Waypoint following dynamics of a quaternion error feedback attitude control system

Closed-loop attitude steering is a concept for implementing an attitude trajectory by using a conventional quaternion error feedback controller to track the time-varying attitude reference, rather than to simply regulate to a desired orientation. This is done by sampling the reference input and executing the maneuver as a sequence of closely spaced regulating commands that are read out from the spacecraft’s command buffer. The idea has been employed in practice to perform zero-propellant maneuvers on the International Space Station and minimum-time maneuvers on NASA’s TRACE space telescope as well as NASA’s Lunar Reconnaissance Orbiter (LRO). A challenge for operational implementation of the idea is the limited capacity of a space vehicle’s command storage buffer, which is normally not designed with attitude tracking in mind. One approach to mitigate the problem is to downsample-and-hold the attitude commands so that the attitude control system (ACS) regulates to a series of waypoints. This article explores the waypoint following dynamics of a quaternion error feedback control law for such an approach. It is shown that downsample-and-hold induces a ripple between downsamples that causes the satellite angular rate to significantly overshoot the desired limit. Analysis in the z-domain is carried out in order to understand the phenomenon. An interpolating Chebyshev-type filter is proposed that allows the desired attitude trajectory to alternatively be encoded in terms of a small set of filter coefficients. Using the interpolating filter, the continuous-time reference trajectory can be reconstructed and issued at the ACS rate but with significantly reduced memory requirements. The ACS of the LRO is used as an example to illustrate the behavior of a practical ACS.