Adaptive Critic-Based Solution to an Orbital Rendezvous Problem

The optimal continuous thrust rendezvous maneuver is investigated in this Note. The objective is for a rigid spacecraft to perform a maneuver into a destination orbit within a given final time. Recently, a method was proposed in that could determine a global optimal solution using local numerical optimization steps. A method developed in for problems with terminal soft constraints gives a closed-form solution to the problem, but only for a pre-specified initial condition and time-to-go. The finite horizon state dependent Riccati equation (Finite-SDRE) developed in gives a suboptimal closed-form solution to the problem for different initial conditions and final times in real time. The rendezvous problem with continuous thrust is defined as follows. A rigid spacecraft is orbiting around the Earth in a circular orbit. It needs to perform a maneuver using continuous thrust, moving to another circular orbit in a fixed given time. The terminal hard constraint positions the spacecraft in the destination orbit precisely, with the desired velocity, to stay in the orbit after the maneuver.