Continuous Sculpting: Persistent Swarm Shape Formation Adaptable to Local Environmental Changes

TL;DR

This work presents a decentralized framework for persistent swarm shape formation that decouples shape duration from individual robot power by cycling robots between a shape and charging stations. Shape persistence is achieved via a default behavior that constructs planar Hamiltonian cycles through valid shapes, supported by a rigorous theory showing linear-time path construction and equivalence to a DFCP assembly. The system is made adaptable through detection, primary changes, and two secondary-change modalities (communication-based and movement-based), enabling real-time addition and subtraction of shape components while preserving or converging to a new preferred path. Demonstrations in simulation and with Coachbot hardware show sustained operation for extended durations and responsiveness to human gestures, with potential applications in agriculture and emergency response. The work lays groundwork for future three-dimensional extensions and flying-robot implementations, expanding the practical reach of persistent, adaptable swarm formations.

Abstract

Despite their growing popularity, swarms of robots remain limited by the operating time of each individual. We present algorithms which allow a human to sculpt a swarm of robots into a shape that persists in space perpetually, independent of onboard energy constraints such as batteries. Robots generate a path through a shape such that robots cycle in and out of the shape. Robots inside the shape react to human initiated changes and adapt the path through the shape accordingly. Robots outside the shape recharge and return to the shape so that the shape can persist indefinitely. The presented algorithms communicate shape changes throughout the swarm using message passing and robot motion. These algorithms enable the swarm to persist through any arbitrary changes to the shape. We describe these algorithms in detail and present their performance in simulation and on a swarm of mobile robots. The result is a swarm behavior more suitable for extended duration, dynamic shape-based tasks in applications such as agriculture and emergency response.

Figures (17)

• Figure 1: Cartoon overhead view of adaptive and persistent shape formation. (a) A swarm of mobile robots (purple circles) leave a charging station (yellow box) to enter and form a shape. The robots move through the shape in the directions indicated by the black arrows until they exit the shape and return to the charging station. (b) A human points to where they would like to add to the shape (purple box). (c) The swarm adjusts to form a path through the new shape while continuing to cycle to and from the charging station.
• Figure 2: (a) An example of a valid shape of 3 boxes. Points indicate nodes of $G$. (b) Robots (purple) approximating shape. Arrows indicate robot heading. (c) The path along which robots travel. Arrows indicate edge direction.
• Figure 3: Images from a simulation (top) and physical robot experiment (bottom). Each set of three images represents a sequence in time of the robots forming the shape (left), stepping to their next node (center), and holding at their next node (right). The charging station is highlighted by the green box, and the desired shape is highlighted by the blue box. Robots in neither box are cycling to or from the shape. The resulting path through the shape for both the simulation and the physical robots is shown in the bottom right image. The LED color of each robot is insignificant for these experiments.
• Figure 4: (a) A clockwise planar Hamiltonian cycle through a unit shape. (b) A counter-clockwise planar Hamiltonian cycle through a unit shape. Arrows indicate edge direction.
• Figure 5: The fundamental operations of path merging (going from $a$ to $b$) and path separation (going from $b$ to $a$). Red indicates impacted edges. Arrows indicate edge direction.

Theorems & Definitions (17)

• Definition 1: Planar Hamiltonian Cycle
• Lemma 1
• Lemma 2
• Theorem 1
• proof : Proof 1
• Lemma 3
• Lemma 4
• Theorem 2
• proof : Proof 2
• Theorem 3