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Due to their compliant mechanics, many soft and flexible robots are well-suited to operate in confined spaces that challenge traditional legged and wheeled robots. In particular, undulatory and peristaltic robots excel in enclosed tunnels and pipes, as their locomotion methods and compliance allow them to wriggle and squeeze through narrowings and gaps. However, these environments frequently contain features that are impassable with passive deformation alone, such as sharp turns and T-junctions. In this work, we developed the first closed-loop, peristaltic turning algorithm that scales turning angle based on contact force feedback in confined spaces. We verified the controller’s effectiveness using a dynamic model of a soft worm robot as our test platform. The model was sent through pipe bends with varying radii of curvature, diameters, and geometries, using both open-loop and closed-loop controllers. The different turning strategies were compared using speed and the cost of transport (COT) as the primary metrics. Our adaptive algorithm was the only turning method which maintained high speed performance across all bends tested. The model averaged just a 1.6% loss in speed compared to the best fixed turning angle strategy for each pipe curvature. Adaptive turning also allowed the model to traverse small radius of curvature (ROC) bends (0.5 and 0.6 m) in which the model became stuck when using straightline locomotion. Furthermore, of the controllers we tested, adaptive turning offered the lowest COT in most pipe bend geometries. We also showed that the controller could autonomously transition from left to right turns (and vice versa) and adjust to a spiral turn with a continuously changing ROC. A worm robot with this controller, these sensors, and turning capabilities would be well equipped for operation in a wide variety of unstructured and confined environments. 

The passive compliance of a soft worm-like body can be a key advantage for traversal of complex confined spaces, but in practice, the body’s stiffness and contact friction often require experimental adjustments. Here, for the first time, we develop a dynamic, 3D simulation that enables systematic testing of robot parameters (e.g. stiffness and friction) in different radius of curvature environments, which will help us better understand design trade-offs in creating soft robots that mimic worm-like locomotion. Specifically, we use the open-source physics engine MuJoCo because it is established for both biomechanical and robotic modeling, as well as multi-point contact dynamics, which are present in confined spaces. The model has sensory capabilities analogous to the stretch and tactile proprioception of an earthworm and is amenable to both feedforward and feedback control. After validating our model by comparing to our previous physical robot, we quantify locomotion performance over a range of friction coefficients, structural stiffnesses, and turning radii. We found that speed increased with friction coefficient on flat ground for higher stiffness models, but decreased with friction coefficient for lower stiffness models, both on flat ground and in pipe bends. For turning radii greater than 0.45 m, speed and stiffness also had a positive correlation, however, below the critical turning radius of 0.45 m, increasing stiffness had no appreciable influence on speed. This simulation can potentially be used to optimize designs for particular environments, to better understand the influence of passive vs. active control on individual and coupled segments, and perhaps offer a deeper understanding of how animals and robots can employ soft structures. For example, we can posit from our results that changing stiffness will not increase speed below the critical turning radius, meaning further experiments should focus on other parameters or actively controlled turning to improve speed through tighter turns. 

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. 

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.