Optimal power-limited rendezvous with upper and lower bounds on thrust

Optimal power-limited rendezvous with variable exhaust velocity is investigated for propulsion systems having both upper and lower bounds on thrust magnitude. In this model the spacecraft thrusters have four admissible states, thrusting at the upper saturation level, unsaturated power-limited thrusting, thrusting at the lower saturation level, and unpowered (i.e., engine off.) A fifth chattering state is also possible. The mathematical structure of the solution of the optimal rendezvous problem associated with this propulsion model is found. Computer simulations of rendezvous with a satellite in circular orbit are presented. For rendezvous near circular orbit four classes of chattering solutions of two types can occur. It is assumed that multiple thrusters can be mounted on the spacecraft and that they can operate independently. Applying the efficiency condition presented in a previous paper, a logic for switching individual thrusters on and off for optimal fuel usage and computational efficiency is presented.