Krishna Kartik, Song Zhuoyuan, Brunton Steven L
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA.
Department of Mechanical Engineering, University of Hawai'i at Mānoa, Honolulu, HI 98116, USA.
Proc Math Phys Eng Sci. 2022 Feb;478(2258):20210255. doi: 10.1098/rspa.2021.0255. Epub 2022 Feb 2.
Intelligent mobile sensors, such as uninhabited aerial or underwater vehicles, are becoming prevalent in environmental sensing and monitoring applications. These active sensing platforms operate in unsteady fluid flows, including windy urban environments, hurricanes and ocean currents. Often constrained in their actuation capabilities, the dynamics of these mobile sensors depend strongly on the background flow, making their deployment and control particularly challenging. Therefore, efficient trajectory planning with partial knowledge about the background flow is essential for teams of mobile sensors to adaptively sense and monitor their environments. In this work, we investigate the use of finite-horizon model predictive control (MPC) for the energy-efficient trajectory planning of an active mobile sensor in an unsteady fluid flow field. We uncover connections between trajectories optimized over a finite-time horizon and finite-time Lyapunov exponents of the background flow, confirming that energy-efficient trajectories exploit invariant coherent structures in the flow. We demonstrate our findings on the unsteady double gyre vector field, which is a canonical model for chaotic mixing in the ocean. We present an exhaustive search through critical MPC parameters including the prediction horizon, maximum sensor actuation, and relative penalty on the accumulated state error and actuation effort. We find that even relatively short prediction horizons can often yield energy-efficient trajectories. We also explore these connections on a three-dimensional flow and ocean flow data from the Gulf of Mexico. These results are promising for the adaptive planning of energy-efficient trajectories for swarms of mobile sensors in distributed sensing and monitoring.
智能移动传感器，如无人飞行器或水下航行器，在环境传感与监测应用中越来越普遍。这些主动传感平台在不稳定的流体流动中运行，包括多风的城市环境、飓风和洋流。这些移动传感器的动力学通常受到其驱动能力的限制，强烈依赖于背景流，这使得它们的部署和控制极具挑战性。因此，利用关于背景流的部分知识进行高效轨迹规划对于移动传感器团队自适应地感知和监测其环境至关重要。在这项工作中，我们研究了有限时域模型预测控制（MPC）在非定常流体流场中主动移动传感器的节能轨迹规划中的应用。我们揭示了在有限时间范围内优化的轨迹与背景流的有限时间李雅普诺夫指数之间的联系，证实了节能轨迹利用了流场中的不变相干结构。我们在非定常双涡旋向量场（一种海洋中混沌混合的典型模型）上展示了我们的发现。我们对包括预测时域、最大传感器驱动以及累积状态误差和驱动努力的相对惩罚等关键MPC参数进行了详尽搜索。我们发现，即使相对较短的预测时域通常也能产生节能轨迹。我们还在来自墨西哥湾的三维流场和海洋流场数据上探索了这些联系。这些结果对于分布式传感与监测中移动传感器群的节能轨迹自适应规划很有前景。
