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.

Centipedes exhibit great maneuverability in diverse environments due to their many legs and body-driven control. By leveraging similar morphologies and control strategies, their robotic counterparts also demonstrate effective terrestrial locomotion. However, the success of these multi-legged robots is largely limited to forward locomotion; steering is substantially less studied, in part because of the difficulty in coordinating a high degree-of-freedom robot to follow predictable, planar trajectories. To resolve these challenges, we take inspiration from control schemes based on geometric mechanics(GM) in elongate systems’ locomotion through highly damped environments. We model the elongate, multi-legged system as a "terrestrial swimmer" in highly frictional environments and implement steering schemes derived from low-order templates. We identify an effective turning strategy by superimposing two traveling waves of lateral body undulation and further explore variations of the "turning wave" to enable a spectrum of arc-following steering primitives. We test our hypothesized modulation scheme on a robophysical model and validate steering trajectories against theoretically predicted displacements producing steering radii between 0 and 0.6 body length. We then apply our control framework to Ground Control Robotics’ elongate multi-legged robot, Major Tom, using these motion primitives to autonomously navigate around obstacles and corners on indoor and outdoor terrain. Our work creates a systematic framework for controlling these highly mobile devices in the plane using a low-order model based on sequences of body shape changes.

Achieving robust legged locomotion on complex terrains poses challenges due to the high uncertainty in robot-environment interactions. Recent advances in bipedal and quadrupedal robots demonstrate good mobility on rugged terrains but rely heavily on sensors for stability due to low static stability from a high center of mass and a narrow base of support [1]. We hypothesize that a multi-legged robotic system can leverage morphological redundancy from additional legs to minimize sensing requirements when traversing challenging terrains. Studies suggest [2], [3] that a multi-legged system with sufficient legs can reliably navigate noisy landscapes without sensing and control, albeit at a low speed of up to 0.1 body lengths per cycle (BLC). However, the feedback control framework to enhance speed of multi-legged robots on challenging terrains remains underexplored due to diverse environmental interactions. Such complexity makes it difficult to identify the key parameters to control in these high-degree-of-freedom systems. Here, using laboratory and field experiments, we demonstrate that a vertical body undulation wave helps mitigate environmental disturbances that affect robot speed. These findings are supported by probabilistic models. Using such insights, we introduce a control framework which monitors foot-ground contact patterns on rugose landscapes using binary foot-ground contact sensors to estimate terrain rugosity. The controller adjusts the vertical body wave based on the deviation of the limb's averaged actual-to-ideal foot-ground contact ratio, achieving a significant enhancement of up to 0.235 BLC on rugose laboratory terrain. We observed a 50% to 60% increase in speed and a 30% to 50% reduction in speed variance compared to the open-loop controller. Additionally, the controller operates in complex terrains outside the lab, including pine straw, robot-sized rocks, mud, and leaves. Project website:https://juntaohe.github.io/TRO_2025/

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 a geometric mechanics framework, the configuration space is decomposed into a shape space and a position space. The internal motion of the system is prescribed by a closed loop in the shape space, which causes net motion in the position space. If the shape space is a simply connected domain in an Euclidean space, then with an optimal choice of the body frame, the displacement in the position space is reasonably approximated by the surface integral of the height function, a functional relationship between the internal shape and position space variables. Our recent work has extended the scope of geometric methods from limbless undulatory system to those with legs; interestingly, the shape space for such systems has a torus structure. However, to the best of our knowledge, the optimal choice of the body frame on the torus shape space was not explored. In this paper, we develop a method to optimally choose the body frame on the torus which results in good approximation of displacement by the integral of the height function. We apply our methods to the centipede locomotion system and observe quantitative agreement of our prediction and experimental results.

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.