Geometric control with model predictive static programming on SO(3)

摘要

This paper proposes a geometric attitude control approach with the model predictive static programming (MPSP) for a rigid body modeled on the Lie group SO(3). The modeling scheme can avoid the defects of the singularity associated with Euler angles and the unwinding phenomenon associated with quatemion, 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 SO(3), using the variational principle, the left-invariance principle of SO(3) and the topology structure of the Lie algebra space so(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.