This paper presents an optimal attitude trajectory planning method for the spacecraft equipped with control moment gyros as the actuators. Both the fixed-time energy-optimal and synthesis performance optimal cases are taken into account. The corresponding nonsingular attitude maneuvering trajectories (i.e. open-loop control trajectories) with the consideration of a series of constraints are generated via Radau pseudospectral method. Compared with the traditional steering laws, the optimal steering law designed by this method can explicitly avoid the singularity from the global perspective. A linear quadratic regulator closed-loop controller is designed to guarantee the trajectory tracking performance in the presence of initial errors, inertia uncertainties and external disturbances. Simulation results verify the validity and feasibility of the proposed open-loop and closed-loop control methods.
Wie B. Space vehicle dynamics and control. AIAA Education Series Reston, VA: AIAA, 1998, pp.435-445.
2.
SchaubHJunkinsJL. Singularity avoidance using null motion and variable-speed control moment gyros. J Guid Control Dynam2000; 23: 11–16.
3.
YoonHTsiotrasP. Singularity analysis of variable-speed control moment gyros. J Guid Control Dynam2004; 27: 374–386.
4.
BedrossianNSParadisoJBergmannEVet al.Redundant single-gimbal control moment gyroscope singularity analysis. J Guid Control Dynam1990; 13: 1096–1101.
5.
BedrossianNSParadisoJBergmannEVet al.Steering law design for redundant single-gimbal control moment gyroscopes. J Guid Control Dynam1990; 13: 1083–1089.
6.
WieBHeibergCBaileyD. Singularity robust steering logic for redundant single-gimbal control moment gyros. J Guid Control Dynam2001; 24: 865–872.
7.
WieBHeibergCBaileyD. Rapid multi-target acquisition and pointing control of agile spacecraft. J Guid Control Dynam2002; 25: 96–104.
8.
WieB. Singularity escape/avoidance steering logic for control moment gyro systems. J Guid Control Dynam2005; 28: 948–956.
9.
ElnagarGKazemiMRazzaghiM. The pseudospectral legendre method for discretizing optimal control problems. IEEE Transact Automat Control1995; 40: 1793–1796.
10.
Benson DA. A Gauss pseudospectral transcription for optimal control. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2004.
11.
BensonDAHuntingtonGTThorvaldsenTPet al.Direct trajectory optimization and costate estimation via an orthogonal collocation method. J Guid Control Dynam2006; 29: 1435–1440.
12.
KameswaranSBieglerLT. Convergence rates for direct transcription of optimal control problems using collocation at Radau points. Computat Optimiz Appl2008; 41: 81–126.
13.
Garg D, Patterson MA, Darby CL, et al. Direct trajectory optimization and costate estimation of general optimal control problems using a Radau pseudospectral method. In: AIAA guidance, navigation, and control conference, Chicago, IL, 10–13 August 2009, AIAA 2009-5989.
14.
Francolin CC and Rao AV. Direct trajectory optimization and costate estimation of state inequality path-constrained optimal control problems using a Radau pseudospectral method. In: AIAA guidance, navigation, and control conference, 13–16 August 2012, Minneapolis, MN, AIAA 2012-4528.
15.
GargDPattersonMAHagerWWet al.A Unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica2010; 46: 1843–1851.
16.
FlemingARossIM. Singularity-free optimal steering of control moment gyros. Adv Astronaut Sci2006; 123: 2681–2700.
BedrossianNBhattSKangWet al.Zero-propellant maneuver guidance. IEEE Control Syst Magazine2009; 29: 53–73.
19.
Bedrossian N and Bhatt S. Space station zero-propellant maneuver guidance trajectories compared to Eigen axis. In: 2008 American control conference, Seattle, WA, 11–13 June 2008, pp.4833-4838.
20.
KarpenkoMBhattSBedrossianNet al.Flight implementation of shortest-time maneuvers for imaging satellites. J Guid Control Dynam2014; 37: 1069–1079.
21.
ShusterMD. A survey of attitude representations. J Astronaut Sci1993; 41: 439–517.
22.
LeffertsEJMarkleyFLShusterMD. Kalman filtering for spacecraft attitude estimation. J Guid Control Dynam1982; 5: 417–429.
23.
Rao AV, Benson DA, Darby CL, et al. User’s manual for GPOPS version 5.0: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive pseudospectral methods, http://www.gpops.org/gpopsManual.pdf (2011, accessed 5 August 2011).
24.
Gill PE, Murray W and Saunders MA. User’s guide for SNOPT Version 7: software for large scale nonlinear programming. San Diego, USA: University of California, 2006.
