Development of mirror stabilization line-of-sight rate equations for an unconventional sensor-to-gimbal orientation

Conventional mirror line-of-sight stabilization approaches, such as the heliostat and coleostat, are configured such that the sensor input line-of-sight is always oriented parallel to a gimbal axis. While provisions must be made to accommodate the inherent two-to-one mirror kinematics in these approaches, the resulting angular rates orthogonal to the line-of-sight are linear functions of the angular rates of the gimbals and of the base to which the sensor and gimbals are attached, and they are un-coupled such that the two orthogonal line-of-sight axes can be controlled independently. If, however, the sensor and gimbal cannot be oriented such that the sensor input line-of-sight is parallel to one of the gimbal axes, the line-of-sight angular rate kinematics become non-linear and coupled. The purpose of this paper is to present the development of the angular rate kinematic equations for such a system. The angular rate equations which result are coupled and non-linear but account for the line-of-sight motion caused by both the angular motion of the gimbals and the angular motion of the base and thus can be used to inertially stabilize and point the line-of-sight about two orthogonal axes using measurements from the two gimbal angle transducers and three orthogonal gyros.