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.

翻译：弹性测地网格通过复杂的非线性运动从平面构型展开至空间构型，这类运动难以在模拟中稳健表征。我们提出一种几何引导框架，将部署离散化为同步的、时间耦合的形变轨迹。首先进行逆向追踪——通过轻质杆模型折叠展开结构，同时记录共享参数下的节点路径——获得可行节点路径，并构建折线逼近问题：在单调性约束下选择全局同步的时间步长，最小化鲁棒性尾部聚合偏差度量。通过全局优化求解所得非光滑优化问题，同步获取所有路径的紧凑位移序列。我们采用以几何为中心的指标（偏差与步数关系、随轨迹数量的缩放特性）评估该方法，并通过驱动有限元部署仿真验证其实用性——该仿真可避免中间屈曲并捕捉部署引起的预应力。