Finite-time Lyapunov exponents (FTLEs) provide a powerful approach to compute time-varying analogs of invariant manifolds in unsteady fluid flow fields. These manifolds are useful to visualize the transport mechanisms of passive tracers advecting with the flow. However, many vehicles and mobile sensors are not passive, but are instead actuated according to some intelligent trajectory planning or control law; for example, model predictive control and reinforcement learning are often used to design energy-efficient trajectories in a dynamically changing background flow. In this work, we investigate the use of FTLE on such controlled agents to gain insight into optimal transport routes for navigation in known unsteady flows. We find that these controlled FTLE (cFTLE) coherent structures separate the flow field into different regions with similar costs of transport to the goal location. These separatrices are functions of the planning algorithm's hyper-parameters, such as the optimization time horizon and the cost of actuation. Computing the invariant sets and manifolds of active agent dynamics in dynamic flow fields is useful in the context of robust motion control, hyperparameter tuning, and determining safe and collision-free trajectories for autonomous systems. Moreover, these cFTLE structures provide insight into effective deployment locations for mobile agents with actuation and energy constraints to traverse the ocean or atmosphere.

翻译：有限时间Lyapunov指数（FTLE）为计算非定常流场中不变流形的时变模拟量提供了一种有效方法。这些流形有助于可视化随流场平流的被动示踪剂的输运机制。然而，许多运载工具和移动传感器并非被动，而是根据某种智能轨迹规划或控制律进行驱动；例如，模型预测控制和强化学习常被用于在动态变化的背景流中设计节能轨迹。本研究探究将FTLE应用于此类受控智能体，以洞察已知非定常流场中导航的最优输运路径。我们发现，这些受控FTLE（cFTLE）相干结构将流场分割为不同区域，各区域至目标位置的输运成本相近。这些分隔面依赖于规划算法的超参数（如优化时域和驱动成本）。计算动态流场中主动智能体动态的不变集与流形，对鲁棒运动控制、超参数调优以及自主系统安全无碰撞轨迹的确定具有实际意义。此外，这些cFTLE结构可为受驱动与能量约束的移动智能体在穿行海洋或大气时提供有效部署位置的深层洞见。