模块化旋转机器人通用可重构性的表征
Characterizing Universal Reconfigurability of Modular Pivoting Robots
摘要：
我们给出了高效的算法和硬度的结果之间的两个连接配置的模块在六边形网格的重新配置。我们考虑的重新配置移动是“枢轴”，其中六边形模块围绕与另一个模块共享的顶点旋转。根据先前的工作模块化机器人，我们定义了两个自然的六边形枢转移动的增加功率：限制和猴子移动。当我们允许这两个动作，我们提出了第一个通用的重新配置算法，它转换之间的任何两个连接的配置使用$O(n^3)$猴子移动。这个结果与正方形的类似问题形成强烈对比，正方形中有刚性的例子，没有一个保持连通性的旋转移动。另一方面，如果我们只允许限制移动，我们证明了重新配置问题成为PSPACE完全。此外，我们表明，与六边形相比，枢转广场的重新配置问题是PSPACE完全的，无论允许的枢转移动的集合。在这个过程中，我们加强了Demaine等人的还原框架。[FUN'18]我们认为是独立的利益。
英文摘要：
We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around a vertex shared with another module. Following prior work on modular robots, we define two natural sets of hexagon pivoting moves of increasing power: restricted and monkey moves. When we allow both moves, we present the first universal reconfiguration algorithm, which transforms between any two connected configurations using $O(n^3)$ monkey moves. This result strongly contrasts the analogous problem for squares, where there are rigid examples that do not have a single pivoting move preserving connectivity. On the other hand, if we only allow restricted moves, we prove that the reconfiguration problem becomes PSPACE-complete. Moreover, we show that, in contrast to hexagons, the reconfiguration problem for pivoting squares is PSPACE-complete regardless of the set of pivoting moves allowed. In the process, we strengthen the reduction framework of Demaine et al. [FUN'18] that we consider of independent interest.
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