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Plane formation by synchronous mobile robots in the three-dimensional Euclidean space
Yamauchi Y., Uehara T., Kijima S., Yamashita M. Journal of the ACM64 (3):1-43,2017.Type:Article
Date Reviewed: Feb 16 2018

This is an interesting and thorough investigation of the plane formation problem. This problem addresses how a large group of robots moving in 3D Euclidean space--that can see but have no identification, no access to a common coordinate system, and cannot communicate with others--can all land on the same 2D surface without collisions. The robots operate using a look-compute-move cycle in which they compute only on what they can see in the look phase and then move, all executing the phases at the same time.

The authors’ analysis shows how fully synchronous robots that do not have local knowledge can perform the task of moving from a 3D space to a 2D plane using a 3D rotation for the solution method. In their analysis, they discover that the robots cannot form a plane when their initial positions form most of the semi-regular polyhedra. This, of course, limited the scope of the solution somewhat, but does not detract from the importance of the overall solution and the demonstration of the methodology. They analyze the problem mathematically and logically and present a solution that works.

This is not a paper for the neophyte, as the logic and math are somewhat complicated. It is, however, a worthy example of logical analysis of an important area of controlling robots. Modeling the movement of synchronous robots in a 3D space to land on a 2D surface without collisions is a not an easy task.

I was particularly impressed with the section on “Recent Development” and its impact on their work, as well as the appendices, which provide additional important information. I only found one error that needs correction. In figure 7, the authors identify the interior sphere space as L(P), while in the text the same area is identified as I(P).

Reviewer:  Michael Moorman Review #: CR145860 (1806-0340)
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