Forward and inverse problems in the mechanics of soft filaments

A comprehensive numerical approach to coil placement in cerebral aneurysms: mathematical modeling and in silico occlusion classification

Endovascular coil embolization is one of the primary treatment techniques for cerebral aneurysms. Although it is a well-established and minimally invasive method, it bears the risk of suboptimal coil placement which can lead to incomplete occlusion of the aneurysm possibly causing recurrence. One of the key features of coils is that they have an imprinted natural shape supporting the fixation within the aneurysm. For the spatial discretization, our mathematical coil model is based on the discrete elastic rod model which results in a dimension-reduced 1D system of differential equations. We include bending and twisting responses to account for the coils natural curvature and allow for the placement of several coils having different material parameters. Collisions between coil segments and the aneurysm wall are handled by an efficient contact algorithm that relies on an octree based collision detection. In time, we use a standard symplectic semi-implicit Euler time stepping method. Our model can be easily incorporated into blood flow simulations of embolized aneurysms. In order to differentiate optimal from suboptimal placements, we employ a suitable in silico Raymond-Roy-type occlusion classification and measure the local packing density in the aneurysm at its neck, wall region and core. We investigate the impact of uncertainties in the coil parameters and embolization procedure. To this end, we vary the position and the angle of insertion of the micro-catheter, and approximate the local packing density distributions by evaluating sample statistics.

Passive elasticity properties of Octopus rubescens arms

In this report, passive elasticity properties of Octopus rubescens arm tissue are investigated using a multidisciplinary approach encompassing biomechanical experiments, computational modeling, and analyses. Tensile tests are conducted to obtain stress-strain relationships of the arm under axial stretch. Rheological tests are also performed to probe the dynamic shear response of the arm tissue. Based on these tests, comparisons against three different viscoelasticity models are reported.

Reversible kink instability drives ultrafast jumping in nematodes and soft robots

Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature hypothesized but not proven to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched closed loop over a slow timescale O (1 s), then rapidly open it O (10 µs), achieving heights of 20 body lengths (BL) and generating ∼ 10 4 W/Kg of power. Using jumping nematodes, a bio-inspired Soft Jumping Model (SoftJM), and computational simulations, we explore the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the impact of aspect ratio on kink instability and jumping performance using SoftJM, and quantified EPN cuticle stiffness with AFM, comparing it with C. elegans . This led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 BL. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumps in soft robots on complex substrates like sand, offering a novel approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.

Soft robotics for farm to fork: applications in agriculture & farming

Agricultural tasks and environments range from harsh field conditions with semi-structured produce or animals, through to post-processing tasks in food-processing environments. From farm to fork, the development and application of soft robotics offers a plethora of potential uses. Robust yet compliant interactions between farm produce and machines will enable new capabilities and optimize existing processes. There is also an opportunity to explore how modeling tools used in soft robotics can be applied to improve our representation and understanding of the soft and compliant structures common in agriculture. In this review, we seek to highlight the potential for soft robotics technologies within the food system, and also the unique challenges that must be addressed when developing soft robotics systems for this problem domain. We conclude with an outlook on potential directions for meaningful and sustainable impact, and also how our outlook on both soft robotics and agriculture must evolve in order to achieve the required paradigm shift.

Automated resolution of the spiral torsion spring inverse design problem

Many mechanical applications take advantage of spiral torsion springs due to their robustness, compactness, and simplicity. Brand-new manufacturing methods allow to create spiral springs with unconventional geometries and materials that suit a wider range of uses demanding either linearity or nonlinearity. Designing a spiral torsion spring with a nonlinear desired torque curve may be a great challenge, due to their many degrees-of-freedom (length, width, thickness, arbor, and barrel diameters, etc.) and the complexity of the geometrical and mechanical requirements to ensure their manufacturability, system compatibility, operation safety and reliability; and the solution is never unique. This manuscript proposes and validates an innovative methodology for the resolution of this inverse design problem based on the application of a nonlinear restrained global optimization algorithm. This algorithm is adjusted to converge, out of the infinity of designs that match the desired torque curve and hold all the functional and manufacturing constraints, to a design solution that minimizes strip mass. The methodology is built on a formulation for the calculation of the torque curve of a generalized spiral spring, with or without coiling and with any along-the-length cross-section, already published by the authors.

A self-organizing robotic aggregate using solid and liquid-like collective states

Designing robotic systems that can change their physical form factor as well as their compliance to adapt to environmental constraints remains a major conceptual and technical challenge. To address this, we introduce the Granulobot, a modular system that blurs the distinction between soft, modular, and swarm robotics. The system consists of gear-like units that each contain a single actuator such that units can self-assemble into larger, granular aggregates using magnetic coupling. These aggregates can reconfigure dynamically and also split into subsystems that might later recombine. Aggregates can self-organize into collective states with solid- and liquid-like properties, thus displaying widely differing compliance. These states can be perturbed locally via actuators or externally via mechanical feedback from the environment to produce adaptive shape-shifting in a decentralized manner. This, in turn, can generate locomotion strategies adapted to different conditions. Aggregates can move over obstacles without using external sensors or coordinates to maintain a steady gait over different surfaces without electronic communication among units. The modular design highlights a physical, morphological form of control that advances the development of resilient robotic systems with the ability to morph and adapt to different functions and conditions.

Odd Cosserat elasticity in active materials

Stress-strain constitutive relations in solids with an internal angular degree of freedom can be modeled using Cosserat (also called micropolar) elasticity. In this paper, we explore Cosserat materials that include chiral active components and hence odd elasticity. We calculate static elastic properties and show that the static response to rotational stresses leads to strains that depend on both Cosserat and odd elasticity. We compute the dispersion relations in odd Cosserat materials in the overdamped regime and find the presence of exceptional points. These exceptional points create a sharp boundary between a Cosserat-dominated regime of complete wave attenuation and an odd-elasticity-dominated regime of propagating waves. We conclude by showing the effect of Cosserat and odd-elasticity terms on the polarization of Rayleigh surface waves.

Reduced order modeling and model order reduction for continuum manipulators: an overview

Soft robot's natural dynamics calls for the development of tailored modeling techniques for control. However, the high-dimensional configuration space of the geometrically exact modeling approaches for soft robots, i.e., Cosserat rod and Finite Element Methods (FEM), has been identified as a key obstacle in controller design. To address this challenge, Reduced Order Modeling (ROM), i.e., the approximation of the full-order models, and Model Order Reduction (MOR), i.e., reducing the state space dimension of a high fidelity FEM-based model, are enjoying extensive research. Although both techniques serve a similar purpose and their terms have been used interchangeably in the literature, they are different in their assumptions and implementation. This review paper provides the first in-depth survey of ROM and MOR techniques in the continuum and soft robotics landscape to aid Soft Robotics researchers in selecting computationally efficient models for their specific tasks.

Elastic Snap-Through Instabilities Are Governed by Geometric Symmetries

Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside out. This snap through is a general motif for the storage and rapid release of elastic energy, and it is exploited by many biological and engineered systems from the Venus flytrap to mechanical metamaterials. Shape transitions are known to be related to the type of bifurcation the system undergoes, however, to date, there is no general understanding of the mechanisms that select these bifurcations. Here we analyze numerically and analytically two systems proposed in recent literature in which an elastic strip, initially in a buckled state, is driven through shape transitions by either rotating or translating its boundaries. We show that the two systems are mathematically equivalent, and identify three cases that illustrate the entire range of transitions described by previous authors. Importantly, using reduction order methods, we establish the nature of the underlying bifurcations and explain how these bifurcations can be predicted from geometric symmetries and symmetry-breaking mechanisms, thus providing universal design rules for elastic shape transitions.

Dynamic behavior of elastic strips near shape transitions

Elastic strips provide a general motif for studying shape transitions. When actuated through rotation of its boundaries, a buckled strip exhibits, depending on the direction of rotation, three types of shape transitions: buckling, algebraic snap-through, or exponential snap-through. The transition dynamics is linked to the character of the bifurcation, which, in turn, is disclosed by the normal form of the system, but deriving normal forms is challenging. Recent work has used asymptotic methods to obtain this form for algebraic snap-through, but, to date, there is no methodology for extending this analysis to other transitions. Here we introduce a method to analyze the dynamic characteristics of an elastic strip near a transition and extend, in a straightforward manner, the previously proposed asymptotic analysis to exponential snap-through and buckling transitions. Importantly, we show that these normal forms dictate all the dynamic characteristics of the elastic strip near a shape transition. Our analysis provides reliable tools to diagnose and anticipate elastic shape transitions.

Biomechanics, motor control and dynamic models of the soft limbs of the octopus and other cephalopods

Muscular hydrostats are organs composed entirely of packed arrays of incompressible muscles and lacking any skeletal support. Found in both vertebrates and invertebrates, they are of great interest for comparative biomechanics from engineering and evolutionary perspectives. The arms of cephalopods (e.g. octopus and squid) are particularly interesting muscular hydrostats because of their flexibility and ability to generate complex behaviors exploiting elaborate nervous systems. Several lines of evidence from octopus studies point to the use of both brain and arm-embedded motor control strategies that have evolved to simplify the complexities associated with the control of flexible and hyper-redundant limbs and bodies. Here, we review earlier and more recent experimental studies on octopus arm biomechanics and neural motor control. We review several dynamic models used to predict the kinematic characteristics of several basic motion primitives, noting the shortcomings of the current models in accounting for behavioral observations. We also discuss the significance of impedance (stiffness and viscosity) in controlling the octopus's motor behavior. These factors are considered in light of several new models of muscle biomechanics that could be used in future research to gain a better understanding of motor control in the octopus. There is also a need for updated models that encompass stiffness and viscosity for designing and controlling soft robotic arms. The field of soft robotics has boomed over the past 15 years and would benefit significantly from further progress in biomechanical and motor control studies on octopus and other muscular hydrostats.

Energy-shaping control of a muscular octopus arm moving in three dimensions

Flexible octopus arms exhibit an exceptional ability to coordinate large numbers of degrees of freedom and perform complex manipulation tasks. As a consequence, these systems continue to attract the attention of biologists and roboticists alike. In this article, we develop a three-dimensional model of a soft octopus arm, equipped with biomechanically realistic muscle actuation. Internal forces and couples exerted by all major muscle groups are considered. An energy-shaping control method is described to coordinate muscle activity so as to grasp and reach in three-dimensional space. Key contributions of this article are as follows: (i) modelling of major muscle groups to elicit three-dimensional movements; (ii) a mathematical formulation for muscle activations based on a stored energy function; and (iii) a computationally efficient procedure to design task-specific equilibrium configurations, obtained by solving an optimization problem in the Special Euclidean group SE ( 3 ) . Muscle controls are then iteratively computed based on the co-state variable arising from the solution of the optimization problem. The approach is numerically demonstrated in the physically accurate software environment Elastica . Results of numerical experiments mimicking observed octopus behaviours are reported.

Remote control of muscle-driven miniature robots with battery-free wireless optoelectronics

Bioengineering approaches that combine living cellular components with three-dimensional scaffolds to generate motion can be used to develop a new generation of miniature robots. Integrating on-board electronics and remote control in these biological machines will enable various applications across engineering, biology, and medicine. Here, we present hybrid bioelectronic robots equipped with battery-free and microinorganic light-emitting diodes for wireless control and real-time communication. Centimeter-scale walking robots were computationally designed and optimized to host on-board optoelectronics with independent stimulation of multiple optogenetic skeletal muscles, achieving remote command of walking, turning, plowing, and transport functions both at individual and collective levels. This work paves the way toward a class of biohybrid machines able to combine biological actuation and sensing with on-board computing.

A Hybrid Controller for a Soft Pneumatic Manipulator Based on Model Predictive Control and Iterative Learning Control

Due to the outstanding characteristics of the large structural flexibility and strong dexterity of soft robots, they have attracted great attention. However, the dynamic modeling and precise control of soft robots face huge challenges. Traditional model-based and model-free control methods find it difficult to obtain a balance between complexity and accuracy. In this paper, a dynamic model of a three-chamber continuous pneumatic manipulator is established based on the modal method. Moreover, a hybrid controller integrating model predictive control (MPC) and iterative learning control (ILC) is proposed, which can simultaneously perform model parameter learning and trajectory tracking control. Experimental results show that the proposed control method can optimize the parameters of the dynamic model in real time with less iterations than the traditional model-free method and have good control performance in trajectory tracking experiments. In the future, the proposed dynamic model and the hybrid controller should be verified on a multi-section manipulator.

Kinematic Analysis of Bionic Elephant Trunk Robot Based on Flexible Series-Parallel Structure

Researchers borrow ideas from biological characteristics and behavior in design to make bionic robots that can meet unstructured and complex operating environments. The elephant trunk has been widely imitated by bionic robots because of its strong dexterity and stiffness adjustability. Due to the complex structure of the current elephant trunk robot, a series-parallel elephant trunk robot based on flexible rod actuation and a 6-degree-of-freedom (6-dof) parallel module is proposed in this paper. The bionic robot has a simple structure and redundant kinematics, which can realize the control of stiffness. This work focuses on the modeling of the flexible driving rod, the kinematics of a single parallel module, and the whole biomimetic robot. The kinematics are verified by simulation, which lays a foundation for future research on stiffness regulation.

Conformational deformation of a multi-jointed elastic loop

A new class of deformation is presented for a planar loop structure made up of slender elastic bodies and joints. In demonstrating the circumferential shortening of the multi-jointed elastic loop, diverse three-dimensional (3D) deformations emerge through piecewise deflections and discrete rotations. These 3D morphologies correspond to conformations of molecular ring systems. Through image processing, the 3D reconstructions of the deformed structures are characterized by number, geometry, and initial imperfections of the body segments. We elucidate from measurements that the conformational deformation without self-stress results from a cyclical assembly of compressive bending of elastic bodies with high shear rigidity. The mechanical insights gained may apply in controlling the polymorphism exhibited by the cyclical structures across scales.

Active entanglement enables stochastic, topological grasping

Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception and motion planning. Here, we circumvent the need for feedback or precise planning by using an array of fluidically actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performance of our strategy and use a computational framework for the collective mechanics of flexible filaments in contact with complex objects to explain our findings. Overall, our study highlights how active collective entanglement of a filament array via an uncontrolled, spatially distributed scheme provides options for soft, adaptable grasping.

MiGriBot: A miniature parallel robot with integrated gripping for high-throughput micromanipulation

Although robotic micromanipulation using microtweezers has been widely explored, the current manipulation throughput hardly exceeds one operation per second. Increasing the manipulation throughput is thus a key factor for the emergence of robotized microassembly industries. This article presents MiGriBot (Millimeter Gripper Robot), a miniaturized parallel robot with a configurable platform and soft joints, designed to perform pick-and-place operations at the microscale. MiGriBot combines in a single robot the benefits of a parallel kinematic architecture with a configurable platform and the use of soft joints at the millimeter scale. The configurable platform of the robot provides an internal degree of freedom that can be used to actuate microtweezers using piezoelectric bending actuators located at the base of the robot, which notably reduces the robot's inertia. The soft joints make it possible to miniaturize the mechanism and to avoid friction. These benefits enable MiGriBot to reach a throughput of 10 pick-and-place cycles per second of micrometer-sized objects, with a precision of 1 micrometer.

On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models

Mechanochemical simulations of actomyosin networks are traditionally based on one-dimensional models of actin filaments having zero width. Here, and in the follow up paper (arXiv, DOI 10.48550/arXiv.2203.01284), approaches are presented for more efficient modeling that incorporates stretching, shearing, and twisting of actin filaments. Our modeling of a semiflexible filament with a small but finite width is based on the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament's backbone. In the variational models presented in this paper, a small and discrete set of parameters is used to describe a smooth filament shape having all degrees of freedom allowed in the Cosserat theory. Two main approaches are introduced: one where polynomial spline functions describe the filament's configuration, and one in which geodesic curves in the space of the configurational degrees of freedom are used. We find that in the latter representation the strain energy function can be calculated without resorting to a small-angle expansion, so it can describe arbitrarily large filament deformations without systematic error. These approaches are validated by a dynamical model of a Cosserat filament, which can be further extended by using multiresolution methods to allow more detailed monomer-based resolution in certain parts of the actin filament, as introduced in the follow up paper. The presented framework is illustrated by showing how torsional compliance in a finite-width filament can induce broken chiral symmetry in the structure of a cross-linked bundle.

Micromechanical Origin of Plasticity and Hysteresis in Nestlike Packings

Disordered packings of unbonded, semiflexible fibers represent a class of materials spanning contexts and scales. From twig-based bird nests to unwoven textiles, bulk mechanics of disparate systems emerge from the bending of constituent slender elements about impermanent contacts. In experimental and computational packings of wooden sticks, we identify prominent features of their response to cyclic oedometric compression: nonlinear stiffness, transient plasticity, and eventually repeatable velocity-independent hysteresis. We trace these features to their micromechanic origins, identified in characteristic appearance, disappearance, and displacement of internal contacts.

Combing a double helix

Combing hair involves brushing away the topological tangles in a collective curl, defined as a bundle of interacting elastic filaments. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the dominant interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix. This minimal model allows us to study the detangling of an elastic double helix driven by a single stiff tine that moves along it and leaves two untangled filaments in its wake. Our results quantify how the mechanics of detangling correlates with the dynamics of a topological quantity, the link density, that propagates ahead of the tine and flows out the free end as a link current. This in turn provides a measure of the maximum characteristic length of a single combing stroke in the many-body problem on a head of hair, producing an optimal combing strategy that balances trade-offs between comfort, efficiency and speed of combing in hair curls of varying geometrical and topological complexity.

Writhing and hockling instabilities in twisted elastic fibers

The buckling and twisting of slender, elastic fibers is a deep and well-studied field. A slender elastic rod that is twisted with respect to a fixed end will spontaneously form a loop, or hockle, to relieve the torsional stress that builds. Further twisting results in the formation of plectonemes-a helical excursion in the fiber that extends with additional twisting. Here we use an idealized, micron-scale experiment to investigate the energy stored, and subsequently released, by hockles and plectonemes as they are pulled apart, in analogy with force spectroscopy studies of DNA and protein folding. Hysteresis loops in the snapping and unsnapping inform the stored energy in the twisted fiber structures.

Simple deformation measures for discrete elastic rods and ribbons

The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph . 27 , 63:1–63:12. ( doi:10.1145/1360612.1360662 )) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Friction modulation in limbless, three-dimensional gaits and heterogeneous terrains

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood through the lens of local friction modulation. Via an effective-friction modeling approach, compounded by 3D simulations, the emergence and disappearance of a range of locomotory behaviors observed in nature is systematically explained in relation to inhabited environments. Our approach also simplifies the treatment of terrain heterogeneity, whereby even solid obstacles may be seen as high friction regions, which we confirm against experiments of snakes ‘diffracting’ while traversing rows of posts, similar to optical waves. We further this optic analogy by illustrating snake refraction, reflection and lens focusing. We use these insights to engineer surface friction patterns and demonstrate passive snake navigation in complex topographies. Overall, our study outlines a unified view that connects active and passive 3D mechanics with heterogeneous interfacial effects to explain a broad set of biological observations, and potentially inspire engineering design.

A long puzzle in snake’s locomotion, sidewinding allows them to travel at an angle and reorient in some environments without loss of speed. Here, authors provide a mathematical argument to the evolution of sidewinding gaits and reinforce an analogy between limbless terrestrial locomotion and optics.

Design Approaches and Computational Tools for DNA Nanostructures

Designing a structure in nanoscale with desired shape and properties has been enabled by structural DNA nanotechnology. Design strategies in this research field have evolved to interpret various aspects of increasingly more complex nanoscale assembly and to realize molecular-level functionality by exploring static to dynamic characteristics of the target structure. Computational tools have naturally been of significant interest as they are essential to achieve a fine control over both shape and physicochemical properties of the structure. Here, we review the basic design principles of structural DNA nanotechnology together with its computational analysis and design tools.

Abrasion Resistant/Waterproof Stretchable Triboelectric Yarns Based on Fermat Spirals

Emerging energy harvesting yarns, via triboelectric effects, have wide application prospects in new-generation wearable electronics. However, few studies have been carried out regarding simultaneously achieving high electrical performance, mechanical robustness, and comfortability in industrial-scalable yarn. Here, an electronic yarn twisted into Fermat spiral, which has outstanding dynamic structure stability, is reported. The Fermat-spiral-based energy yarns (FSBEY) can simultaneously realize ultrahigh abrasion resistance (over 5000 Martindale standard abrasion cycles), stable reversible strain (100%), and excellent electrical output. Considerably high output (105 V, ≈1.2 µA under 2 Hz) can be attained upon contacting a single yarn (30 cm) with latex material, which is superior to most state-of-the-art stretchable triboelectric yarns. The application of these FSBEY in wireless gesture recognition, smart screen information protection, and harvesting of energy from water dropletsis demonstrated. Moreover, textiles knitted from the FSBEY have distinguished waterproof nature and are breathable. This work shows a feasible proposal for building future "energy garments".

Modeling and Fabrication of Soft Actuators Based on Fiber-Reinforced Elastomeric Enclosures

Unlike rigid actuators, soft actuators can easily adapt to complex environments. Understanding the relationship between the deformation of soft actuators and external factors such as pressure would enable rapid designs based on specific requirements, such as flexible, compliant endoscopes. An effective model is demonstrated that predicts the deformation of a soft actuator based on the virtual work principle and the geometrically exact Cosserat rod theory. The deformation process is analyzed for extension, bending, and twisting modules. A new manufacturing method is then introduced. Through any combination of modules, the soft actuator can have a greater workspace and more dexterity. The proposed model was verified for various fiber-reinforced elastomeric enclosures. There is good agreement between the model analysis and the experimental data, which indicates the effectiveness of the model.

Spontaneous knotting of a flexible fiber in chaotic flows

We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question of whether the fiber can spontaneously knot itself. Using a one-dimensional Cosserat model, a simple local viscous drag model and discrete contact forces, we explore the probability of finding knots at any given time when the fiber is interacting with the ABC class of flows. The bending rigidity is shown to have a marginal effect compared to that of increasing the fiber length. Complex knots are formed up to 11 crossings, but some knots are more probable than others. The finite-time Lyapunov exponent of the flow is shown to have a positive effect on the knot probability. Finally, contact forces appear to be crucial since knotted configurations can remain stable for times much longer than the turnover time of the flow, something that is not observed when the fiber can freely cross itself.

Design, Modeling, Control, and Application of Everting Vine Robots

In nature, tip-localized growth allows navigation in tightly confined environments and creation of structures. Recently, this form of movement has been artificially realized through pressure-driven eversion of flexible, thin-walled tubes. Here we review recent work on robots that "grow" via pressure-driven eversion, referred to as "everting vine robots," due to a movement pattern that is similar to that of natural vines. We break this work into four categories. First, we examine the design of everting vine robots, highlighting tradeoffs in material selection, actuation methods, and placement of sensors and tools. These tradeoffs have led to application-specific implementations. Second, we describe the state of and need for modeling everting vine robots. Quasi-static models of growth and retraction and kinematic and force-balance models of steering and environment interaction have been developed that use simplifying assumptions and limit the involved degrees of freedom. Third, we report on everting vine robot control and planning techniques that have been developed to move the robot tip to a target, using a variety of modalities to provide reference inputs to the robot. Fourth, we highlight the benefits and challenges of using this paradigm of movement for various applications. Everting vine robot applications to date include deploying and reconfiguring structures, navigating confined spaces, and applying forces on the environment. We conclude by identifying gaps in the state of the art and discussing opportunities for future research to advance everting vine robots and their usefulness in the field.

A General 3D Model for Growth Dynamics of Sensory-Growth Systems: From Plants to Robotics

In recent years, there has been a rise in interest in the development of self-growing robotics inspired by the moving-by-growing paradigm of plants. In particular, climbing plants capitalize on their slender structures to successfully negotiate unstructured environments while employing a combination of two classes of growth-driven movements: tropic responses, growing toward or away from an external stimulus, and inherent nastic movements, such as periodic circumnutations, which promote exploration. In order to emulate these complex growth dynamics in a 3D environment, a general and rigorous mathematical framework is required. Here, we develop a general 3D model for rod-like organs adopting the Frenet-Serret frame, providing a useful framework from the standpoint of robotics control. Differential growth drives the dynamics of the organ, governed by both internal and external cues while neglecting elastic responses. We describe the numerical method required to implement this model and perform numerical simulations of a number of key scenarios, showcasing the applicability of our model. In the case of responses to external stimuli, we consider a distant stimulus (such as sunlight and gravity), a point stimulus (a point light source), and a line stimulus that emulates twining of a climbing plant around a support. We also simulate circumnutations, the response to an internal oscillatory cue, associated with search processes. Lastly, we also demonstrate the superposition of the response to an external stimulus and circumnutations. In addition, we consider a simple example illustrating the possible use of an optimal control approach in order to recover tropic dynamics in a way that may be relevant for robotics use. In all, the model presented here is general and robust, paving the way for a deeper understanding of plant response dynamics and also for novel control systems for newly developed self-growing robots.

Linearized Bayesian inference for Young's modulus parameter field in an elastic model of slender structures

The deformations of several slender structures at nano-scale are conceivably sensitive to their non-homogenous elasticity. Owing to their small scale, it is not feasible to discern their elasticity parameter fields accurately using observations from physical experiments. Molecular dynamics simulations can provide an alternative or additional source of data. However, the challenges still lie in developing computationally efficient and robust methods to solve inverse problems to infer the elasticity parameter field from the deformations. In this paper, we formulate an inverse problem governed by a linear elastic model in a Bayesian inference framework. To make the problem tractable, we use a Gaussian approximation of the posterior probability distribution that results from the Bayesian solution of the inverse problem of inferring Young's modulus parameter fields from available data. The performance of the computational framework is demonstrated using two representative loading scenarios, one involving cantilever bending and the other involving stretching of a helical rod (an intrinsically curved structure). The results show that smoothly varying parameter fields can be reconstructed satisfactorily from noisy data. We also quantify the uncertainty in the inferred parameters and discuss the effect of the quality of the data on the reconstructions.

Intermittent sliding locomotion of a two-link body

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.

Inverse Design Strategies for 3D Surfaces Formed by Mechanically Guided Assembly

Deterministic transformations of 2D patterns of materials into well-controlled 3D mesostructures serve as the basis for manufacturing methods that can bypass limitations of conventional 3D micro/nanofabrication. Here, guided mechanical buckling processes provide access to a rich range of complex 3D mesostructures in high-performance materials, from inorganic and organic semiconductors, metals and dielectrics, to ceramics and even 2D materials (e.g., graphene, MoS₂ ). Previous studies demonstrate that iterative computational procedures can define design parameters for certain targeted 3D configurations, but without the ability to address complex shapes. A technical need is in efficient, generalized inverse design algorithms that directly yield sets of optimized parameters. Here, such schemes are introduced, where the distributions of thicknesses across arrays of separated or interconnected ribbons provide scalable routes to 3D surfaces with a broad range of targeted shapes. Specifically, discretizing desired shapes into 2D ribbon components allows for analytic solutions to the inverse design of centrally symmetric and even general surfaces, in an approximate manner. Combined theoretical, numerical, and experimental studies of ≈20 different 3D structures with characteristic sizes (e.g., ribbon width) ranging from ≈200 µm to ≈2 cm and with geometries that resemble hemispheres, fire balloons, flowers, concave lenses, saddle surfaces, waterdrops, and rodents, illustrate the essential ideas.

TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.

Soft Robotics as an Enabling Technology for Agroforestry Practice and Research

The shortage of qualified human labor is a key challenge facing farmers, limiting profit margins and preventing the adoption of sustainable and diversified agroecosystems, such as agroforestry. New technologies in robotics could offer a solution to such limitations. Advances in soft arms and manipulators can enable agricultural robots that can have better reach and dexterity around plants than traditional robots equipped with hard industrial robotic arms. Soft robotic arms and manipulators can be far less expensive to manufacture and significantly lighter than their hard counterparts. Furthermore, they can be simpler to design and manufacture since they rely on fluidic pressurization as the primary mechanisms of operation. However, current soft robotic arms are difficult to design and control, slow to actuate, and have limited payloads. In this paper, we discuss the benefits and challenges of soft robotics technology and what it could mean for sustainable agriculture and agroforestry.

Topology, Geometry, and Mechanics of Strongly Stretched and Twisted Filaments: Solenoids, Plectonemes, and Artificial Muscle Fibers

Soft elastic filaments that can be stretched, bent, and twisted exhibit a range of topologically and geometrically complex morphologies. Recently, a number of experiments have shown how to use these building blocks to create filament-based artificial muscles that use the conversion of writhe to extension or contraction, exposing the connection between topology, geometry, and mechanics. Here, we combine numerical simulations of soft elastic filaments that account for geometric nonlinearities and self-contact to map out the basic structures underlying artificial muscle fibers in a phase diagram that is a function of the extension and twist density. We then use ideas from computational topology to track the interconversion of link, twist, and writhe in these geometrically complex physical structures to explain the physical principles underlying artificial muscle fibers and provide guidelines for their design.

Instability-driven oscillations of elastic microfilaments

Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory and low-order bead-spring models. Our results show that, away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella.

Modeling and simulation of complex dynamic musculoskeletal architectures

Natural creatures, from fish and cephalopods to snakes and birds, combine neural control, sensory feedback and compliant mechanics to effectively operate across dynamic, uncertain environments. In order to facilitate the understanding of the biophysical mechanisms at play and to streamline their potential use in engineering applications, we present here a versatile numerical approach to the simulation of musculoskeletal architectures. It relies on the assembly of heterogenous, active and passive Cosserat rods into dynamic structures that model bones, tendons, ligaments, fibers and muscle connectivity. We demonstrate its utility in a range of problems involving biological and soft robotic scenarios across scales and environments: from the engineering of millimeter-long bio-hybrid robots to the synthesis and reconstruction of complex musculoskeletal systems. The versatility of this methodology offers a framework to aid forward and inverse bioengineering designs as well as fundamental discovery in the functioning of living organisms.

Neuromuscular actuation of biohybrid motile bots

The integration of muscle cells with soft robotics in recent years has led to the development of biohybrid machines capable of untethered locomotion. A major frontier that currently remains unexplored is neuronal actuation and control of such muscle-powered biohybrid machines. As a step toward this goal, we present here a biohybrid swimmer driven by on-board neuromuscular units. The body of the swimmer consists of a free-standing soft scaffold, skeletal muscle tissue, and optogenetic stem cell-derived neural cluster containing motor neurons. Myoblasts embedded in extracellular matrix self-organize into a muscle tissue guided by the geometry of the scaffold, and the resulting muscle tissue is cocultured in situ with a neural cluster. Motor neurons then extend neurites selectively toward the muscle and innervate it, developing functional neuromuscular units. Based on this initial construct, we computationally designed, optimized, and implemented light-sensitive flagellar swimmers actuated by these neuromuscular units. Cyclic muscle contractions, induced by neural stimulation, drive time-irreversible flagellar dynamics, thereby providing thrust for untethered forward locomotion of the swimmer. Overall, this work demonstrates an example of a biohybrid robot implementing neuromuscular actuation and illustrates a path toward the forward design and control of neuron-enabled biohybrid machines.

Efficient sliding locomotion with isotropic friction

Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots, for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction. We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction.