Effect of Timing Error: A Case Study of Navigation Camera

Abstract: We focus on the problem of timing errors in navigation camera as a case study in a broader problem of the effect of a timing error in cyber-physical systems. These systems rely on the requirement that certain things happen at the same time or certain things happen periodically at some period $T$. However, as these systems get more complex, timing errors can occur between the components thereby violating the assumption about events being simultaneous (or periodic). We consider the problem of a surgical navigation system where optical markers detected in the 2D pictures taken by two cameras are used to localize the markers in 3D space. A predefined array of such markers, known as a reference element, is used to navigate the corresponding CAD model of a surgical instrument on patient's images. The cameras rely on the assumption that the pictures from both cameras are taken exactly at the same time. If a timing error occurs then the instrument may have moved between the pictures. We find that, depending upon the location of the instrument, this can lead to a substantial error in the localization of the instrument. Specifically, we find that if the actual movement is $\delta$ then the observed movement may be as high as $5\delta$ in the operating range of the camera. Furthermore, we also identify potential issues that could affect the error in case there are changes to the camera system or to the operating range.