Control of soft robots with inertial dynamics.

Soft robots promise improved safety and capability over rigid robots when deployed near humans or in complex, delicate, and dynamic environments. However, infinite degrees of freedom and the potential for highly nonlinear dynamics severely complicate their modeling and control. Analytical and machine learning methodologies have been applied to model soft robots but with constraints: quasi-static motions, quasi-linear deflections, or both. Here, we advance the modeling and control of soft robots into the inertial, nonlinear regime. We controlled motions of a soft, continuum arm with velocities 10 times larger and accelerations 40 times larger than those of previous work and did so for high-deflection shapes with more than 110° of curvature. We leveraged a data-driven learning approach for modeling, based on Koopman operator theory, and we introduce the concept of the static Koopman operator as a pregain term in optimal control. Our approach is rapid, requiring less than 5 min of training; is computationally low cost, requiring as little as 0.5 s to build the model; and is design agnostic, learning and accurately controlling two morphologically different soft robots. This work advances rapid modeling and control for soft robots from the realm of quasi-static to inertial, laying the groundwork for the next generation of compliant and highly dynamic robots.

Engineered jumpers overcome biological limits via work multiplication.

For centuries, scientists have explored the limits of biological jump height1,2, and for decades, engineers have designed jumping machines3-18 that often mimicked or took inspiration from biological jumpers. Despite these efforts, general analyses are missing that compare the energetics of biological and engineered jumpers across scale. Here we show how biological and engineered jumpers have key differences in their jump energetics. The jump height of a biological jumper is limited by the work its linear motor (muscle) can produce in a single stroke. By contrast, the jump height of an engineered device can be far greater because its ratcheted or rotary motor can 'multiply work' during repeated strokes or rotations. As a consequence of these differences in energy production, biological and engineered jumpers should have divergent designs for maximizing jump height. Following these insights, we created a device that can jump over 30 metres high, to our knowledge far higher than previous engineered jumpers and over an order of magnitude higher than the best biological jumpers. Our work advances the understanding of jumping, shows a new level of performance, and underscores the importance of considering the differences between engineered and biological systems.

Controlling subterranean forces enables a fast, steerable, burrowing soft robot.

Robotic navigation on land, through air, and in water is well researched; numerous robots have successfully demonstrated motion in these environments. However, one frontier for robotic locomotion remains largely unexplored-below ground. Subterranean navigation is simply hard to do, in part because the interaction forces of underground motion are higher than in air or water by orders of magnitude and because we lack for these interactions a robust fundamental physics understanding. We present and test three hypotheses, derived from biological observation and the physics of granular intrusion, and use the results to inform the design of our burrowing robot. These results reveal that (i) tip extension reduces total drag by an amount equal to the skin drag of the body, (ii) granular aeration via tip-based airflow reduces drag with a nonlinear dependence on depth and flow angle, and (iii) variation of the angle of the tip-based flow has a nonmonotonic effect on lift in granular media. Informed by these results, we realize a steerable, root-like soft robot that controls subterranean lift and drag forces to burrow faster than previous approaches by over an order of magnitude and does so through real sand. We also demonstrate that the robot can modulate its pullout force by an order of magnitude and control its direction of motion in both the horizontal and vertical planes to navigate around subterranean obstacles. Our results advance the understanding and capabilities of robotic subterranean locomotion.

Hard questions for soft robotics.

The establishment of a new academic field is often characterized by a phase of rapid growth, as seen over the last decade in the field of soft robotics. However, such growth can be followed by an equally rapid decline if concerted efforts are not made by the community. Here, we argue that for soft robotics to take root and have impact in the next decade, we must move beyond "soft for soft's sake" and ensure that each study makes a meaningful contribution to the field and, ideally, to robotics and engineering more broadly. We present a three-tiered categorization to help researchers and reviewers evaluate work and guide studies toward higher levels of contribution. We ground this categorization with historical examples of soft solutions outside of robotics that were transformative. We believe that the proposed self-reflection is essential if soft robotics is to be an impactful field in the next decade, advancing robotics and engineering both within and beyond academia and creating soft solutions that are quantitatively superior to the current state of the art-soft, rigid, or otherwise.

Mechanism and function of root circumnutation.

Early root growth is critical for plant establishment and survival. We have identified a molecular pathway required for helical root tip movement known as circumnutation. Here, we report a multiscale investigation of the regulation and function of this phenomenon. We identify key cell signaling events comprising interaction of the ethylene, cytokinin, and auxin hormone signaling pathways. We identify the gene Oryza sativa histidine kinase-1 (HK1) as well as the auxin influx carrier gene OsAUX1 as essential regulators of this process in rice. Robophysical modeling and growth challenge experiments indicate circumnutation is critical for seedling establishment in rocky soil, consistent with the long-standing hypothesis that root circumnutation facilitates growth past obstacles. Thus, the integration of robotics, physics, and biology has elucidated the functional importance of root circumnutation and uncovered the molecular mechanisms underlying its regulation.

Forcing the issue: testing gecko-inspired adhesives.

Materials are traditionally tested either by imposing controlled displacements and measuring the corresponding forces, or by imposing controlled forces. The first of these approaches is more common because it is straightforward to control the displacements of a stiff apparatus and, if the material suddenly fails, little energy is released. However, when testing gecko-inspired adhesives, an applied force paradigm is closer to how the adhesives are loaded in practice. Moreover, we demonstrate that the controlled displacement paradigm can lead to artefacts in the assumed behaviour unless the imposed loading trajectory precisely matches the deflections that would occur in applications. We present the design of a controlled-force system and protocol for testing directional gecko-inspired adhesives and show that results obtained with it are in some cases substantially different from those with controlled-displacement testing. An advantage of the controlled-force testing approach is that it allows accurate generation of adhesive limit curves without prior knowledge of the expected behaviour of the material or the loading details associated with practical applications.

Tunable Photothermal Actuation Enabled by Photoswitching of Donor-Acceptor Stenhouse Adducts.

We report a visible light-responsive bilayer actuator driven by the photothermal properties of a unique molecular photoswitch: donor-acceptor Stenhouse adduct (DASA). We demonstrate a synthetic platform to chemically conjugate DASA to a load-bearing poly(hexyl methacrylate) (PHMA) matrix via Diels-Alder click chemistry that enables access to stimuli-responsive materials on scale. By taking advantage of the negative photochromism and switching kinetics of DASA, we can tune the thermal expansion and actuation performance of DASA-PHMA under constant light intensity. This extends the capabilities of currently available responsive soft actuators for which mechanical response is determined exclusively by light intensity and enables the use of abundant broadband light sources to trigger tunable responses. We demonstrate actuation performance using a visible light-powered cantilever capable of lifting weight against gravity as well as a simple crawler. These results add a new strategy to the toolbox of tunable photothermal actuation by using the molecular photoswitch DASA.

An untethered isoperimetric soft robot.

For robots to be useful for real-world applications, they must be safe around humans, be adaptable to their environment, and operate in an untethered manner. Soft robots could potentially meet these requirements; however, existing soft robotic architectures are limited by their ability to scale to human sizes and operate at these scales without a tether to transmit power or pressurized air from an external source. Here, we report an untethered, inflated robotic truss, composed of thin-walled inflatable tubes, capable of shape change by continuously relocating its joints, while its total edge length remains constant. Specifically, a set of identical roller modules each pinch the tube to create an effective joint that separates two edges, and modules can be connected to form complex structures. Driving a roller module along a tube changes the overall shape, lengthening one edge and shortening another, while the total edge length and hence fluid volume remain constant. This isoperimetric behavior allows the robot to operate without compressing air or requiring a tether. Our concept brings together advantages from three distinct types of robots-soft, collective, and truss-based-while overcoming certain limitations of each. Our robots are robust and safe, like soft robots, but not limited by a tether; are modular, like collective robots, but not limited by complex subunits; and are shape-changing, like truss robots, but not limited by rigid linear actuators. We demonstrate two-dimensional (2D) robots capable of shape change and a human-scale 3D robot capable of punctuated rolling locomotion and manipulation, all constructed with the same modular rollers and operating without a tether.

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.

Connecting the legs with a spring improves human running economy.

Human running is inefficient. For every 10 calories burned, less than 1 is needed to maintain a constant forward velocity - the remaining energy is, in a sense, wasted. The majority of this wasted energy is expended to support the bodyweight and redirect the center of mass during the stance phase of gait. An order of magnitude less energy is expended to brake and accelerate the swinging leg. Accordingly, most devices designed to increase running efficiency have targeted the costlier stance phase of gait. An alternative approach is seen in nature: spring-like tissues in some animals and humans are believed to assist leg swing. While it has been assumed that such a spring simply offloads the muscles that swing the legs, thus saving energy, this mechanism has not been experimentally investigated. Here, we show that a spring, or 'exotendon', connecting the legs of a human reduces the energy required for running by 6.4±2.8%, and does so through a complex mechanism that produces savings beyond those associated with leg swing. The exotendon applies assistive forces to the swinging legs, increasing the energy optimal stride frequency. Runners then adopt this frequency, taking faster and shorter strides, and reduce the joint mechanical work to redirect their center of mass. Our study shows how a simple spring improves running economy through a complex interaction between the changing dynamics of the body and the adaptive strategies of the runner, highlighting the importance of considering each when designing systems that couple human and machine.

Spatially variant microstructured adhesive with one-way friction.

Surface microstructures in nature enable diverse and intriguing properties, from the iridescence of butterfly wings to the hydrophobicity of lotus leaves to the controllable adhesion of gecko toes. Many artificial analogues exist; however, there is a key characteristic of the natural materials that is largely absent from the synthetic versions-spatial variation. Here we show that exploiting spatial variation in the design of one class of synthetic microstructure, gecko-inspired adhesives, enables one-way friction, an intriguing property of natural gecko adhesive. When loaded along a surface in the preferred direction, our adhesive material supports forces 100 times larger than when loaded in the reverse direction, representing an asymmetry significantly larger than demonstrated in spatially uniform adhesives. Our study suggests that spatial variation has the potential to advance artificial microstructures, helping to close the gap between synthetic and natural materials.

A Soft, Steerable Continuum Robot That Grows via Tip Extension.

Soft continuum robots exhibit access and manipulation capabilities in constrained and cluttered environments not achievable by traditional robots. However, navigation of these robots can be difficult due to the kinematics of these devices. Here we describe the design, modeling, and control of a soft continuum robot with a tip extension degree of freedom. This design enables extremely simple navigation of the robot through decoupled steering and forward movement. To navigate to a destination, the robot is steered to point at the destination and the extension degree of freedom is used to reach it. Movement of the tip is always in the direction tangent to the end of the robot's backbone, independent of the shape of the rest of the backbone. Steering occurs by inflating multiple series pneumatic artificial muscles arranged radially around the backbone and extending along the robot's whole length, while extension is implemented using pneumatically driven tip eversion. We present models and experimentally verify the growing robot kinematics. Control of the growing robot is demonstrated using an eye-in-hand visual servo control law that enables growth and steering of the robot to designated locations.

Pilot Study of Cadence, a Novel Shoe for Patients with Foot Drop.

Foot Drop is a mobility disorder that limits ankle dorsiflexion, complicating the swing phase of gait and balance. It is a common result of a neurological injury or disease such as stroke, cerebral palsy or multiple sclerosis. Here we present Cadence, a low-cost assistive shoe designed to passively improve the biomechanics and rhythmicity of gait for people with foot drop. The shoe reduces the magnitude of scuffing forces when dragging the foot forward across the ground by using regions of low-friction material that can retract into the shoe to restore friction during stance phase. We report the results from a pilot study of Cadence, which show the biomechanical and performance effects of the device for five adults with foot drop due to neurological disorder. In 3 of the 5 subjects, we found that the shoe immediately improved gait mechanics, speed over ground, and qualitative gait comfort.

Toward the Design of Personalized Continuum Surgical Robots.

Robot-assisted minimally invasive surgical systems enable procedures with reduced pain, recovery time, and scarring compared to traditional surgery. While these improvements benefit a large number of patients, safe access to diseased sites is not always possible for specialized patient groups, including pediatric patients, due to their anatomical differences. We propose a patient-specific design paradigm that leverages the surgeon's expertise to design and fabricate robots based on preoperative medical images. The components of the patient-specific robot design process are a virtual reality design interface enabling the surgeon to design patient-specific tools, 3-D printing of these tools with a biodegradable polyester, and an actuation and control system for deployment. The designed robot is a concentric tube robot, a type of continuum robot constructed from precurved, elastic, nesting tubes. We demonstrate the overall patient-specific design workflow, from preoperative images to physical implementation, for an example clinical scenario: nonlinear renal access to a pediatric kidney. We also measure the system's behavior as it is deployed through real and artificial tissue. System integration and successful benchtop experiments in ex vivo liver and in a phantom patient model demonstrate the feasibility of using a patient-specific design workflow to plan, fabricate, and deploy personalized, flexible continuum robots.

A soft robot that navigates its environment through growth.

Across kingdoms and length scales, certain cells and organisms navigate their environments not through locomotion but through growth. This pattern of movement is found in fungal hyphae, developing neurons, and trailing plants, and is characterized by extension from the tip of the body, length change of hundreds of percent, and active control of growth direction. This results in the abilities to move through tightly constrained environments and form useful three-dimensional structures from the body. We report a class of soft pneumatic robot that is capable of a basic form of this behavior, growing substantially in length from the tip while actively controlling direction using onboard sensing of environmental stimuli; further, the peak rate of lengthening is comparable to rates of animal and robot locomotion. This is enabled by two principles: Pressurization of an inverted thin-walled vessel allows rapid and substantial lengthening of the tip of the robot body, and controlled asymmetric lengthening of the tip allows directional control. Further, we demonstrate the abilities to lengthen through constrained environments by exploiting passive deformations and form three-dimensional structures by lengthening the body of the robot along a path. Our study helps lay the foundation for engineered systems that grow to navigate the environment.

A robotic device using gecko-inspired adhesives can grasp and manipulate large objects in microgravity.

Grasping and manipulating uncooperative objects in space is an emerging challenge for robotic systems. Many traditional robotic grasping techniques used on Earth are infeasible in space. Vacuum grippers require an atmosphere, sticky attachments fail in the harsh environment of space, and handlike opposed grippers are not suited for large, smooth space debris. We present a robotic gripper that can gently grasp, manipulate, and release both flat and curved uncooperative objects as large as a meter in diameter while in microgravity. This is enabled by (i) space-qualified gecko-inspired dry adhesives that are selectively turned on and off by the application of shear forces, (ii) a load-sharing system that scales small patches of these adhesives to large areas, and (iii) a nonlinear passive wrist that is stiff during manipulation yet compliant when overloaded. We also introduce and experimentally verify a model for determining the force and moment limits of such an adhesive system. Tests in microgravity show that robotic grippers based on dry adhesion are a viable option for eliminating space debris in low Earth orbit and for enhancing missions in space.

Series Pneumatic Artificial Muscles (sPAMs) and Application to a Soft Continuum Robot.

We describe a new series pneumatic artificial muscle (sPAM) and its application as an actuator for a soft continuum robot. The robot consists of three sPAMs arranged radially round a tubular pneumatic backbone. Analogous to tendons, the sPAMs exert a tension force on the robot's pneumatic backbone, causing bending that is approximately constant curvature. Unlike a traditional tendon driven continuum robot, the robot is entirely soft and contains no hard components, making it safer for human interaction. Models of both the sPAM and soft continuum robot kinematics are presented and experimentally verified. We found a mean position accuracy of 5.5 cm for predicting the end-effector position of a 42 cm long robot with the kinematic model. Finally, closed-loop control is demonstrated using an eye-in-hand visual servo control law which provides a simple interface for operation by a human. The soft continuum robot with closed-loop control was found to have a step-response rise time and settling time of less than two seconds.

Fruit fly scale robots can hover longer with flapping wings than with spinning wings.

Hovering flies generate exceptionally high lift, because their wings generate a stable leading edge vortex. Micro flying robots with a similar wing design can generate similar high lift by either flapping or spinning their wings. While it requires less power to spin a wing, the overall efficiency depends also on the actuator system driving the wing. Here, we present the first holistic analysis to calculate how long a fly-inspired micro robot can hover with flapping versus spinning wings across scales. We integrate aerodynamic data with data-driven scaling laws for actuator, electronics and mechanism performance from fruit fly to hummingbird scales. Our analysis finds that spinning wings driven by rotary actuators are superior for robots with wingspans similar to hummingbirds, yet flapping wings driven by oscillatory actuators are superior at fruit fly scale. This crossover is driven by the reduction in performance of rotary compared with oscillatory actuators at smaller scale. Our calculations emphasize that a systems-level analysis is essential for trading-off flapping versus spinning wings for micro flying robots.

Stress distribution and contact area measurements of a gecko toe using a high-resolution tactile sensor.

The adhesive systems of geckos have been widely studied and have been a great source of bioinspiration. Load-sharing (i.e. preventing stress concentrations through equal distribution of loads) is necessary to maximize the performance of an adhesive system, but it is not known to what extent load-sharing occurs in gecko toes. In this paper, we present in vivo measurements of the stress distribution and contact area on the toes of a tokay gecko (Gekko gecko) using a custom tactile sensor with 100 µm spatial resolution. We found that the stress distributions were nonuniform, with large variations in stress between and within lamellae, suggesting that load-sharing in the tokay gecko is uneven. These results may be relevant to the understanding of gecko morphology and the design of improved synthetic adhesive systems.

Human climbing with efficiently scaled gecko-inspired dry adhesives.

Since the discovery of the mechanism of adhesion in geckos, many synthetic dry adhesives have been developed with desirable gecko-like properties such as reusability, directionality, self-cleaning ability, rough surface adhesion and high adhesive stress. However, fully exploiting these adhesives in practical applications at different length scales requires efficient scaling (i.e. with little loss in adhesion as area grows). Just as natural gecko adhesives have been used as a benchmark for synthetic materials, so can gecko adhesion systems provide a baseline for scaling efficiency. In the tokay gecko (Gekko gecko), a scaling power law has been reported relating the maximum shear stress σmax to the area A: σmax ∝ A(-1/4). We present a mechanical concept which improves upon the gecko's non-uniform load-sharing and results in a nearly even load distribution over multiple patches of gecko-inspired adhesive. We created a synthetic adhesion system incorporating this concept which shows efficient scaling across four orders of magnitude of area, yielding an improved scaling power law: σmax ∝ A(-1/50). Furthermore, we found that the synthetic adhesion system does not fail catastrophically when a simulated failure is induced on a portion of the adhesive. In a practical demonstration, the synthetic adhesion system enabled a 70 kg human to climb vertical glass with 140 cm(2) of adhesive per hand.