This paper presents AquaMILR+, an untethered limbless robot designed for agile navigation in complex aquatic environments. The robot features a bilateral actuation mechanism that models musculoskeletal actuation in many anguilliform swimming organisms which propagates a moving wave from head to tail allowing open fluid undulatory swimming. This actuation mechanism employs mechanical intelligence through programmable body compliance, enhancing the robot's open-loop maneuverability when interacting with obstacles. AquaMILR+ also includes a compact depth control system inspired by the swim bladder and lung structures of eels and sea snakes. The mechanism, driven by a syringe and telescoping leadscrew, enables depth and pitch control - capabilities that are difficult for most anguilliform swimming robots to achieve. Additional structures, such as fins and a tail, further improve stability and propulsion efficiency. Our tests in both open water and laboratory models of 2D and 3D heterogeneous aquatic environments highlight AquaMILR+'s capabilities and suggest a promising system for complex underwater tasks such as search and rescue and deep-sea exploration.

Characterized by their elongate bodies and relatively simple legs, multi-legged robots have the potential to locomote through complex terrains for applications such as search-and-rescue and terrain inspection. Prior work has developed effective and reliable locomotion strategies for multilegged robots by propagating the two waves of lateral body undulation and leg stepping, which we will refer to as the twowave template. However, these robots have limited capability to climb over obstacles with sizes comparable to their heights. We hypothesize that such limitations stem from the twowave template that we used to prescribe the multi-legged locomotion. Seeking effective alternative waves for obstacleclimbing, we designed a five-segment robot with static (nonactuated) legs, where each cable-driven joint has a rotational degree-of-freedom (DoF) in the sagittal plane (vertical wave) and a linear DoF (peristaltic wave). We tested robot locomotion performance on a flat terrain and a rugose terrain. While the benefit of peristalsis on flat-ground locomotion is marginal, the inclusion of a peristaltic wave substantially improves the locomotion performance in rugose terrains: it not only enables obstacle-climbing capabilities with obstacles having a similar height as the robot, but it also significantly improves the traversing capabilities of the robot in such terrains. Our results demonstrate an alternative actuation mechanism for multilegged robots, paving the way towards all-terrain multi-legged robots.

Centipede-like robots offer an effective and robust solution to navigation over complex terrain with minimal sensing. However, when climbing over obstacles, such multi-legged robots often elevate their center-of-mass into unstable configurations, where even moderate terrain uncertainty can cause tipping. Robust mechanisms for such elongate multi-legged robots to self-right remain unstudied. Here, we use a comparative biological and robophysical approach to investigate self-righting strategies. We first released S. polymorpha upside down from a 10 cm height and recorded their self-righting behaviors using top and side view high-speed cameras. Using kinematic analysis, we hypothesize that these behaviors can be prescribed by two traveling waves superimposed in the body's lateral and vertical planes, respectively. We tested our hypothesis on an elongate robot with static (non-actuated) limbs, and we successfully reconstructed these self-righting behaviors. We further evaluated how wave parameters affect self-righting effectiveness. We identified two key wave parameters: the spatial frequency, which characterizes the sequence of body-rolling, and the wave amplitude, which characterizes body curvature. By empirically obtaining a behavior diagram of spatial frequency and amplitude, we identify effective and versatile self-righting strategies for general elongate multi-legged robots, which greatly enhances these robots' mobility and robustness in practical applications such as agricultural terrain inspection and search-and-rescue.

While undulatory swimming of elongate limbless robots has been extensively studied in open hydrodynamic environments, less research has been focused on limbless locomotion in complex, cluttered aquatic environments. Motivated by the concept of mechanical intelligence [1], where controls for obstacle navigation can be offloaded to passive body mechanics in terrestrial limbless locomotion, we hypothesize that principles of mechanical intelligence can be extended to cluttered hydrodynamic regimes. To test this, we developed an untethered limbless robot capable of undulatory swimming on water surfaces, utilizing a bilateral cable-driven mechanism inspired by organismal muscle actuation morphology to achieve programmable anisotropic body compliance. We demonstrated through robophysical experiments that, similar to terrestrial locomotion, an appropriate level of body compliance can facilitate emergent swim through complex hydrodynamic environments under pure open-loop control. Moreover, we found that swimming performance depends on undulation frequency, with effective locomotion achieved only within a specific frequency range. This contrasts with highly damped terrestrial regimes, where inertial effects can often be neglected. Further, to enhance performance and address the challenges posed by nondeterministic obstacle distributions, we incorporated computational intelligence by developing a real-time body compliance tuning controller based on cable tension feedback. This controller improves the robot's robustness and overall speed in heterogeneous hydrodynamic environments.

Sidewinding, a locomotion strategy characterized by the coordination of lateral and vertical body undulations, is frequently observed in rattlesnakes and has been successfully implemented by limbless robotic systems for effective movement across diverse terrestrial terrains. However, the integration of compliant mechanisms into sidewinding limbless robots remains less explored, posing challenges for navigation in complex, rheologically diverse environments. Inspired by a notable control simplification via mechanical intelligence in lateral undulation [1], which offloads feedback control to passive body mechanics and interactions with the environment, we present an innovative design of a mechanically intelligent limbless robot for sidewinding. This robot features a decentralized bilateral cable actuation system that resembles organismal muscle actuation mechanisms. We develop a feedforward controller that incorporates programmable body compliance into the sidewinding gait template. Our experimental results highlight the emergence of mechanical intelligence when the robot is equipped with an appropriate level of body compliance. This allows the robot to 1) locomote more energetically efficiently, as evidenced by a reduced cost of transport, and 2) navigate through terrain heterogeneities, all achieved in an open-loop manner, without the need for environmental awareness.

Reorientation (turning in plane) plays a critical role for all robots in any field application, especially those that in confined spaces. While important, reorientation remains a relatively unstudied problem for robots, including limbless mechanisms, often called snake robots. Instead of looking at snakes, we take inspiration from observations of the turning behavior of tiny nematode worms C. elegans. Our previous work presented an in-place and in-plane turning gait for limbless robots, called an omega turn, and prescribed it using a novel two-wave template [1]. In this work, we advance omega turn-inspired controllers in three aspects: 1) we use geometric methods to vary joint angle amplitudes and forward wave spatial frequency in our turning equation to establish a wide and precise amplitude modulation and frequency modulation on omega turn; 2) we use this new relationship to enable robots with fewer internal degrees of freedom (i.e., fewer joints in the body) to achieve desirable performance, and 3) we apply compliant control methods to this relationship to handle unmodelled effects in the environment. We experimentally validate our approach on a limbless robot that the omega turn can produce effective and robust turning motion in various types of environments, such as granular media and rock pile.

In this work, we focus on the autonomous navigation of snake robots in densely-cluttered environments, where collisions between the robot and obstacles are frequent, which could happen often in disaster scenarios, underground caves, or grassland/forest environments. This work takes the view that obstacles are not to be avoided, but rather exploited to support and direct the motion of the snake robot. We build upon a decentralized state-of-the-art compliant controller for serpenoid locomotion, and develop a bi-stable dynamical system that relies on inertial feedback to continuously steer the robot toward a desired direction. We experimentally show that this controller allows the robot to autonomously navigate dense environments by consistently locomoting along a given, global direction of travel in the world, which could be selected by a human operator or a higher level planner. We further equip the robot with an onboard vision system, allowing the robot to autonomously select its own direction of travel, based on the obstacle distribution ahead of its position (i.e., enacting feedforward control). In those additional experiments on hardware, we show how such an exteroceptive sensor can allow the robot to steer before hitting obstacles and to preemptively avoid challenging regions where proprioception-only (i.e., torque and inertial) feedback control would not suffice.

Snake robots have the potential to locomote through tightly packed spaces, but turning effectively within unmodelled and unsensed environments remains challenging. Inspired by a behavior observed in the tiny nematode worm C. elegans, we propose a novel in-place turning gait for elongated limbless robots. To simplify the control of the robots' many internal degrees-of-freedom, we introduce a biologically-inspired template in which two co-planar traveling waves are superposed to produce an in-plane turning motion, the omega turn. The omega turn gait arises from modulating the wavelengths and amplitudes of the two traveling waves. We experimentally test the omega turn on a snake robot, and show that this turning gait outperforms previous turning gaits: it results in a larger angular displacement and a smaller area swept by the body over a gait cycle, allowing the robot to turn in highly confined spaces.