Physical synchronization of soft self-oscillating limbs for fast and autonomous locomotion

Abstract

Animals achieve robust locomotion by offloading regulation from the brain to physical couplings within the body. In contrast, locomotion in artificial systems often depends on centralized processors. We introduce a rapid and autonomous locomotion strategy with synchronized gaits emerging through physical interactions between self-oscillating limbs and the environment, without control signals. Each limb is a single soft tube that only requires constant flow of air to perform cyclic stepping motions at frequencies reaching 300 hertz. By combining several of these self-oscillating limbs, their physical synchronization enables locomotion speeds that are orders of magnitude faster than comparable state-of-the-art. Through body-environment dynamics, these seemingly simple devices exhibit autonomy, including obstacle avoidance, amphibious gait transitions, and phototaxis.

Figures (5)

• Figure 1: Self-oscillating limbs that cyclically perform full-step motions. (A) Animals locomote by coordinating multiple limbs via explicit coupling through neural connections or implicit coupling through interaction with the environment insect_walking_couplingseastar_heydariseastar_nerve_ring. Each limb of the animal performs oscillating and asymmetric (full-step) motions with stance and swing phases biorobotics_agile_locomotionhow_animals_move. (B) We exploit these principles of explicit and implicit couplings between self-oscillating limbs for autonomous locomotion in robots. Our artificial limb is a soft tube bent 180° that, in static conditions, displays (C) one or (D) two kinks. (E) When constant airflow of $15$ standard liter per minute () is provided at the inlet on the left end, the tube self-oscillates at a frequency of 115Hz (snapshots of one oscillation cycle). (F) The tip of the limb is the point on the tube closest to a defined surface (photograph with 0.5s exposure time, capturing $\sim50$ consecutive oscillations). (G) The tip cyclically undergoes a full-step loop trajectory, with a stance phase followed by a swing phase (the reported tip trajectory coordinates $\hat{x}$ and $\hat{y}$ are normalized). Scale bars are 1cm.
• Figure 2: Interplay between pressure and kinks' state enables self-oscillation at a range of frequencies. (A) Detected edges of the tube (dark red) and coordinate system along the tube (pink). (B) The dominant and non-dominant kinks correspond to the local minima (black and grey dots) of the local width along the tube. The (C) location of the kinks along the tube and (D) pressure inside the tube are coupled. (E, F, G, H) State of the tube at four instants of the oscillating cycle. (I) The oscillation frequency displays three regimes for different inflow rates. Orange and blue dots correspond to the non-resonating and resonating study cases at $6.5$ and $16$, respectively. The tube has lower structural displacement in the (J) non-resonating domain than in the (K) resonating domain, as shown by the kink covering a shorter distance. (L) In the resonating case, the structure undergoes high quasi-sinusoidal velocities, in comparison to the near-zero velocities of the non-resonating case. (M) The kink locations along the tube itself, for the two cases, overlap.
• Figure 3: Synchronization of multiple limbs through explicit, internal coupling for ultrafast locomotion. (A) We couple two limbs in parallel to the same input flow source of $15$ with two identical silicone tubes. We observe in-phase synchronization, with (B) simultaneous kink traveling and (C) aligned pressure signals, or anti-phase synchronization, with (D, E) alternate activation of the limbs. We scan the length of the coupling tubes, observing two separated in-phase and anti-phase domains, as (F) the oscillation frequency of left and right limbs match, and (G) the phase-shift is either $\sim0°$ or $\sim180°$. (H) The tethered robot has four limbs connected to a 3D-printed monolithic body, with four inner coupling channels. (I) The robot achieves ultrafast locomotion on a flat surface (speed $\sim30\BL\per s$, 1.1ms). (J) Comparison between tethered soft robots with internal and external control and our robot equipped with synchronizing self-oscillating limbs, in terms of relative speed and body length. (K) Speed of the robot for six runs (grey) and mean speed (black). The four limbs, within $\sim3ms$, simultaneously go through a (L, M) stance phase, followed by a (N, O) swing phase. All scale bars are 1cm.
• Figure 4: Synchronization of limbs through implicit interaction for fast, untethered locomotion. The updated pouch limb (A) cyclically performs full-step motions with a low inflow of $0.3$, (B) displaying large hysteresis and stroke enabled by a hinge joint. (C) We mount two self-oscillating limbs on an untethered robot that carries a LiPo battery and two pumps. (D) The robot cyclically hops with (i, ii) a stance phase followed by (iii, iv) a swing phase. (E) The two limbs are not synchronized when the system is upside down, because they are independently powered by the two pumps. (F) When the robot interacts with the ground, the two limbs synchronize. (G) While interacting, the pressure signals of the two limbs increase, and the frequencies equalize. All scale bars are 2cm.
• Figure 5: Autonomy through physical interactions with the environment. (A) After diving into the water, the robot equipped with buoyancy pouches ($50mL$ of air) autonomously transitions to an anti-phase swimming gait, through the implicit coupling with the new aquatic environment. (B) The phase shift between the two self-oscillating limbs is $\sim0°$ (in-phase) when hopping on the ground and spontaneously transitions to $\sim180°$ (anti-phase) when interacting with water. (C) When encountering an obstacle, the mechanical interactions (white circles) cause the limbs to activate asynchronously and, as a consequence, the robot steers in place, avoiding the obstacle. (D) To provide the robot with a high-level sense of direction, and inspired by Braitenberg's 'aggressive vehicle' vehicles, we cross-link light sensors (eyes) and the pumps so that a limb is active when the opposite eye detects light. (E) This robot achieves autonomous phototaxis by steering in place when only one eye is active and hopping forward when both eyes are, following an operator that carries a light in a real-world environment. Wherever not otherwise stated, scale bars are 2cm.