A Simple Structure Constrained Attitude Control for Rigid Bodies: A PD-Type Control

This study investigates the challenging and complicated issue of full-state constraint attitude control for rigid bodies under actuators physical limitation. Using the concept of prescribed performance control (PPC), a novel proportional-derivative (PD)-type control is introduced by which both the attitude quaternion and the rotation velocity of the rigid body are enforced to possess specific behaviors in transient and steady state. To this end, a prescribed performance function (PPF) with finite-time convergence is first defined as the predefined boundaries for the quaternion and rotation velocity. Subsequently, a constrained PD-type attitude control for rigid body attitude system is developed. The significant difference between the proposed methodology and the PPC is the simple structure of the controller making it more applicable from practical implementation point of view. Indeed, due to the use of error transformation in the PPC, the controller contains partial derivative terms and complicated functions even for only constraining the attitude quaternion. When it comes to angular velocity constraint as well, the complexity of the control design procedure is doubled. It is rigorously proved that the suggested control framework can successfully satisfy constraints not only on the quaternion but also on the angular velocity, simultaneously. These interesting results are obtained even when the actuator saturation is considered. The simulation results conducted on a rigid spacecraft verify the efficacy and applicability of the suggested constrained attitude control approach.