Modular representation and control of floppy networks
This provides a framework for optimizing floppy networks in diverse systems like proteins and robots, though it appears incremental as it builds on existing concepts of rigidity and sparsity.
The paper tackled the problem of representing and controlling floppy, under-constrained networks common in nature and technology by combining geometric rigidity and algebraic sparsity to identify zero-energy floppy modes, demonstrating applications in robotic reaching tasks and predicting elastic network responses with physical experiments.
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.