Sliding Motions on SO(3), Sliding Subgroups

We propose a sliding surface for systems on the Lie group SO(3) ×ℝ3. The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for the attitude control of rigid bodies. The closed-loop system is robust against matched disturbances and does not exhibit the undesired unwinding phenomenon.

[1]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[2]  Augusto Sarti,et al.  Control on the Sphere and Reduced Attitude Stabilization , 1995 .

[3]  Félix A. Miranda-Villatoro,et al.  Continuous and discrete-time stability of a robust set-valued nested controller , 2019, Autom..

[4]  W. F. Phillips,et al.  Review of attitude representations used for aircraft kinematics , 2001 .

[5]  John L. Crassidis,et al.  Fundamentals of Spacecraft Attitude Determination and Control , 2014 .

[6]  N. McClamroch,et al.  Rigid-Body Attitude Control , 2011, IEEE Control Systems.

[7]  Dennis S. Bernstein,et al.  Inertia-free spacecraft attitude trajectory tracking with internal-model-based disturbance rejection and almost global stabilization , 2009, 2009 American Control Conference.

[8]  Lorenzo Marconi,et al.  Output regulation for systems on matrix Lie-groups , 2016, Autom..

[9]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

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

[11]  R. Murray,et al.  Proportional Derivative (PD) Control on the Euclidean Group , 1995 .

[12]  Malcolm D. Shuster.  Survey of attitude representations , 1993 .

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

[14]  M. Shuster.  A survey of attitude representation , 1993 .

[15]  Robert E. Mahony,et al.  Nonlinear Complementary Filters on the Special Orthogonal Group , 2008, IEEE Transactions on Automatic Control.

[16]  R. Brockett.  Lie Theory and Control Systems Defined on Spheres , 1973 .

[17]  Shih-Che Lo,et al.  Smooth Sliding-Mode Control for Spacecraft Attitude Tracking Maneuvers , 1995 .

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

[19]  Lorenzo Marconi,et al.  Adding an integrator for output regulation of systems with matrix Lie-group states , 2015, 2015 American Control Conference (ACC).

[20]  David W. Miller,et al.  Reduced-Attitude Boresight Guidance and Control on Spacecraft for Pointing, Tracking, and Searching , 2015 .