plate located nearby, it was found that C. cinerea collected the most airborne moisture followed by M. columbiana, P. mammulosa and F. wislizenii respectively, with mean efficiency ratio with respect to the Plexiglas reference of 3.48 ± 0.5, 2.44 ± 0.06, 1.81 ± 0.14 and 1.27 ± 0.49 on observed dewy nights. A maximum yield of normalized performance of 0.72 ± 0.006 l/m⁻² on one dewy night was recorded for C. cinerea. Removing the spines from M. columbiana was found to significantly decrease its dew harvesting efficiency. The spines of three of the species were found to be hydrophilic in nature, while F. wislizenii was hydrophobic; the stems of all four species were hydrophilic. The results of this study could be translated into designing a biomimetic water collecting device that utilizes cactus spines and their microstructures.

Crustaceans contain a great variety of sensilla along their antennules that enable them to sense both hydrodynamic and chemical stimuli in aquatic environments, and can be used to inspire the design of engineered sensing systems. For example, along the antennule of the freshwater crayfish, Procambarus clarkii, four predominant mechanosensory sensilla morphologies are found. To study their response to upstream flow perturbations, atomic force microscopy was utilized to determine P. clarkii sensilla bending in response to an applied force and a mean torsional stiffness, k_t = 1 × 10⁻¹² N m degree⁻¹ was found. A numerical model was developed to quantify the deformation of the four sensilla morphologies due to flow perturbations within their surrounding fluid. These flow perturbations were intended to mimic predator and ambient fluid movements. Results show that upstream fluid motion causes alterations in velocity near the sensilla, accompanied by corresponding variations in pressure along the sensilla surface. The feathered and filamentous sensilla, which are hydrodynamic sensilla, were found to be highly sensitive to flow perturbations. The beaked and asymmetric sensilla, which are bimodal chemo-mechanoreceptors, were found to be much less sensitive to hydrodynamic disturbances. Results also show that sensilla are most sensitive to fluid movement in the along-axis plane of the antennule, with a sharp drop in sensitivity perpendicular to this axis. This sensitivity agrees well with neural responses measured directly from the paired sensory neurons associated with each sensillum. Greater along-axis sensitivity is likely beneficial for determining the direction of fluid movements, which may be important for both aquatic organisms and biomimetic sensing systems.

Fruit flies have flexible wings that deform during flight. To explore the fluid-structure interaction of flexible flapping wings at fruit fly scale, we use a well-validated Navier–Stokes equation solver, fully-coupled with a structural dynamics solver. Effects of chordwise flexibility on a two dimensional hovering wing is studied. Resulting wing rotation is purely passive, due to the dynamic balance between aerodynamic loading, elastic restoring force, and inertial force of the wing. Hover flight is considered at a Reynolds number of Re = 100, equivalent to that of fruit flies. The thickness and density of the wing also corresponds to a fruit fly wing. The wing stiffness and motion amplitude are varied to assess their influences on the resulting aerodynamic performance and structural response. Highest lift coefficient of 3.3 was obtained at the lowest-amplitude, highest-frequency motion (reduced frequency of 3.0) at the lowest stiffness (frequency ratio of 0.7) wing within the range of the current study, although the corresponding power required was also the highest. Optimal efficiency was achieved for a lower reduced frequency of 0.3 and frequency ratio 0.35. Compared to the water tunnel scale with water as the surrounding fluid instead of air, the resulting vortex dynamics and aerodynamic performance remained similar for the optimal efficiency motion, while the structural response varied significantly. Despite these differences, the time-averaged lift scaled with the dimensionless shape deformation parameter γ. Moreover, the wing kinematics that resulted in the optimal efficiency motion was closely aligned to the fruit fly measurements, suggesting that fruit fly flight aims to conserve energy, rather than to generate large forces.

A major difference between manmade underwater robotic vehicles (URVs) and undersea animals is the dense arrays of sensors on the body of the latter which enable them to execute extreme control of their limbs and demonstrate super-maneuverability. There is a high demand for miniaturized, low-powered, lightweight and robust sensors that can perform sensing on URVs to improve their control and maneuverability. In this paper, we present the design, fabrication and experimental testing of two types of microelectromechanical systems (MEMS) sensors that benefit the situational awareness and control of a robotic stingray. The first one is a piezoresistive liquid crystal polymer haircell flow sensor which is employed to determine the velocity of propagation of the stingray. The second one is Pb(Zr_0.52Ti_0.48)O₃ piezoelectric micro-diaphragm pressure sensor which measures various flapping parameters of the stingray's fins that are key parameters to control the robot locomotion. The polymer flow sensors determine that by increasing the flapping frequency of the fins from 0.5 to 3 Hz the average velocity of the stingray increases from 0.05 to 0.4 BL s⁻¹, respectively. The role of these sensors in detecting errors in control and functioning of the actuators in performing tasks like flapping at a desired amplitude and frequency, swimming at a desired velocity and direction are quantified. The proposed sensors are also used to provide inputs for a model predictive control which allows the robot to track a desired trajectory. Although a robotic stingray is used as a platform to emphasize the role of the MEMS sensors, the applications can be extended to most URVs.

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.