Geometric Guidance for Globally Synchronized Deployment of Elastic Geodesic Grids

Abstract

Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized, time-coupled deformation trajectories. Starting from inverse tracing -- collapsing the deployed structure with a lightweight rod model while recording node paths under a shared parameter -- we obtain feasible node paths and formulate a polyline approximation problem that selects {globally synchronized} time steps and minimizes a robust tail-aggregated deviation measure under monotonicity constraints. {We solve the resulting non-smooth optimization problem via global optimization to obtain compact, synchronized displacement sequences for all paths simultaneously}. We evaluate the method using geometry-centric metrics (deviation versus step count, scaling with trajectory count) and demonstrate its utility by driving finite element deployment simulations that avoid intermediate buckling and capture deployment-induced prestress.