Fuel-Optimal Spacecraft Rendezvous via an Improved Collocation Method

Finite-thrust rendezvous optimization problem is solved based on an improved collocation method. Compared to the standard collocation method, the improved method has the advantage of higher accuracy with the same number of constraints. First, a finite-thrust rendezvous optimization control model is established. Then, an optimal control problem is converted into a nonlinear programming problem via state and control variables discretion. A fifth-order polynomial is used to approximate the state over the time segments with a series of constraints. Finally, the sequence quadratic programming (SQP) method is used to solve the parameter optimization problem. The simulation results show that the proposed improved method has high accuracy applying to fuel-optimal rendezvous with free terminal time.