Models and Algorithms for Optimal Vision-Based Surveillance and Exploration of Complex Environments

PI计划开发数学和相应的算法，以确定观察和绘制具有移动障碍物的复杂未知区域的最佳位置。该项目的动机是越来越多的配备传感器的移动机器人设备和执行监视任务所需的无人驾驶车辆。在许多这样的任务中，效率是至关重要的- -以最少的传感器（观察）测量来最大限度地获得信息，减少数据传输、功耗并增加稳健性和容量。这种优化是研究计划的主要目的。该奖学金每年资助1名研究生，为期3年。PI将开发迭代贪婪算法来确定观测位置，以优化每一步的信息增益。“增益”被表述为域形状上的积分算子，计算成本很高。PI建议开发深度学习方法，使计算可行，特别是在域形状最多部分已知的情况下。所提出的算法需要通过离线数值模拟生成训练数据。这种方法对于以与控制数学算法指示的动态过程一致的方式对高维形状空间进行采样至关重要。本项目主要包括三个方面：1)开发非近视眼贪婪算法，并研究其性质和效率。2)开发深度学习模型和生成用于学习增益函数的数据。3)使用项目中使用的深度学习模型开发U-net的数学理解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The PI plans to develop the mathematics and corresponding algorithms to determine optimal locations to observe and map out complex unknown domains with moving obstacles. This project is motivated by the increasing number of sensor-equipped mobile robotic devices and unmanned vehicles required to perform surveillance missions. In many of these missions, efficiency is essential — maximizing the information gain with minimal measurements by the sensors (observations) reduces data transmission, power consumption and increases robustness and capacity. Such optimization is the principal aim of the research program. This grant will support 1 graduate student per year for the 3 year duration of the grant. The PI will develop iterative greedy algorithms that determine observation locations to optimize each step's information gain. The "gain" is formulated as an integral operator on the domain shape and is costly to compute. The PI proposes developing Deep Learning approaches that make computations feasible, particularly when the domain shapes are at best partially known. The proposed algorithms will require generating training data by offline numerical simulations. This approach is crucial to sample high-dimensional shape space in a manner consistent with the dynamical processes dictated by the governing mathematical algorithms. This project includes three main thrusts: 1) Development of non-myopic greedy algorithms and study their properties and efficiency. 2) Development of Deep Learning models and data generation for learning the gain functions. 3) Development of mathematical understanding of U-net used the Deep Learning models used in the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.