Attitude control strategies overcoming the topological obstruction on SO(3)

Global tracking strategies are presented for the attitude dynamics of a rigid body. Due to the inherent topological restriction, it is impossible to achieve global attractivity with any continuous attitude control system on the special orthogonal group. Recently, the topological restriction has been dealt with switching between multiple configuration error functions according to the hybrid system framework. This paper proposes an alternative attitude control strategy to achieve exponential stability where the region of attraction covers the entire special orthogonal group. This is achieved by the novel ideal of adjusting the desired attitude trajectory via a conjugacy class. The unique contribution is that the topological restriction in attitude controls is addressed without introducing discontinuities with respect to time.

[1]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[2]  S. Bhat,et al.  A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon , 2000 .

[3]  D. Koditschek.  The Application of Total Energy as a Lyapunov Function for Mechanical Control Systems , 1989 .

[4]  N. McClamroch,et al.  Stable Manifolds of Saddle Points for Pendulum Dynamics on S^2 and SO(3) , 2011, 1103.2822.

[5]  Taeyoung Lee,et al.  Exponential stability of an attitude tracking control system on SO(3) for large-angle rotational maneuvers , 2012, Syst. Control. Lett..

[6]  Floris Takens,et al.  The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelman category , 1968 .

[7]  Andrew R. Teel,et al.  Global stabilization of spherical orientation by synergistic hybrid feedback with application to reduced-attitude tracking for rigid bodies , 2013, Autom..

[8]  Wilfrid Perruquetti,et al.  Retraction obstruction to time-varying stabilization , 2013, Autom..

[9]  Abdelhamid Tayebi,et al.  Construction of Synergistic Potential Functions on SO(3) With Application to Velocity-Free Hybrid Attitude Stabilization , 2015, IEEE Transactions on Automatic Control.

[10]  Daniel Feltey.  MATRIX GROUPS , 2008 .

[11]  Andrew R. Teel,et al.  Synergistic Hybrid Feedback for Global Rigid-Body Attitude Tracking on $\hbox{ SO }(3)^{\ast}$ ${\ssr {SO}}(3)^{\ast}$ , 2013, IEEE Transactions on Automatic Control.

[12]  Taeyoung Lee.  Global Exponential Attitude Tracking Controls on ${\mathsf {SO}}({\mathsf 3})$ , 2015 .

[13]  F. Wilson.  The structure of the level surfaces of a Lyapunov function , 1967 .