柔軟ネットワークのモジュール表現と制御
Modular representation and control of floppy networks
幾何剛性と代数的スパース性を組み合わせ、柔軟で過少拘束なネットワークのゼロエネルギー変形モードを階層的・モジュール的に同定し、ロボットの到達動作や弾性ネットワークの応答予測に応用した研究。
著者: Siheng Chen, Fabio Giardina, Gary P. T. Choi, L. Mahadevan
分類: cs.RO, cond-mat.dis-nn, cond-mat.mtrl-sci, cond-mat.soft, math.OC
原文アブストラクト
Geometric graph models of systems as diverse as proteins, robots, and mechanical structures from DNA assemblies to architected materials point towards a unified way to represent and control them in space and time. While much work has been done in the context of characterizing the behavior of these networks close to critical points associated with bond and rigidity percolation, isostaticity, etc., much less is known about floppy, under-constrained networks that are far more common in nature and technology. Here we combine geometric rigidity and algebraic sparsity to provide a framework for identifying the zero-energy floppy modes via a representation that illuminates the underlying hierarchy and modularity of the network, and thence the control of its nestedness and locality. Our framework allows us to demonstrate a range of applications of this approach that include robotic reaching tasks with motion primitives, and predicting the linear and nonlinear response of elastic networks based solely on infinitesimal rigidity and sparsity, which we test using physical experiments. Our approach is thus likely to be of use broadly in dissecting the geometrical properties of floppy networks using algebraic sparsity to optimize their function and performance.
