Optimal nonlinear tracking of spacecraft attitude maneuvers

A nonlinear-optimal control strategy is devised using Hamilton-Jacobi formulation for tracking attitude maneuvers of rigid-asymmetric spacecraft. The exact motion model employs kinematical representation by the modified Rodrigues parameters (MRP) for large principal rotations. For tracking a constant attitude trajectory, an infinite-horizon optimal control problem is posed, wherein nonlinear feedforward and feedback control torques minimize a performance index with a quadratic control cost and a fourth-order attitude- and angular-velocity error cost. Closed-form solution is obtained employing a Lyapunov function of the same form as the error cost, and by solving the Hamilton-Jacobi equation. Numerical results are presented for a practical tracking case with arbitrarily large initial conditions and desired state.