Reconfiguration of a 2D Structure Using Spatio-Temporal Planning and Load Transferring

TL;DR

Two reconfiguration methods are developed, one based on spatio-temporal planning, and one based on target swapping, to increase building efficiency and reduce planning times compared to other multi-robot planners.

Abstract

We present progress on the problem of reconfiguring a 2D arrangement of building material by a cooperative group of robots. These robots must avoid collisions, deadlocks, and are subjected to the constraint of maintaining connectivity of the structure. We develop two reconfiguration methods, one based on spatio-temporal planning, and one based on target swapping, to increase building efficiency. The first method can significantly reduce planning times compared to other multi-robot planners. The second method helps to reduce the amount of time robots spend waiting for paths to be cleared, and the overall distance traveled by the robots.

Figures (8)

• Figure 1: This paper implements and compares algorithms for automated reconfiguration using multiple robots. Above is a physical representation of the problem, and a sequence of frames showing a Bill-E bot moving a tile. See video overview at https://youtu.be/tCKMjhkzbp8.
• Figure 2: Symbolic overview of the construction used to show -hardness of the Bill-E reconfiguration problem, see proof of \ref{['thm:bille-reconf-np-complete']}.
• Figure 3: The gadget that is used in the proof of \ref{['thm:cooperative-hardness']}, showing that the cooperative variant of the problem is NP-hard.
• Figure 4: Starting from a configuration (middle), Bill-E can reach several configurations after a single motion. For clarity, the front foot is drawn as a circle, and configurations are color coded. (Left) The motions in $S_5$ are $\bullet$ waiting, $\bullet$ stepping forward, $\bullet$ backward, and placing the front foot one tile to the right $\bullet$ or one tile to the left $\bullet$ and moving the back foot one tile forward. (Right) $S_7$ is expanded to include placing the back foot one tile to the left $\bullet$ or right $\bullet$ and moving the front foot one tile backward.
• Figure 5: The collision set of a motion is used to determine validity. (Left) The Bill-E rotates $90^\circ$ counterclockwise, and the highlighted squares represent the respective collision set. (Right) Example of a collision resulting from moving two Bill-E bots in a certain way.

Theorems & Definitions (5)

• Theorem 1
• proof
• corollary 1
• Theorem 2
• proof