Learning manipulation of steep granular slopes for fast Mini Rover turning

Future planetary exploration missions will require reaching challenging regions such as craters and steep slopes. Such regions are ubiquitous and present science-rich targets potentially containing information regarding the planet's internal structure. Steep slopes consisting of low-cohesion regolith are prone to flow downward under small disturbances, making it very challenging for autonomous rovers to traverse. Moreover, the navigation trajectories of rovers are heavily limited by the terrain topology and future systems will need to maneuver on flowable surfaces without getting trapped, allowing them to further expand their reach and increase mission efficiency. In this work, we used a laboratory-scale rover robot and performed maneuvering experiments on a steep granular slope of poppy seeds to explore the rover's turning capabilities. The rover is capable of lifting, sweeping, and spinning its wheels, allowing it to execute leg-like gait patterns. The high-dimensional actuation capabilities of the rover facilitate effective manipulation of the underlying granular surface. We used Bayesian Optimization (BO) to gain insight into successful turning gaits in high dimensional search space and found strategies such as differential wheel spinning and pivoting around a single sweeping wheel. We then used these insights to further fine-tune the turning gait, enabling the rover to turn 90 degrees at just above 4 seconds with minimal slip. Combining gait optimization and human-tuning approaches, we found that fast turning is empowered by creating anisotropic torques with the sweeping wheel.

Anisotropic body compliance facilitates robotic sidewinding in complex environments

Sidewinding, a locomotion strategy characterized by the coordination of lateral and vertical body undulations, is frequently observed in rattlesnakes and has been successfully reconstructed 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, 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.

Robust self-propulsion in sand using simply controlled vibrating cubes

Much of the Earth and many surfaces of extraterrestrial bodies are composed of in-cohesive particle matter. Locomoting on granular terrain is challenging for common robotic devices, either wheeled or legged. In this work, we discover a robust alternative locomotion mechanism on granular media -- generating movement via self-vibration. To demonstrate the effectiveness of this locomotion mechanism, we develop a cube-shaped robot with an embedded vibratory motor and conduct systematic experiments on diverse granular terrains of various particle properties. We investigate how locomotion changes as a function of vibration frequency/intensity on granular terrains. Compared to hard surfaces, we find such a vibratory locomotion mechanism enables the robot to move faster, and more stable on granular surfaces, facilitated by the interaction between the body and surrounding granules. The simplicity in structural design and controls of this robotic system indicates that vibratory locomotion can be a valuable alternative way to produce robust locomotion on granular terrains. We further demonstrate that such cube-shape robots can be used as modular units for morphologically structured vibratory robots with capabilities of maneuverable forward and turning motions, showing potential practical scenarios for robotic systems.

Multi-legged matter transport: a framework for locomotion on noisy landscapes

While the transport of matter by wheeled vehicles or legged robots can be guaranteed in engineered landscapes like roads or rails, locomotion prediction in complex environments like collapsed buildings or crop fields remains challenging. Inspired by principles of information transmission which allow signals to be reliably transmitted over noisy channels, we develop a ``matter transport" framework demonstrating that non-inertial locomotion can be provably generated over ``noisy" rugose landscapes (heterogeneities on the scale of locomotor dimensions). Experiments confirm that sufficient spatial redundancy in the form of serially-connected legged robots leads to reliable transport on such terrain without requiring sensing and control. Further analogies from communication theory coupled to advances in gaits (coding) and sensor-based feedback control (error detection/correction) can lead to agile locomotion in complex terradynamic regimes.

Mechanical Intelligence Simplifies Control in Terrestrial Limbless Locomotion

Limbless locomotors, from microscopic worms to macroscopic snakes, traverse complex, heterogeneous natural environments typically using undulatory body wave propagation. Theoretical and robophysical models typically emphasize body kinematics and active neural/electronic control. However, we contend that because such approaches often neglect the role of passive, mechanically controlled processes (i.e., those involving mechanical intelligence), they fail to reproduce the performance of even the simplest organisms. To discover principles of how mechanical intelligence aids limbless locomotion in heterogeneous terradynamic regimes, here we conduct a comparative study of locomotion in a model of heterogeneous terrain (lattices of rigid posts). We use a model biological system, the highly studied nematode worm C. elegans, and a novel robophysical device whose bilateral actuator morphology models that of limbless organisms across scales. The robot's kinematics quantitatively reproduce the performance of the nematodes with purely open-loop control; mechanical intelligence simplifies control of obstacle navigation and exploitation by reducing the need for active sensing and feedback. An active behavior observed in C. elegans, undulatory wave reversal upon head collisions, robustifies locomotion via exploitation of the systems' mechanical intelligence. Our study provides insights into how neurally simple limbless organisms like nematodes can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments. These principles likely apply to neurally more sophisticated organisms and also provide a new design and control paradigm for limbless robots for applications like search and rescue and planetary exploration.

Gait design for limbless obstacle aided locomotion using geometric mechanics

Limbless robots have the potential to maneuver through cluttered environments that conventional robots cannot traverse. As illustrated in their biological counterparts such as snakes and nematodes, limbless locomotors can benefit from interactions with obstacles, yet such obstacle-aided locomotion (OAL) requires properly coordinated high-level self-deformation patterns (gait templates) as well as low-level body adaptation to environments. Most prior work on OAL utilized stereotyped traveling-wave gait templates and relied on local body deformations (e.g., passive body mechanics or decentralized controller parameter adaptation based on force feedback) for obstacle navigation, while gait template design for OAL remains less studied. In this paper, we explore novel gait templates for OAL based on tools derived from geometric mechanics (GM), which thus far has been limited to homogeneous environments. Here, we expand the scope of GM to obstacle-rich environments. Specifically, we establish a model that maps the presence of an obstacle to directional constraints in optimization. In doing so, we identify novel gait templates suitable for sparsely and densely distributed obstacle-rich environments respectively. Open-loop robophysical experiments verify the effectiveness of our identified OAL gaits in obstacle-rich environments. We posit that when such OAL gait templates are augmented with appropriate sensing and feedback controls, limbless locomotors will gain robust function in obstacle rich environments.

Geometry of contact: contact planning for multi-legged robots via spin models duality

Contact planning is crucial in locomoting systems.Specifically, appropriate contact planning can enable versatile behaviors (e.g., sidewinding in limbless locomotors) and facilitate speed-dependent gait transitions (e.g., walk-trot-gallop in quadrupedal locomotors). The challenges of contact planning include determining not only the sequence by which contact is made and broken between the locomotor and the environments, but also the sequence of internal shape changes (e.g., body bending and limb shoulder joint oscillation). Most state-of-art contact planning algorithms focused on conventional robots (e.g.biped and quadruped) and conventional tasks (e.g. forward locomotion), and there is a lack of study on general contact planning in multi-legged robots. In this paper, we show that using geometric mechanics framework, we can obtain the global optimal contact sequence given the internal shape changes sequence. Therefore, we simplify the contact planning problem to a graph optimization problem to identify the internal shape changes. Taking advantages of the spatio-temporal symmetry in locomotion, we map the graph optimization problem to special cases of spin models, which allows us to obtain the global optima in polynomial time. We apply our approach to develop new forward and sidewinding behaviors in a hexapod and a 12-legged centipede. We verify our predictions using numerical and robophysical models, and obtain novel and effective locomotion behaviors.

Robophysical modeling of spacetime dynamics

Systems consisting of spheres rolling on elastic membranes have been used as educational tools to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, previous studies have revealed that such schemes cannot accurately represent relativistic dynamics in the laboratory. Dissipative forces cause the initially GR-like dynamics to be transient and consequently restrict experimental study to only the beginnings of trajectories; dominance of Earth's gravity forbids the difference between spatial and temporal spacetime curvatures. Here by developing a mapping between dynamics of a wheeled vehicle on a spandex membrane, we demonstrate that an active object that can prescribe its speed can not only obtain steady-state orbits, but also use the additional parameters such as speed to tune the orbits towards relativistic dynamics. Our mapping demonstrates how activity mixes space and time in a metric, shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow programming a desired spacetime such as the Schwarzschild metric near a non-rotating black hole. Our mapping and framework point the way to the possibility to create a robophysical analog gravity system in the laboratory at low cost and provide insights into active matter in deformable environments and robot exploration in complex landscapes.

Generalized Omega Turn Gait Enables Agile Limbless Robot Turning in Complex Environments

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. 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.

A general locomotion control framework for serially connected multi-legged robots

Serially connected robots are promising candidates for performing tasks in confined spaces such as search-and-rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve mobility. However, a challenge in designing and controlling such devices lies in the coordination of high-dimensional redundant modules in a way that improves mobility. Here we develop a general framework to control serially connected multi-legged robots. Specifically, we combine two approaches to build a general shape control scheme which can provide baseline patterns of self-deformation ("gaits") for effective locomotion in diverse robot morphologies. First, we take inspiration from a dimensionality reduction and a biological gait classification scheme to generate cyclic patterns of body deformation and foot lifting/lowering, which facilitate generation of arbitrary substrate contact patterns. Second, we use geometric mechanics methods to facilitates identification of optimal phasing of these undulations to maximize speed and/or stability. Our scheme allows the development of effective gaits in multi-legged robots locomoting on flat frictional terrain with diverse number of limbs (4, 6, 16, and even 0 limbs) and body actuation capabilities (including sidewinding gaits on limbless devices). By properly coordinating the body undulation and the leg placement, our framework combines the advantages of both limbless robots (modularity) and legged robots (mobility). We expect that our framework can provide general control schemes for the rapid deployment of general multi-legged robots, paving the ways toward machines that can traverse complex environments under real-life conditions.