Optimal feedback guidance for low-thrust orbit insertion

An optimal feedback guidance scheme is developed for the terminal orbit insertion phase of a low-thrust planar transfer to geosynchronous orbit. The minimum fuel trajectory between specified energy levels is utilized as a reference trajectory and the guidance law is derived using linear quadratic regulator optimization. The feedback guidance scheme responds effectively to a wide range of initial conditions and results in very precise terminal orbit conditions with near-optimal performance. The guidance scheme also successfully handles propulsion system uncertainties and extremely large initial state deviations. Numerical results are presented for a variety of orbit insertion manoeuvres.