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

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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.