Loopy Movements: Emergence of Rotation in a Multicellular Robot

TL;DR

The paper investigates how a looped multicellular robot, Loopy, achieves coordinated rotation through purely local interactions among homogeneous 1-DoF cells. By modeling morphogens with reaction-diffusion-reaction dynamics and active transport, joint angles are driven by local chemical states, enabling emergent rotation without centralized control. Key findings include (i) inner valleys rotate faster than outer lobes, (ii) cells rotate opposite to the overall morphology, and (iii) the system scales linearly with wave speed $v$ and remains functional despite substantial actuator failures. This work demonstrates a resilient, bio-inspired pathway to decentralized control and morphologically adaptive locomotion with potential applications in dynamic, fault-tolerant robotics.

Abstract

Unlike most human-engineered systems, many biological systems rely on emergent behaviors from low-level interactions, enabling greater diversity and superior adaptation to complex, dynamic environments. This study explores emergent decentralized rotation in the Loopy multicellular robot, composed of homogeneous, physically linked, 1-degree-of-freedom cells. Inspired by biological systems like sunflowers, Loopy uses simple local interactions-diffusion, reaction, and active transport of simulated chemicals, called morphogens-without centralized control or knowledge of its global morphology. Through these interactions, the robot self-organizes to achieve coordinated rotational motion and forms lobes-local protrusions created by clusters of motor cells. This study investigates how these interactions drive Loopy's rotation, the impact of its morphology, and its resilience to actuator failures. Our findings reveal two distinct behaviors: 1) inner valleys between lobes rotate faster than the outer peaks, contrasting with rigid body dynamics, and 2) cells rotate in the opposite direction of the overall morphology. The experiments show that while Loopy's morphology does not affect its angular velocity relative to its cells, larger lobes increase cellular rotation and decrease morphology rotation relative to the environment. Even with up to one-third of its actuators disabled and significant morphological changes, Loopy maintains its rotational abilities, highlighting the potential of decentralized, bio-inspired strategies for resilient and adaptable robotic systems.

Figures (9)

• Figure 1: A) Simulated cellular interactions, including diffusion, reaction, and active transport, enable the decentralized emergence and propagation of diverse chemical distributions. B) These chemical patterns propagate through Loopy’s cells, determining the desired joint angles of its actuators. C) This leads to the emergence of Loopy’s rotational movement about its centroid (red dot) and lobed morphology, where the cells rotate in the opposite direction to the overall morphology.
• Figure 2: The morphology space of the Loopy robot. Increasing the inhibition rate ($\beta$) reduces lobe size, while increasing the activator diffusion rate ($\gamma_{act}$) decreases the number of lobes formed.
• Figure 3: Two coordinate frames are utilized, both centered on Loopy's centroid (red circle): $E$ (black), fixed to the environment, and $C$ (white), fixed to Loopy's cells, with $C_x$ pointing to the first cell. The rotation of $C$ relative to $E$ describes the angular velocity of Loopy's cells in the environment ($\omega_{ce}$, green). The rotation of Loopy's morphology, indicated by the motion of its lobe peaks (purple), is described by $\omega_{me}$ (blue). Lastly, $\omega_{mc}$ (yellow) represents the rate at which the morphology shifts along Loopy's closed cellular chain.
• Figure 4: A representative path (blue) and corresponding velocities (orange) of one of Loopy's cells as it completes a full environment cycle in a three-lobed morphology. The tangential velocity is highest in the valleys between the lobes and approaches zero at the tips of the lobes.
• Figure 5: A three-lobed Loopy subjected to step changes in wave speed $v$ (indicated by grey dashed sections). The mean angular velocities of Loopy's cells, along with their first standard deviation ($\sigma$), are displayed. As wave speed magnitude increased, all angular velocities increased. The sign of $v$ determined the direction of rotation, with Loopy's cells (green) rotating opposite to its morphology (blue and yellow).