Enveloping multi-pocket obstacles with hexagonal metamorphic robots

Abstract

Abslracl-The problem addressed is reconfiguration planning for a metamorphic robotic system composed of any number of hexagonal robots when a single obstacle with multiple indentations or "pockets" is embedded in the goal environment.We extend our earlier work on filling a single pocket in an obstacle to the case where the obstacle surface may contain multiple pockets. The planning phase of our algorithm first determines whether the obstacle pockets provide sufficient clearance for module movement, i.e., whether the obstacle is "admissible''. In this paper, we present algorithms that sequentially order indhidoal pockets and order module placement inside each pocker These algorithms ensure that every cell in each pocket is filled and that module deadlock and collision do not occur during reeonfiguration. This paper also provjdes a complete o%eniew of the planning stage that is executed prior to reconfiguration and presents a distributed reconfiguration schema for filling more than one obstacle pocket concurrently, followed by the envelopment of the entire obstacle. Lastly, we present examples of obstacles with multiple pockets that were successfullj filled using our distributed reconfiguration simulator.

A Stochastic Approach to Shortcut Bridging in Programmable Matter

“…Modular self-reconfigurable robotic systems focus on the motion planning and control of kinematic robots to achieve dynamic morphology [30], and metamorphic robots form a subclass of self-reconfiguring robots [9] that share some characteristics with our geometric amoebot model. Walter et al have conducted some algorithmic research on these systems (e.g., [26,25]), but focus on problems disjoint from those we consider.…”

Using a pocket-filling strategy for distributed reconfiguration of a system of hexagonal metamorphic robots in an obstacle-cluttered environment

“…A proof by induction on the number of configurations in the execution of our algorithm was given in [6] to show that filling a pocket cell with 2 or 3 contiguous free sides will not result in a neighboring pocket cell with < 2 contiguous free sides or in a neighboring pocket cell with non-contiguous free sides (i.e., with a contact pattern like that shown in Fig. 3.)…”

“…We modify techniques developed in our past work on filling obstacle pockets [6] to create a new algorithm for filling a goal configuration that contains obstacles. Informally, an obstacle pocket exists when unoccupied goal cells are "sandwiched" between obstacle cells.…”

“…The new contributions of this paper are the presentation of a novel adaptation of a pocket-filling algorithm [6] to plan reconfiguration in an obstacle-cluttered environment, along with an analysis and proof of algorithm correctness. The planning algorithm presented in this paper applies to a larger set of obstacle-containing goal configurations than did our earlier work on enveloping obstacles [7].…”

Using hexagonal metamorphic robots to form temporary bridges

“…In this paper, we use techniques presented in [12] and [13] to locate and form bridges over pockets in S. The algorithms presented in [13] cannot handle cases in which the length of the gap to be bridged is greater than the number of modules in the system, n. We solve this problem in this paper using a four-phase pre-processing algorithm that will bridge any nontraversable segment of a surface using at most four bridge modules. We present a sketch of the proof of correctness of our algorithm and describe complex surfaces successfully traversed using our algorithms.…”