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：有限时间李雅普诺夫指数（FTLEs）为计算非定常流场中不变流形的时变模拟量提供了有效方法。这些流形有助于可视化随流体输运的被动示踪剂的传输机制。然而，许多运载器与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，模型预测控制与强化学习常被用于在动态变化的背景流中设计节能轨迹。本研究探索将FTLE应用于此类受控智能体，以揭示在已知非定常流中导航的最优传输路径。我们发现，这些受控FTLE（cFTLE）相干结构将流场划分为不同区域，每个区域具有到达目标位置的相似输运代价。这些分界线依赖于规划算法的超参数，例如优化时域与控制代价。计算动态流场中主动智能体动力学的不变集与流形，对自主系统的鲁棒运动控制、超参数调优以及安全无碰撞轨迹确定具有重要意义。此外，这些cFTLE结构为具有驱动与能量约束的移动智能体在海洋或大气中穿行时，其有效部署位置的选择提供了关键见解。