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Abstract Bio-inspired robot controllers are becoming more complex as we strive to make them more robust to, and flexible in, noisy, real-world environments. A stable heteroclinic network (SHN) is a dynamical system that produces cyclical state transitions using noisy input. SHN-based robot controllers enable sensory input to be integrated at the phase-space level of the controller, thus simplifying sensor-integrated, robot control methods. In this work, we investigate the mechanism that drives branching state trajectories in SHNs. We liken the branching state trajectories to decision-splits imposed into the system, which opens the door for more sophisticated controls -- all driven by sensory input. This work provides guidelines to systematically define an SHN topology, and increase the rate at which desired decision states in the topology are chosen. Ultimately, we are able to control the rate at which desired decision states activate for input signal-to-noise ratios across six orders of magnitude. 

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. 

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. 

Dynamic systems which underlie controlled systems are expected to increase in complexity as robots, devices, and connected networks become more intelligent. While classical stable systems converge to a stable point (a sink), another type of stability is to consider a stable path rather than a single point. Such stable paths can be made of saddle points that draw in trajectories from certain regions, and then push the trajectory toward the next saddle point. These chains of saddles are called stable heteroclinic channels (SHCs) and can be used in robotic control to represent time sequences. While we have previously shown that each saddle is visualizable as a trajectory waypoint in phase space, how to increase the fidelity of the trajectory was unclear. In this paper, we hypothesized that the waypoints can be individually modified to locally vary fidelity. Specifically, we expected that increasing the saddle value (ratio of saddle eigenvalues) causes the trajectory to slow to more closely approach a particular saddle. Combined with other parameters that control speed and magnitude, a system expressed with an SHC can be modified locally, point by point, without disrupting the rest of the path, supporting their use in motion primitives. While some combinations can enable a trajectory to better reach into corners, other combinations can rotate, distort, and round the trajectory surrounding the modified saddle. Of the system parameters, the saddle value provides the most predictable tunability across 3 orders of magnitude. 

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. 

Shape‐morphing capabilities of metamaterials can be expanded by developing approaches that enable the integration of different types of cellular structures. Herein, a rational material design process is presented that fits together auxetic (anti‐tetrachiral) and non‐auxetic (the novel nodal honeycomb) lattice structures with a shared grid of nodes to obtain desired values of Poisson's ratios and Young's moduli. Through this scheme, deformation properties can be easily set piece by piece and 3D printed in useful combinations. For example, such nodally integrated tubular lattice structures undergo worm‐like peristalsis or snake‐like undulations that result in faster speeds than the monophasic counterpart in narrow channels and in wider channels, respectively. In a certain scenario, the worm‐like hybrid metamaterial structure traverses between confined spaces that are otherwise impassable for the isotropic variant. These deformation mechanisms allow us to design shape‐morphing structures into customizable soft robot skins that have improved performance in confined spaces. The presented analytical material design approach can make metamaterials more accessible for applications not only in soft robotics but also in medical devices or consumer products. 

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.