Bi-Level Global Optimization Method for Multi-Branching Trajectory

To solve the problems of the staging point selection and control variables jumping faced during design of the multi-branching trajectory, a bi-level global optimization method is proposed. In the given method, the sub-level optimization problem is set up for each trajectory section, and the system level optimization problem is set up to coordinate the coupling variables of the staging point. For these coupling variables, the mass variable is transformed to the local variable of the sub-level optimization problem, and other state variables are transformed as the global variables of the system level optimization problem. By this strategy, the couplings between the sub-level optimizations are decoupled hierarchically, and the optimal staging point can be obtained. Meanwhile, the first-order derivatives of control is introduced as the system-level coordinating variables to ensure the smooth transition of the control variables between the trajectory sections. The global trajectory optimization problem of a two-stage-to-orbit reusable launch vehicle is tested. The results show that the provided method is able to transform the highly coupled trajectory optimization problem into the simple and efficient bi-level optimization formulation, therefore can support the design of the multi-branching trajectory.