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来确定最佳位置，以观察和绘制具有移动障碍物的复杂未知域。该项目的动机是执行监视任务所需的配备传感器的移动机器人设备和无人驾驶车辆的数量不断增加。在许多这样的任务中，效率是必不可少的--以传感器(观测)的最小测量最大化信息增益，减少数据传输、功率消耗，并增加稳健性和容量。这样的优化是研究计划的主要目标。这笔助学金在为期3年的时间里每年资助1名研究生。PI将开发迭代贪婪算法，确定观测位置，以优化每一步的信息增益。“增益”被表示为区域形状上的积分运算符，并且计算成本很高。PI建议开发深度学习方法，使计算变得可行，特别是在域形状充其量是部分已知的情况下。所提出的算法将需要通过离线数值模拟来生成训练数据。这种方法对于以与主导数学算法所规定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。该项目主要包括三个方面的工作：1)开发非近视贪婪算法，并研究其性质和效率。2)深度学习模型的建立和学习增益函数的数据生成。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NSF的法定使命，并通过使用基金会的智力优势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.