Quaternion Constrained Structured Adaptive Attitude Control

Abstract

In this paper, a novel, attitude-constrained, structured adaptive control strategy is proposed for a spacecraft in the presence of parametric uncertainties. A set of cone angles are defined as a way to quantify the relative orientation error between two reference frames. While tracking the desired attitude, the corresponding cone angles are driven to zero while being constrained to lie within a maximum value. Using an error transformation, the restriction on the cone angles is converted into quaternion constraints that are subsequently used in barrier Lyapunov function (BLF) based controller synthesis. Attitude error constraints are satisfied by ensuring the boundedness of BLFs in the closed-loop Lyapunov stability analysis. Eventually, an adaptive control law is synthesized that drives the spacecraft to the desired attitude with the help of approximate and nominal spacecraft dynamics. While doing so, a function approximation strategy is used to obtain a stable weight update rule to estimate the disturbance term. Finally, the effectiveness of the proposed adaptive control law is demonstrated via numerical simulations.