Constrained Control of Underactuated Spacecraft Using Artificial Potentials

A nonlinear control algorithm is proposed for the attitude reorientation of underactuated spacecraft in the presence of multiple types of attitude-constrained zones. The spacecraft's attitude dynamics are characterized by a unit quaternion, with two orthogonally applied torques serving as inputs. Through the conservation of angular momentum conditions, the nonholonomic constraints imposed on the spacecraft are transformed into inequality constraints on the attitude Euler axis with respect to the unactuated axis. Moreover, conical attitude-forbidden zones and -mandatory zones are formulated by quaternion. Considering the constraints based on quaternion representation, a specific potential function is proposed to facilitate the design of control laws. Simultaneously, an effective remedy is provided for the unique antiunwinding phenomenon associated with quaternions. Based on this potential function, a nonlinear feedback controller is proposed. The local asymptotic stability of the closed-loop system is rigorously proven by employing the Lyapunov direct method and LaSalle's invariance principle. A set of numerical simulations and semi-physical experiments are conducted to corroborate the effectiveness and performance of the proposed control scheme.