Spacecraft Attitude Control under Constrained Zones via Quadratically Constrained Quadratic Programming

This paper examines an optimal spacecraft attitude control problem in the presence of complicated attitude forbidden zones. The objective is to design an optimal reorientation trajectory for a rigid body spacecraft under constraints, which is originally formulated as a nonlinear programming problem. The attitude forbidden zones are considered to prevent the light-sensitive instruments operated on-board from exposure to bright light while the mandatory zone to keep the communication instrument in certain zones to transmit and receive signals. When unit quaternions are used to represent the attitude of spacecraft, the dynamics and constraints are formulated as quadratic functions. By discretizing the reorientation trajectory into discrete nodes, the optimal attitude control problem can be formulated as general quadratically constrained quadratic programming (QCQP). Due to nonconvexity of general QCQP problems, the traditional semide nite relaxation method can only obtain a bound on the optimal solution. In this paper, we proposed an iterative rank minimization approach to gradually reduce the gap between the bound and the optimal solution and will nally converges to the optima. Simulation results are presented to demonstrate the feasibility of proposed algorithm.

[1]  Colin R. McInnes.  Large angle slew maneuvers with autonomous sun vector avoidance , 1994 .

[2]  Panagiotis Tsiotras,et al.  A novel approach to the attitude control of axisymmetric spacecraft , 1995, Autom..

[3]  Hutao Cui,et al.  Onboard Spacecraft Slew-Planning by Heuristic State-Space Search and Optimization , 2007, 2007 International Conference on Mechatronics and Automation.

[4]  William Rowan Hamilton,et al.  ON QUATERNIONS, OR ON A NEW SYSTEM OF IMAGINARIES IN ALGEBRA , 1847 .

[5]  W. Hamilton.  II. On quaternions; or on a new system of imaginaries in algebra , 1844 .

[6]  Hari B. Hablani.  Attitude Commands Avoiding Bright Objects and Maintaining Communication With Ground Station (AAS 98-376) , 1998 .

[7]  M. Mesbahi,et al.  Spacecraft reorientation in presence of attitude constraints via logarithmic barrier potentials , 2011, Proceedings of the 2011 American Control Conference.

[8]  Bong Wie,et al.  Quaternion feedback for spacecraft large angle maneuvers , 1985 .

[9]  Emilio Frazzoli,et al.  A RANDOMIZED ATTITUDE SLEW PLANNING ALGORITHM FOR AUTONOMOUS SPACECRAFT , 2001 .

[10]  F. L. Markley,et al.  Sampex science pointing with velocity avoidance , 1992 .

[11]  J. Kuipers.  Quaternions and Rotation Sequences , 1998 .

[12]  R. Kornfeld.  On-board autonomous attitude maneuver planning for planetary spacecraft using genetic algorithms , 2003 .

[13]  FAIZ A. AL-KHAYYAL,et al.  A relaxation method for nonconvex quadratically constrained quadratic programs , 1995, J. Glob. Optim..