Realistic Reconfiguration of Crystalline (and Telecube) Robots

Abstract

In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2 ) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2 ) parallel steps [8,10,4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω (n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations.

Linear reconfiguration of cube-style modular robots

“…Subsequent to the short version of this result appearing in [4], there have been two significant new advances: an algorithm that reconfigures in O (n) parallel operations while taking into account the physical forces associated with mass or inertia during the moves by restricting to constant force per operation [9], and an algorithm for reconfiguring in O (log n) parallel moves [10].…”

Efficient reconfiguration of lattice-based modular robots

“…We note that the worst-case optimality cannot be deduced directly from [2], because we have only proved a one-way reduction. However, the same reasoning and example suffice: reconfiguring from a horizontal straight configuration to a vertical straight configuration.…”

“…The total number of atom operations (counting multiple steps per time unit) is O(n 2 ), and both bounds are worst-case optimal [2]. This model even restricts the communication range and on-board memory of each atom.…”

A bio-inspired mobile agent-based coalition formation system for multiple modular-robot systems

“…Many groups have investigated into modular robotics such as M-TRAN [7], [8], ATRON [9], [10], [11], Telecubes [12], [13], SuperBot [14], [15], [16] iMobot [17], [18]. Selfreconfigurable modular robotics field addressed physical design, planning and control challenges [1].…”