Single step optimization of feedback-decoupled spacecraft attitude manuevers

Recent research on nonlinear guidance of either manipulators or spacecraft concerns the use of feedback linearization and decoupling to generate exact nominal commands. The advantage of such transformation is that the otherwise highly nonlinear controller can be implemented with parallel, systolic or pipelined microprocessor architectures. Such global linearization based on quaternion kinematics leads to a possible feedback singularity so that Gibbs vector kinematics is used here instead. In practice limits on available actuators could still lead to unsatisfactory or unstable response. Current investigation on the analytical side includes correction for saturation effects and oscillation prevention during saturated operating regimes. The desired controller is one that would fully utilize the available actuators while smoothly approaching the target state as well as avoiding oscillations. In the case of spacecraft maneuvered by momentum transfer devices, real time command generation is possible by pointwise minimization of the sum of the squares of the norms of the "next state error" of the equivalent system and the linear system input. This is possible by the use of a suitable discretization of the linear system. It is also possible to track a nominal trajectory, such as a critically damped harmonic oscillator response, by minimizing the square of the norm of the error between the actual and the tracked states. The required solution of a sequence of state-dependent constrained quadratic minimization problems could also be done instantaneously by currently experimental sensor signal-biased nonlinear analog circuits.