Real-time optimal guidance for orbital maneuvering.

A new formulation for soft-constraint trajectory optimization is presented as a real-time optimal feedback guidance method for multiburn orbital maneuvers. Control is always chosen to minimize burn time plus a quadratic penalty for end condition errors, weighted so that early in the mission (when controllability is greatest) terminal errors are held negligible. Eventually, as controllability diminishes, the method partially relaxes but effectively still compensates perturbations in whatever subspace remains controllable. Although the soft-constraint concept is well-known in optimal control, the present formulation is novel in addressing the loss of controllability inherent in multiple burn orbital maneuvers. Moreover the necessary conditions usually obtained from a Bolza formulation are modified in this case so that the fully hard constraint formulation is a numerically well behaved subcase. As a result convergence properties have been greatly improved.