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.

Animal size impacts locomotion, due to its effect on the influence of gravity, inertia, and an animal's internal elasticity and damping. We are developing a cat robot to further explore the impact of these four characteristics on animal locomotion. This paper details the mechanical design of this cat robot's rear limbs, as well as the simulated validation of this design. In future work, we plan to design forelimbs with a floating scapula and test the robot in split-belt treadmill experiments similar to those done in mammalian experiments as we develop its synthetic nervous system controller.

The passive dynamics of stance can explain why large animals, like horses and humans, require neuromuscular activity to maintain stance whereas smaller animals like cockroaches do not [20]. The dynamic properties that govern an animal's movement, like inertia, stiffness, and damping, are dictated by its size, scaling with its length [28]. The natural frequency of an animal's limb in stance can be predicted using its stiffness to inertia ratio, which scales inversely with length. We theorize that the passive mechanics of smaller animal limbs, with higher resonant frequencies than walking cycle frequencies, restore limb position quickly enough that neuromuscular intervention is not needed to correct perturbations during stance. Larger animals, however, require muscle activation since their mechanics depend more on inertia and are less dominated by viscoelastic effects, leading to a lower natural frequency.

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.

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.

This paper details the development and analysis of a computational neuroscience model, known as a Synthetic Nervous System, for the control of a simulated worm robot. Using a Synthetic Nervous System controller allows for adaptability of the network with minimal changes to the system. The worm robot kinematics are inspired by earthworm peristalsis which relies on the hydrostatic properties of the worm’s body to produce soft-bodied locomotion. In this paper the hydrostatic worm body is approximated as a chain of two dimensional rhombus shaped segments. Each segment has rigid side lengths, joints at the vertices, and a linear actuator to control the segment geometry. The control network is composed of non-spiking neuron and synapse models. It utilizes central pattern generators, coupled via interneurons and sensory feedback, to coordinate segment contractions and produce a peristaltic waveform that propagates down the body of the robot. A direct perturbation Floquet multiplier analysis was performed to analyze the stability of the peristaltic wave’s limit cycle.