cs.ROMar 18, 2026

Huddle: Parallel Shape Assembly using Decentralized, Minimalistic Robots

Authors: Khai Yi Chin, Tingwei Meng, Zhe Chen, Daniel Bassett, Yuri Ivanov

Organizations: Amazon Robotics

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Abstract

We propose a novel algorithm for forming arbitrarily shaped assemblies using decentralized robots. By relying on local interactions, the algorithm ensures there are no unreachable states or gaps in the assembly, which are global properties. The in-assembly robots attract passing-by robots into expanding the assembly via a simple implementation of signaling and alignment. Our approach is minimalistic, requiring only communication between attached, immediate neighbors. It is motion-agnostic and requires no pose localization, enabling asynchronous and order-independent assembly. We prove the algorithm's correctness and demonstrate its effectiveness in forming a 107-robot assembly.

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Figure 1: (a) Axial coordinate system for the 2-D hexagonal space H\mathcal{H} that Huddle uses, where pp and qq are the column and row coordinates, respectively. (b) An unreachable position shown by the dashed hexagon. (c) Layout of wall indices and their corresponding directional unit vectors u^w\hat{u}_{w} .
Figure 2: Example of a 5-robot assembly. Dashed hexagons are target positions in SS . (a) A root robot (0,0)(0,0) in its Signal Activation phase, signaling (green) on its F wall to attract passing-by robots. (b) A passing-by robot detects and follows the signal to attach to the root robot. Upon connection, the root robot communicates its position (0,0)(0,0) and the unit vector of the admitting wall u^0\hat{u}_{0} to the newly attached robot. As a right nucleus—determined prior to its entering the Signal Activation phase—the root robot now signals on its FR wall. (c) The newly attached robot enters the Initialization phase, computing its coordinate (0,1)(0,1) and identifying its wall statuses. (d) The (0,1)(0,1) robot determines its role as a left nucleus and its growth direction as gi=−1g_{i}=-1 , as it shares a row with the (rounded down) midpoint (−1,1)(-1,1) of the left column (Algorithms 1 – 4 ). (e) The (0,1)(0,1) robot enters the Signal Activation phase, signaling its left flank (Algorithms 5 and 6 ). The robots remain in that phase until their connection walls are occupied.
Algorithm 1 Determine robot role
Algorithm 2 Determine robot role using self-wall status
Algorithm 3 Determine robot role using target adjacent column
Algorithm 4 Determine growth direction
Algorithm 5 Identify walls to activate signals
Figure 4: (a) Notable situations during robot ii ’s determination of its role, where it lies on a different row from the midpoint m=(−1,3)m=(-1,3) of Q−1(2)Q^{(2)}_{-1} . Dashed hexagons are target positions for SS , with color overlays indicating membership to target segments. (i) Located on the midpoint’s row, a robot occupying (0,3)(0,3) —in the future—will be the nucleus (Algorithm 3 , lines 12 – 13 ). (ii) Without a target (0,3)(0,3) position, the new attachment point is m⋆=(−1,2)m^{\star}=(-1,2) , thus (0,2)(0,2) is the nucleus position (Algorithm 3 , lines 18 – 19 ). (iii) With its FL wall between two null walls, robot ii is solely responsible for nucleating to the left (Algorithm 2 ). (b) Suppose gi=gj=−1g_{i}=g_{j}=-1 and robot ii does not delay its signal (red) while robot jj ’s front wall is free. An unreachable position will occur if robot ii ’s front wall is occupied before robot jj ’s.
Algorithm 6 Identify walls to delay signal activation
Figure 5: 256256 -robot assembly example from the Monte Carlo experiments (one robot attachment per step). Dashed hexagons represent XbX_{b} , which are eventually populated by robots marked with red circles; hexagons marked with blue circles are interior robots. Note that our approach does not distinguish between perimeter and interior robots.
Figure 6: (a) Robot diffusion motion state diagram. (b) Completion time of a 107-robot assembly forming “ H\mathcal{H} ”, where \nicefrac230\nicefrac{{2}}{{30}} trials timed out (1 robot remaining).
Figure 7: 107 robots forming “ H\mathcal{H} ”. (a) We place the root robot at the world origin, while the rest of the robots start in two clusters. (b) The robots diffuse within an arena bounded by four walls, joining the assembly as attracted by signals. (c) Each robot eventually finds an opening to attach, completing the assembly.
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