Consideration of three-dimensional attitude and position control for a free-floating rigid body using three thrusters

The study examines the control algorithm of a three-dimensional attitude and position of a free-floating rigid body with three thruster forces in which the force directions are fixed with respect to the body. This study provides a theory to develop a control method of an underactuated satellite with the minimum thruster number. In the procedure, three switching controllers are used in conjunction with motion planning in the final angular-rate deceleration phase to individually control the six state variables to the target values. The switching controllers have a hierarchical structure by using invariant manifolds as switching surfaces. The state variables in higher class manifolds that include lower class ones are adjusted by repeatedly adding intentional disturbances while the lower class state variables are returned to the original values by using lower class invariant manifolds. This study describes methods to define the invariant manifolds and also the intentional disturbance for achieving the forementioned control strategy. Finally, the motion planning in the angular-rate deceleration phase from a remained single-axis rotation finalizes the six state values of the body to the target values. Numerical simulations verify the proposed method.