Attitude Control of Rigid Bodies: An Energy-Optimal Geometric Switching Control Approach

In this article, the attitude control problem for a class of rigid body systems with switching submodes is investigated. To address such issue, an energy-optimal geometric switching control method is proposed for the first time. First, a switching Lie group method and a switching Lie group discrete variational integrator method based on the variational principle are developed. Then, continuous-time and discrete-time attitude switching dynamics models for rigid bodies are globally expressed on a special orthogonal matrix group (i.e., SO(3) group) to avoid the locality, singularity, and ambiguity caused by using the traditional Euler angle method, minimum representation method, or quaternion method. Second, the switching process of rigid bodies from initial attitude and angular velocity to desired attitude and angular velocity within a fixed maneuver time and the minimum energy consumption of rigid bodies with control saturation are solved. Furthermore, by solving the energy-optimal geometric control problem of attitude switching dynamics models, the global optimal geometric switching control and optimal switching time conditions under continuous-time and discrete-time are first derived. The obtained criteria ensure that the intrinsic geometric properties of attitude switching dynamics models will not be lost during the optimization process. Finally, some simulation results are presented to demonstrate the feasibility of the proposed techniques.