Nodes for modes: nodal honeycomb metamaterial enables a soft robot with multimodal locomotion.

Soft-bodied animals, such as worms and snakes, use many muscles in different ways to traverse unstructured environments and inspire tools for accessing confined spaces. They demonstrate versatility of locomotion which is essential for adaptation to changing terrain conditions. However, replicating such versatility in untethered soft-bodied robots with multimodal locomotion capabilities have been challenging due to complex fabrication processes and limitations of soft body structures to accommodate hardware such as actuators, batteries and circuit boards. Here, we present MetaCrawler, a 3D printed metamaterial soft robot designed for multimodal and omnidirectional locomotion. Our design approach facilitated an easy fabrication process through a discrete assembly of a modular nodal honeycomb lattice with soft and hard components. A crucial benefit of the nodal honeycomb architecture is the ability of its hard components, nodes, to accommodate a distributed actuation system, comprising servomotors, control circuits, and batteries. Enabled by this distributed actuation, MetaCrawler achieves five locomotion modes: peristalsis, sidewinding, sideways translation, turn-in-place, and anguilliform. Demonstrations showcase MetaCrawler's adaptability in confined channel navigation, vertical traversing, and maze exploration. This soft robotic system holds the potential to offer easy-to-fabricate and accessible solutions for multimodal locomotion in applications such as search and rescue, pipeline inspection, and space missions.

Probing with Each Step: How a Walking Crab-like Robot Classifies Buried Cylinders in Sand with Hall-Effect Sensors.

Shallow underwater environments around the world are contaminated with unexploded ordnances (UXOs). Current state-of-the-art methods for UXO detection and localization use remote sensing systems. Furthermore, human divers are often tasked with confirming UXO existence and retrieval which poses health and safety hazards. In this paper, we describe the application of a crab robot with leg-embedded Hall effect-based sensors to detect and distinguish between UXOs and non-magnetic objects partially buried in sand. The sensors consist of Hall-effect magnetometers and permanent magnets embedded in load bearing compliant segments. The magnetometers are sensitive to magnetic objects in close proximity to the legs and their movement relative to embedded magnets, allowing for both proximity and force-related feedback in dynamically obtained measurements. A dataset of three-axis measurements is collected as the robot steps near and over different UXOs and UXO-like objects, and a convolutional neural network is trained on time domain inputs and evaluated by 5-fold cross validation. Additionally, we propose a novel method for interpreting the importance of measurements in the time domain for the trained classifier. The results demonstrate the potential for accurate and efficient UXO and non-UXO discrimination in the field.

Elastic/viscoelastic polymer bilayers: a model-based approach to stretch-responsive constructs.

The use of polymers in the fabrication of bilayers for stimuli-responsive systems is well-known, yet viscoelasticity and viscoelastic models representing bilayer behavior have received surprisingly little attention. Of particular recent interest to us are simple polymeric bilayers in which one material, such as styrene-ethylene-propylene-styrene (SEPS) or styrene-isobutylene-styrene (SIBS), shows typical rubbery elastic response upon extension and retraction, and the other, an unvulcanized, low-Tg polymer such as butyl rubber (butyl), exhibits a viscoelastic response. When such a bilayer strip is extended to a fixed strain and held for several seconds followed by sudden release of this strain, rapid curling is observed, achieving a maximum curvature within 1 second, with a gradual uncurling, typically taking 300-600 seconds to eventually return to a flat strip. Attention has been directed to modeling the observed bilayer behavior. We compare predicted curvature and relaxation time constants from finite element analysis (FEA) simulations using Maxwell, Zener, Generalized Maxwell, and Parallel Rheological Framework (PRF) viscoelastic models to the experimentally measured values. We find that the Generalized Maxwell model predicts curvature over time with the lowest overall mean absolute scaled error (MASE) of 0.519, corresponding to a 4.9% difference from the second lowest error model and a 76.8% difference from the highest error model. Building upon an understanding of the material mechanics in simple bilayer strips, more complex bilayer systems can be designed. Samples of cross and weave geometries were fabricated from bilayer films and initial testing demonstrates how these materials can be used in potential applications.

Modular Design of a Polymer-Bilayer-Based Mechanically Compliant Worm-Like Robot.

Soft earthworm-like robots that exhibit mechanical compliance can, in principle, navigate through uneven terrains and constricted spaces that are inaccessible to traditional legged and wheeled robots. However, unlike the biological originals that they mimic, most of the worm-like robots reported to date contain rigid components that limit their compliance, such as electromotors or pressure-driven actuation systems. Here, a mechanically compliant worm-like robot with a fully modular body that is based on soft polymers is reported. The robot is composed of strategically assembled, electrothermally activated polymer bilayer actuators, which are based on a semicrystalline polyurethane with an exceptionally large nonlinear thermal expansion coefficient. The segments are designed on the basis of a modified Timoshenko model, and finite element analysis simulation is used to describe their performance. Upon electrical activation of the segments with basic waveform patterns, the robot can move through repeatable peristaltic locomotion on exceptionally slippery or sticky surfaces and it can be oriented in any direction. The soft body enables the robot to wriggle through openings and tunnels that are much smaller than its cross-section.

Fundamentals of burrowing in soft animals and robots.

Creating burrows through natural soils and sediments is a problem that evolution has solved numerous times, yet burrowing locomotion is challenging for biomimetic robots. As for every type of locomotion, forward thrust must overcome resistance forces. In burrowing, these forces will depend on the sediment mechanical properties that can vary with grain size and packing density, water saturation, organic matter and depth. The burrower typically cannot change these environmental properties, but can employ common strategies to move through a range of sediments. Here we propose four challenges for burrowers to solve. First, the burrower has to create space in a solid substrate, overcoming resistance by e.g., excavation, fracture, compression, or fluidization. Second, the burrower needs to locomote into the confined space. A compliant body helps fit into the possibly irregular space, but reaching the new space requires non-rigid kinematics such as longitudinal extension through peristalsis, unbending, or eversion. Third, to generate the required thrust to overcome resistance, the burrower needs to anchor within the burrow. Anchoring can be achieved through anisotropic friction or radial expansion, or both. Fourth, the burrower must sense and navigate to adapt the burrow shape to avoid or access different parts of the environment. Our hope is that by breaking the complexity of burrowing into these component challenges, engineers will be better able to learn from biology, since animal performance tends to exceed that of their robotic counterparts. Since body size strongly affects space creation, scaling may be a limiting factor for burrowing robotics, which are typically built at larger scales. Small robots are becoming increasingly feasible, and larger robots with non-biologically-inspired anteriors (or that traverse pre-existing tunnels) can benefit from a deeper understanding of the breadth of biological solutions in current literature and to be explored by continued research.

Optimal planar leg geometry in robots and crabs for idealized rocky terrain.

Natural terrain is uneven so it may be beneficial to grasp onto the depressions or 'valleys' between obstacles when walking over such a surface. To examine how leg geometry influences walking across obstacles with valleys, we (1) modeled the performance of a two-linkage leg with parallel axis 'hip' and 'knee' joints to determine how relative segment lengths influence stepping across rocks of varying diameter, and (2) measured the walking limbs in two species of intertidal crabs,Hemigrapsus nudusandPachygrapsus crassipes, which live on rocky shores and granular terrains. We idealized uneven terrains as adjacent rigid hemispherical 'rocks' with valleys between them and calculated kinematic factors such as workspace, limb angles with respect to the ground, and body configurations needed to step over rocks. We first find that the simulated foot tip radius relative to the rock radius is limited by friction and material failure. To enable force closure for grasping, and assuming that friction coefficients above 0.5 are unrealistic, the foot tip radius must be at least 10 times smaller than that of the rocks. However, ratios above 15 are at risk of fracture. Second, we find the theoretical optimal leg geometry for robots is, with the distal segment 0.63 of the total length, which enables the traversal of rocks with a diameter that is 37% of the total leg length. Surprisingly, the intertidal crabs' walking limbs cluster around the same limb ratio of 0.63, showing deviations for limbs less specialized for walking. Our results can be applied broadly when designing segment lengths and foot shapes for legged robots on uneven terrain, as demonstrated here using a hexapod crab-inspired robot. Furthermore, these findings can inform our understanding of the evolutionary patterns in leg anatomy associated with adapting to rocky terrain.

Hands to Hexapods, Wearable User Interface Design for Specifying Leg Placement for Legged Robots.

Specifying leg placement is a key element for legged robot control, however current methods for specifying individual leg motions with human-robot interfaces require mental concentration and the use of both arm muscles. In this paper, a new control interface is discussed to specify leg placement for hexapod robot by using finger motions. Two mapping methods are proposed and tested with lab staff, Joint Angle Mapping (JAM) and Tip Position Mapping (TPM). The TPM method was shown to be more efficient. Then a manual controlled gait based on TPM is compared with fixed gait and camera-based autonomous gait in a Webots simulation to test the obstacle avoidance performance on 2D terrain. Number of Contacts (NOC) for each gait are recorded during the tests. The results show that both the camera-based autonomous gait and the TPM are effective methods in adjusting step size to avoid obstacles. In high obstacle density environments, TPM reduces the number of contacts to 25% of the fixed gaits, which is even better than some of the autonomous gaits with longer step size. This shows that TPM has potential in environments and situations where autonomous footfall planning fails or is unavailable. In future work, this approach can be improved by combining with haptic feedback, additional degrees of freedom and artificial intelligence.

Sideways crab-walking is faster and more efficient than forward walking for a hexapod robot.

Articulated legs enable the selection of robot gaits, including walking in different directions such as forward or sideways. For longer distances, the best gaits might maximize velocity or minimize the cost of transport (COT). While animals often have morphology suited to walking either forward (like insects) or sideways (like crabs), hexapod robots often default to forward walking. In this paper, we compare forward walking with crab-like sideways walking. To do this, a simple gait design method is introduced for determining forward and sideways gaits with equivalent body heights and step heights. Specifically, the frequency and stride lengths are tuned within reasonable constraints to find gaits that represent a robot's performance potential in terms of speed and energy cost. Experiments are performed in both dynamic simulation in Webots and a laboratory environment with our 18 degree-of-freedom hexapod robot, Sebastian. With the common three joint leg design, the results show that sideways walking is overall better (75% greater walking speed and 40% lower COT). The performance of sideways walking was better on both hard floors and granular media (dry play sand). This supports development of future crab-like walking robots for future applications. In future work, this approach may be used to develop nominal gaits without extensive optimization, and to explore whether the advantages of sideways walking persist for other hexapod designs.

Obstacle Avoidance Path Planning for Worm-like Robot Using Bézier Curve.

Worm-like robots have demonstrated great potential in navigating through environments requiring body shape deformation. Some examples include navigating within a network of pipes, crawling through rubble for search and rescue operations, and medical applications such as endoscopy and colonoscopy. In this work, we developed path planning optimization techniques and obstacle avoidance algorithms for the peristaltic method of locomotion of worm-like robots. Based on our previous path generation study using a modified rapidly exploring random tree (RRT), we have further introduced the Bézier curve to allow more path optimization flexibility. Using Bézier curves, the path planner can explore more areas and gain more flexibility to make the path smoother. We have calculated the obstacle avoidance limitations during turning tests for a six-segment robot with the developed path planning algorithm. Based on the results of our robot simulation, we determined a safe turning clearance distance with a six-body diameter between the robot and the obstacles. When the clearance is less than this value, additional methods such as backward locomotion may need to be applied for paths with high obstacle offset. Furthermore, for a worm-like robot, the paths of subsequent segments will be slightly different than the path of the head segment. Here, we show that as the number of segments increases, the differences between the head path and tail path increase, necessitating greater lateral clearance margins.

Dactyls and inward gripping stance for amphibious crab-like robots on sand.

Sandy beaches are areas that challenge robots of all sizes, especially smaller scale robots. Sand can hinder locomotion and waves apply hydrodynamic forces which can displace, reorient, or even invert the robot. Crab-like legs and gaits are well suited for this environment and could be used as inspiration for an improved design of robots operating in this terrain. Tapered, curved feet (similar to crab dactyl shape) paired with a distributed inward gripping method are hypothesized to enable better anchoring in sand to resist hydrodynamic forces. This work demonstrates that crab-like legs can withstand vertical forces that are larger than the body weight (e.g. in submerged sand, the force required to lift the robot can be up to 138% of the robot weight). Such legs help the robot hold its place against hydrodynamic forces imparted by waves (e.g. compared to displacement of 42.7 mm with the original feet, crab-like feet reduced displacement to 1.6 mm in lab wave tests). These feet are compatible with walking on sandy and rocky terrain (tested at three speeds: slow, medium, and fast), albeit at reduced speeds from traditional feet. This work shows potential for future robots to utilize tapered and curved feet to traverse challenging surf zone terrain where biological crabs thrive.

An Analysis of Peristaltic Locomotion for Maximizing Velocity or Minimizing Cost of Transport of Earthworm-Like Robots.

Earthworm-like peristaltic locomotion has been implemented in >50 robots, with many potential applications in otherwise inaccessible terrain. Design guidelines for peristaltic locomotion have come from observations of biology, but robots have empirically explored different structures, actuators, and control waveform shapes than those observed in biological organisms. In this study, we suggest a template analysis based on simplified segments undergoing beam deformations. This analysis enables calculation of the minimum power required by the structure for locomotion and maximum speed of locomotion. Thus, design relationships are shown that apply to peristaltic robots and potentially to earthworms. Specifically, although speed is maximized by moving as many segments as possible, cost of transport (COT) is optimized by moving fewer segments. Furthermore, either soft or relatively stiff segments are possible, but the anisotropy of the stiffnesses is important. Experimentally, we show on our earthworm robot that this method predicts which control waveforms (equivalent to different gaits) correspond to least input power or to maximum velocity. We extend our analysis to 150 segments (similar to that of earthworms) to show that reducing COT is an alternate explanation for why earthworms have so few moving segments. The mathematical relationships developed here between structural properties, actuation power, and waveform shape will enable the design of future robots with more segments and limited onboard power.

Rapidly Exploring Random Tree Algorithm-Based Path Planning for Worm-Like Robot.

Inspired by earthworms, worm-like robots use peristaltic waves to locomote. While there has been research on generating and optimizing the peristalsis wave, path planning for such worm-like robots has not been well explored. In this paper, we evaluate rapidly exploring random tree (RRT) algorithms for path planning in worm-like robots. The kinematics of peristaltic locomotion constrain the potential for turning in a non-holonomic way if slip is avoided. Here we show that adding an elliptical path generating algorithm, especially a two-step enhanced algorithm that searches path both forward and backward simultaneously, can make planning such waves feasible and efficient by reducing required iterations by up around 2 orders of magnitude. With this path planner, it is possible to calculate the number of waves to get to arbitrary combinations of position and orientation in a space. This reveals boundaries in configuration space that can be used to determine whether to continue forward or back-up before maneuvering, as in the worm-like equivalent of parallel parking. The high number of waves required to shift the body laterally by even a single body width suggests that strategies for lateral motion, planning around obstacles and responsive behaviors will be important for future worm-like robots.

Turning in Worm-Like Robots: The Geometry of Slip Elimination Suggests Nonperiodic Waves.

Inspired by earthworms, soft robots have demonstrated locomotion using segments with coupled length-wise elongation and radial contraction. However, peristaltic turning has primarily been studied empirically. Surface-dependent slip, which results in frictional forces that deform the body segments, makes accurate models challenging and limited to a specific robot and environment. Here, instead of modeling specific surfaces and segments, we take a geometric approach to analyzing the constraints that result from elimination of slip for the general case of peristaltic locomotion. Thus, our abstract two-dimensional model applies to many different mechanical designs (e.g., fluidic actuation, origami, woven mesh). Specifically, we show how turning is limited by segment range of motion, which means that more than one wave will be required to completely reorient the body in an environment where slip is not possible. As a result, to eliminate slip, segments must undergo nonperiodic shape changes. By representing segments as isosceles trapezoids with reasonable ranges of motion, we can determine control waves that in simulation do not require slip. These waves follow from an initial "reach" (i.e., kinematic movement range) of the second segment. A strategy for choosing the second segment reach is proposed based on evaluating long-term turn stability. To demonstrate the value of the approach, we applied the nonperiodic waveform (NPW) to our earthworm-inspired soft robot, Compliant Modular Mesh Worm with Steering (CMMWorm-S). With the NPW, the robot slips less when compared with a naive periodic waveform, where each segment of the robot has the same kinematic reach of each wave, as indicated by the difference between predicted and actual body position over multiple waves. Using an NPW for turning, we observe a decrease in prediction error compared with a naive periodic waveform by 66%. Thus, while our model ignores many factors (inertial dynamics, radial deformation, surface forces), the resulting turn strategies can improve kinematic motion prediction for planning. The theoretical constraints on NPWs that eliminate slip during turning will help robot designers make application-specific design choices about body stiffness, frictional properties, body length, and degrees of freedom.

Design and Actuation of a Fabric-Based Worm-Like Robot.

Soft-bodied animals, such as earthworms, are capable of contorting their body to squeeze through narrow spaces, create or enlarge burrows, and move on uneven ground. In many applications such as search and rescue, inspection of pipes and medical procedures, it may be useful to have a hollow-bodied robot with skin separating inside and outside. Textiles can be key to such skins. Inspired by earthworms, we developed two new robots: FabricWorm and MiniFabricWorm. We explored the application of fabric in soft robotics and how textile can be integrated along with other structural elements, such as three-dimensional (3D) printed parts, linear springs, and flexible nylon tubes. The structure of FabricWorm consists of one third the number of rigid pieces as compared to its predecessor Compliant Modular Mesh Worm-Steering (CMMWorm-S), while the structure of MiniFabricWorm consists of no rigid components. This article presents the design of such a mesh and its limitations in terms of structural softness. We experimentally measured the stiffness properties of these robots and compared them directly to its predecessors. FabricWorm and MiniFabricWorm are capable of peristaltic locomotion with a maximum speed of 33 cm/min (0.49 body-lengths/min) and 13.8 cm/min (0.25 body-lengths/min), respectively.

Haltere removal alters responses to gravity in standing flies.

Animals detect the force of gravity with multiple sensory organs, from subcutaneous receptors at body joints to specialized sensors like the vertebrate inner ear. The halteres of flies, specialized mechanoreceptive organs derived from hindwings, are known to detect body rotations during flight, and some groups of flies also oscillate their halteres while walking. The dynamics of halteres are such that they could act as gravity detectors for flies standing on substrates, but their utility during non-flight behaviors is not known. We observed the behaviors of intact and haltere-ablated flies during walking and during perturbations in which the acceleration due to gravity suddenly changed. We found that intact halteres are necessary for flies to maintain normal walking speeds on vertical surfaces and to respond to sudden changes in gravity. Our results suggest that halteres can serve multiple sensory purposes during different behaviors, expanding their role beyond their canonical use in flight.

How cockroaches exploit tactile boundaries to find new shelters.

Animals such as cockroaches depend on exploration of unknown environments, and their strategies may inspire robotic approaches. We have previously shown that cockroach behavior, with respect to shelters and the walls of an otherwise empty arena, can be captured with a stochastic state-based algorithm. We call this algorithm RAMBLER, randomized algorithm mimicking biased lone exploration in roaches. In this work, we verified and extended this model by adding a barrier in the previously used arena and conducted more cockroach experiments. In two arena configurations, our simulated model's path length distribution was similar to the experimental distribution (mean experimental path length 3.4 and 3.2 m, mean simulated path length 3.9 and 3.3 m). By analyzing cockroach behavior before, along, and at the end of the barrier, we have generalized RAMBLER to address arbitrarily complex 2D mazes. For biology, this is an abstract behavioral model of a decision-making process in the cockroach brain. For robotics, this is a strategy that may improve exploration for goals, especially in unpredictable environments with non-convex obstacles. Generally, cockroach behavior seems to recommend variability in the absence of planning, and following paths defined by walls.

Designing responsive pattern generators: stable heteroclinic channel cycles for modeling and control.

A striking feature of biological pattern generators is their ability to respond immediately to multisensory perturbations by modulating the dwell time at a particular phase of oscillation, which can vary force output, range of motion, or other characteristics of a physical system. Stable heteroclinic channels (SHCs) are a dynamical architecture that can provide such responsiveness to artificial devices such as robots. SHCs are composed of sequences of saddle equilibrium points, which yields exquisite sensitivity. The strength of the vector fields in the neighborhood of these equilibria determines the responsiveness to perturbations and how long trajectories dwell in the vicinity of a saddle. For SHC cycles, the addition of stochastic noise results in oscillation with a regular mean period. In this paper, we parameterize noise-driven Lotka-Volterra SHC cycles such that each saddle can be independently designed to have a desired mean sub-period. The first step in the design process is an analytic approximation, which results in mean sub-periods that are within 2% of the specified sub-period for a typical parameter set. Further, after measuring the resultant sub-periods over sufficient numbers of cycles, the magnitude of the noise can be adjusted to control the mean period with accuracy close to that of the integration step size. With these relationships, SHCs can be more easily employed in engineering and modeling applications. For applications that require smooth state transitions, this parameterization permits each state's distribution of periods to be independently specified. Moreover, for modeling context-dependent behaviors, continuously varying inputs in each state dimension can rapidly precipitate transitions to alter frequency and phase.

Efficient worm-like locomotion: slip and control of soft-bodied peristaltic robots.

In this work, we present a dynamic simulation of an earthworm-like robot moving in a pipe with radially symmetric Coulomb friction contact. Under these conditions, peristaltic locomotion is efficient if slip is minimized. We characterize ways to reduce slip-related losses in a constant-radius pipe. Using these principles, we can design controllers that can navigate pipes even with a narrowing in radius. We propose a stable heteroclinic channel controller that takes advantage of contact force feedback on each segment. In an example narrowing pipe, this controller loses 40% less energy to slip compared to the best-fit sine wave controller. The peristaltic locomotion with feedback also has greater speed and more consistent forward progress

Deciding which way to go: how do insects alter movements to negotiate barriers?

Animals must routinely deal with barriers as they move through their natural environment. These challenges require directed changes in leg movements and posture performed in the context of ever changing internal and external conditions. In particular, cockroaches use a combination of tactile and visual information to evaluate objects in their path in order to effectively guide their movements in complex terrain. When encountering a large block, the insect uses its antennae to evaluate the object's height then rears upward accordingly before climbing. A shelf presents a choice between climbing and tunneling that depends on how the antennae strike the shelf; tapping from above yields climbing, while tapping from below causes tunneling. However, ambient light conditions detected by the ocelli can bias that decision. Similarly, in a T-maze turning is determined by antennal contact but influenced by visual cues. These multi-sensory behaviors led us to look at the central complex as a center for sensori-motor integration within the insect brain. Visual and antennal tactile cues are processed within the central complex and, in tethered preparations, several central complex units changed firing rates in tandem with or prior to altered step frequency or turning, while stimulation through the implanted electrodes evoked these same behavioral changes. To further test for a central complex role in these decisions, we examined behavioral effects of brain lesions. Electrolytic lesions in restricted regions of the central complex generated site specific behavioral deficits. Similar changes were also found in reversible effects of procaine injections in the brain. Finally, we are examining these kinds of decisions made in a large arena that more closely matches the conditions under which cockroaches forage. Overall, our studies suggest that CC circuits may indeed influence the descending commands associated with navigational decisions, thereby making them more context dependent.

Kinematic and behavioral evidence for a distinction between trotting and ambling gaits in the cockroach Blaberus discoidalis.

Earlier observations had suggested that cockroaches might show multiple patterns of leg coordination, or gaits, but these were not followed by detailed behavioral or kinematic measurements that would allow a definite conclusion. We measured the walking speeds of cockroaches exploring a large arena and found that the body movements tended to cluster at one of two preferred speeds, either very slow (<10 cm s(-1)) or fairly fast (∼30 cm s(-1)). To highlight the neural control of walking leg movements, we experimentally reduced the mechanical coupling among the various legs by tethering the animals and allowing them to walk in place on a lightly oiled glass plate. Under these conditions, the rate of stepping was bimodal, clustering at fast and slow speeds. We next used high-speed videos to extract three-dimensional limb and joint kinematics for each segment of all six legs. The angular excursions and three-dimensional motions of the leg joints over the course of a stride were variable, but had different distributions in each gait. The change in gait occurs at a Froude number of ∼0.4, a speed scale at which a wide variety of animals show a transition between walking and trotting. We conclude that cockroaches do have multiple gaits, with corresponding implications for the collection and interpretation of data on the neural control of locomotion.