Time optimal attitude control for a rigid body

A time optimal control problem is studied for the attitude dynamics of a rigid body. The objective is to minimize the maneuver time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control input. Necessary conditions for optimality are developed directly on the special orthogonal group using rotation matrices. They completely avoid singularities associated with local parameterizations such as Euler angles, and they are expressed as compact vector equations. In addition, a discrete-time control method based on a geometric numerical integrator, referred to as a Lie group variational integrator, is proposed to compute the optimal control input that respects the underlying geometric properties of the rigid body. The proposed method is demonstrated by a large-angle time optimal maneuver for an elliptic cylinder rigid body.