Almost global finite time stabilization of rigid body attitude dynamics using rotation matrices
Summary This work considers continuous finite time stabilization of rigid body attitude dynamics using a coordinate free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3) Using a Holder continuous Morse Lyapunov function, a finite time feedback stabilization scheme for rigid body attitude motion to a desired attitude with continuous state feedback is obtained. Attitude feedback control with finite time convergence has been considered in the past using the unit quaternion representation. However, it is known that the unit quaternion representation of attitude is ambiguous, with two antipodal unit quaternions representing a single rigid body attitude. Continuous feedback control using unit quaternions may therefore lead to the unstable unwinding phenomenon if this ambiguity is not resolved in the control design, and this has adverse effects on actuators, settling time, and control effort expended. The feedback control law designed here leads to almost global finite time stabilization of the attitude motion of a rigid body with Holder continuous feedback to the desired attitude. As a result, this control scheme avoids chattering in the presence of measurement noise, does not excite unmodeled high frequency structural dynamics, and can be implemented with actuators that can only provide continuous control inputs. Numerical simulation results for a spacecraft in low Earth orbit, obtained using a Lie group variational integrator, confirm the theoretically obtained stability and robustness properties of this attitude feedback stabilization scheme. Copyright (c) 2015 John Wiley Sons, Ltd.