重み付き組合せラプラシアンとセンサネットワークにおける被覆修復への応用
Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks
単体複体上の重み付き組合せラプラシアンを定義し、そのスペクトル特性を用いてほぼn次元の穴を検出する手法を提案。勾配降下法による動的被覆修復アルゴリズムをモバイルロボットチームのセンサネットワークに適用し、障害物環境へも拡張した。
著者: Shunsaku Yadokoro, Subhrajit Bhattacharya
分類: cs.RO, math.AT
原文アブストラクト
We define the weighted combinatorial Laplacian operators on a simplicial complex and investigate their spectral properties. Eigenvalues close to zero and the corresponding eigenvectors of them are especially of our interest, and we show that they can detect almost $n$-dimensional holes in the given complex. Real-valued weights on simplices allow gradient descent based optimization, which in turn gives an efficient dynamic coverage repair algorithm for the sensor network of a mobile robot team. Using the theory of relative homology, we also extend the problem of dynamic coverage repair to environments with obstacles.
