Abstract:

An attitude motion tracking control algorithm is studied via the indirect Legendre pseudospectral method for the asymmetric underactuated rigid spacecraft equipped with only two pairs of jet thrusters. Firstly, the Legendre pseudospectral method (LPM) is employed to plan a reference trajectory of the min-time attitude maneuver for the system. Secondly, defining the deviation between the actual and reference trajectories as the variable, and then the attitude motion tracking problem can be transformed into a two-point boundary value problem (TPBVP) according to the necessary condition of the Pontryagin minimal value theory. At last, the Legendre-Gauss-Lobatto (LGL) points are utilized to transfer the TPBVP into a system of linear equations to be solved. It avoids the integral operating for the traditional Riccati differential equations. The effectiveness of the attitude motion tracking control algorithm based on indirect LPM for an initial disturbance in the underactuated spacecraft is verified through the numerical simulation.

Key words: Underactuated spacecraft, Indirect Legendre pseudospectral method, Attitude maneuver, Two point boundary value problem (TPBVP), Trajectory tracking