Three-Dimensional Optical Pointing System Encoded by Radial Trifocal Tensor

摘要

Using imaging sensors in a pointing, acquisition and tracking (PAT) system provides a high degree of accuracy and the capability of controlling multiple transceivers simultaneously. However, this kind of system can suffer from a narrow field-of-view (FOV). Also, for a single image sensor, the resulting PAT system can only accurately acquire a target located far away or moving on a plane. In this paper, we describe an optical PAT system, which has a FOV of almost 180 degrees and is also capable of locating targets at any distance. It is well known that two regular cameras are sufficient to reconstruct three dimensional coordinates by triangulating with two incident rays. The uniqueness of our system is that one of the cameras is an omnidirectional fisheye camera and the other is a regular camera (with a FOV of 30 degrees). Their geometric relationship is encoded by a radial trifocal tensor, which is further discussed in this paper. This scheme leads to a hierarchical structure in the design of PAT systems. A regular camera and an omnidirectional camera form a camera pair. Each of the transceivers on a rotary gimbal and the camera pair is first calibrated in order to retrieve their individual radial trifocal tensor. After the calibration, the camera pair monitors the target of interest and further computes the rotation angles for each of transceivers. A transceiver is then selected and rotates toward the target. The selection process is based on network objectives. The resulting system is fully optical and has three distinct advantages: 1) the radial trifocal tensor is invariant with the motion of the entire platform, 2) a wide field-of-view (close to 180 degrees); 3) three dimensional acquisition capability. However, there is a small penalty to be paid because an additional geometric limit exists compared with a PAT system using two regular cameras.