Motion control of the wedge prisms in Risley-prism-based beam steering system for precise target tracking.

Two exact inverse solutions of Risley prisms have been given by previous authors, based on which we calculate the gradients of the scan field that open a way to investigate the nonlinear relationship between the slewing rate of the beam and the required angular velocities of the two wedge prisms in the Risley-prism-based beam steering system for target tracking. The limited regions and singularity point at the center and the edge of the field of regard are discussed. It is found that the maximum required rotational velocities of the two prisms for target tracking are nearly the same and are dependent on the altitude angle. The central limited region is almost independent of the prism parameters. The control singularity at the crossing center path can be avoided by switching the two solutions.