SGER: Vision-Based Control of Mechanical Systems via Spatial Sampling Kernels

基于视觉的控制体现了复杂的高维数据必须转化为有意义的行动的问题，这是控制系统理论中的一个基本问题。在典型的基于视觉的控制系统中，视觉信号中的信息被抽象出来并作为几何测量值发送给控制算法。该框架以信息丰富的视觉信号先验地分解为几个图像坐标为基础，依赖于可靠的视觉跟踪和完美的特征对应。虽然在概念上很方便，但这种方法从根本上是有限的。该项目旨在创建一种统一的基于视觉的控制方法，直接利用潜在的视觉信号，而不仅仅是视觉几何。该方法将空间采样核与李雅普诺夫稳定性理论相结合。这些技术将有助于设计可证明稳定的基于视觉的控制系统，用于广泛的视觉信号，几何运动和系统动力学。如何将高维数据转化为有用的行动？答案在于将大量数据（例如视频流）提炼成低维的、特定于任务的信息（例如，机器人的实时运动）的能力。这个项目力求为有效地将复杂的数据流转化为有效的行动建立科学基础。特别是，该项目使用基于视觉的控制来研究新的数学方法，以特定任务的方式分解复杂信号，这种方法允许清晰的分析和可证明的性能。这项研究的核心思想是，信息处理和控制之间的联系不需要是特别的；相反，将信息与行动联系起来的数学定理可以在现实环境中提供性能保证。

Vision-based control exemplifies problems in which complex high-dimensional data must be transformed into meaningful action, a fundamental problem in control systems theory. In typical vision-based control systems, information in the visual signal is abstracted and sent to a control algorithm as a geometric measurement. This framework, predicated on the a priori collapse of information-rich visual signals to a few image coordinates, relies on infallible visual tracking and perfect feature correspondence. While conceptually convenient, this approach is fundamentally limited. This project aims to create a unified approach to vision-based control that directly utilizes the underlying visual signals, not simply visual geometry. The approach combines spatial sampling kernels with Lyapunov stability theory. These techniques will facilitate the design of provably stable vision-based control systems for wide classes of visual signals, geometric motions, and system dynamics. How does one convert high-dimensional data into useful action? The answer lies in the ability to distill massive amounts of data for example, a video stream into to low-dimensional, task-specific information for example, robotic movements in real time. This project seeks to develop a scientific basis for the efficient reduction of complex data streams into effective action. In particular, this project uses vision-based control to investigate new mathematical methods for collapsing complex signals in a task-specific way that admits clear analysis and provable performance. Central to the research is the idea that the connection between information processing and control need-not be ad hoc; instead, mathematical theorems that link information to action can provide performance guarantees under real-world circumstances.