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Stable Heteroclinic Channels (SHCs) are dynamical systems composed of connected saddle equilibria. This work demonstrates a control system that combines SHCs with movement primitives to enable swimming in a simulated six segment snake robot. We identify control system parameters for lateral undulation, where all joints oscillate with the same amplitude, and anguilliform swimming, where joint amplitudes increase linearly from the head to the tail. Swimming speed is improved by learning SHC movement primitive parameters. We also propose a method for adapting the gait amplitude and frequency with tactile sensor input to accommodate obstacles. Then, we evaluate the relationship between SHC movement primitive parameters and the resulting trajectories. The swimming speed and efficiency of SHC controllers for each gait are compared against a conventional serpenoid controller, which derives joint trajectories from sinusoids. Controllers are evaluated first in an unobstructed environment, then in straight passages of various widths, and finally in 65 randomly generated uneven channels. We find that the amplitudes of joint oscillations scale proportionally with the SHC controller parameters. Due to gait optimization, as well as adaptive amplitude and frequency in response to tactile input, the learned SHC control system exhibits an average 28.8% greater speed than a serpenoid controller that only adapts amplitude during contact. This research demonstrates that SHCs benefit from intuitive tuning like serpenoid control, while also effectively incorporating sensory information to generate smooth kinematic trajectories. 

This paper details the development and validation of a dynamic 3D compliant worm-like robot model controlled by a Synthetic Nervous System (SNS). The model was built and simulated in the physics engine Mujoco which is able to approximate soft bodied dynamics and generate contact, gravitational, frictional, and internal forces. These capabilities allow the model to realistically simulate the movements and dynamic behavior of a physical soft-bodied worm-robot. For validation, the results of this simulation were compared to data gathered from a physical worm robot and found to closely match key behaviors such as deformation propagation along the compliant structure and actuator efficiency losses in the middle segments. The SNS controller was previously developed for a simple 2D kinematic model and has been successfully implemented on this 3D model with little alteration. It uses coupled oscillators to generate coordinated actuator control signals and induce peristaltic locomotion. This model will be useful for analyzing dynamic effects during peristaltic locomotion like contact forces and slip as well as developing and improving control algorithms that avoid unwanted slip. 

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. 

Abstract 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. 

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. 

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. 

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. 

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.