Control of Large Angle Attitude Maneuvers for Rigid Bodies Using Sum of Squares

The main contribution of this paper is the development of a two step integrated and systematic approach for modeling and control of large angle maneuvers of a rigid body through convex optimization. In the first step, the attitude dynamics of the rigid body are represented by modified Rodriguez parameters (MRP). In the second step, a Lyapunov- based controller synthesis is performed based on the Sum of Squares (SOS) technique. The key observation that makes rigid body control amenable to an efficient (convex) design technique such as SOS is that both quaternions and modified Rodriguez parameters enable the representation of the attitude dynamics of a rigid body by polynomial vector fields. The model proposed in this paper will use MRP instead of quaternions to represent the rigid body attitude to yield a minimal parameterization. The effectiveness of the proposed control technique is shown in simulations for a large angle maneuver corresponding to a satellite rotation about a fixed axis.