Geometric control with model predictive static programming on SO(3). (June 2019) - Wang, Yulin; Hong, Haichao; Tang, Shengjing
Abstract: This paper proposes a geometric attitude control approach with the model predictive static programming (MPSP) for a rigid body modeled on the Lie group S O ( 3 ) . The modeling scheme can avoid the defects of the singularity associated with Euler angles and the unwinding phenomenon associated with quaternion, and the MPSP technique features a high computational efficiency and is capable of achieving hard terminal constraints. In this paper, the MPSP is extended to the geometric control on S O ( 3 ), using the variational principle, the left-invariance principle of S O ( 3 ) and the topology structure of the Lie algebra space s o ( 3 ) . The desired attitude is considered as the hard terminal constraint and the energy consumption is optimized in the optimal control formulation of the MPSP. Moreover, the system disturbance and the measurement error of the states are taken into account in the online application of the MPSP. Simulation results of a spacecraft attitude control illustrate the effectiveness of the proposed method. Highlights: The model predictive static programming (MPSP) is extended on SO(3). A method for geometric attitude control on SO(3) is developed by the MPSP. The MPSP on SO(3) is implemented online for the closed-loop attitude control.