Waypoint Following Dynamics of a Quaternion Error Feedback Attitude Control System

TL;DR

This paper analyzes the dynamics of waypoint following in quaternion error feedback attitude control systems, proposing a Chebyshev filter to reduce memory usage while maintaining control accuracy, demonstrated on NASA's Lunar Reconnaissance Orbiter.

Contribution

It introduces an interpolating Chebyshev-type filter for encoding attitude commands, reducing memory needs in quaternion feedback control systems.

Findings

Downsample-and-hold causes angular rate overshoot.

The proposed filter effectively encodes commands with fewer memory resources.

Analysis in the z-domain explains the ripple phenomenon.

Abstract

Closed-loop attitude steering can be used to implement a non-standard attitude maneuver by using a conventional attitude control system to track a non-standard attitude profile. The idea has been employed to perform zero-propellant maneuvers on the International Space Station and minimum time maneuvers on NASA's TRACE space telescope. A challenge for operational implementation of the idea is the finite capacity of a space vehicle's command storage buffer. One approach to mitigate the problem is to downsample-and-hold the attitude commands as a set of waypoints for the attitude control system to follow. In this paper, we explore the waypoint following dynamics of a quaternion error feedback control law for downsample-and-hold. 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 attitude commands to be encoded in terms of a set of filter coefficients. Using the interpolating filter, commands can be issued at the ACS rate but with significantly reduced memory requirements. The attitude control system of NASA's Lunar Reconnaissance Orbiter is used as an example to illustrate the behavior of a practical attitude control system.