Almost global finite-time stabilization of rigid body attitude dynamics using rotation matrices

Abstract

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 Hölder 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 Hölder 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 © 2015 John Wiley & Sons, Ltd.

Finite time stable attitude estimation of rigid bodies with unknown dynamics

“…The proof of this result is given in [33], and is omitted here for brevity. The proof of this result is given in [33], and is omitted here for brevity.…”

“…Remark 1. In the presence of bounded measurement errors, the errors in the estimated states will converge to a bounded neighborhood of (I, 0) as shown in [29,30,33]. In practice, there would be measurement errors and U m will be as given in Equation (7).…”

Global finite-time attitude consensus of leader-following spacecraft systems based on distributed observers

“…Nonetheless, the influence of the possible unwinding can be mitigated in the sense that the observer convergence time T p can be made arbitrarily small by increasing λ i , i = 1, 2, 3. How to design global (asymptotic or finite-time) distributed attitude observers together with controllers on S 3 or even directly on SO(3), like those for single spacecraft by [28]- [30], remains an interesting open problem.…”

Adaptive fault‐tolerant spacecraft attitude control using a novel integral terminal sliding mode

“…Obviously, the steady-state values ofθ 1 are larger than θ 1 , while the steady-state values ofθ 2 are smaller than θ 2 . This is attributable to, after analyzing (21), the fact that θ 2 ϖ(e v , ω e ) vanishes as (e v , ω e ) → (0, 0) and the system perturbations dominant in steady phase are represented by θ 1 . Hence,θ 2 does not necessarily converge to a value equal to or larger than θ 2 in order to achieve attitude tracking.…”