A Solution Method of Guidance Commands via Low-Pass Filter for Convex Trajectory Planning Problem

In the convex optimization problem for entry trajectory planning, the middle variables as new controls are defined to reduce the difficulty of convexification of original problem. Because of some reasons, the discontinuous or non-smooth of profiles of commands appear when solving commands using middle variables. For handling the phenomenon, a solution method of guidance commands via low-pass filter is proposed in this paper. Firstly, a discretized convex trajectory planning problem is formulated. Secondly, the solution errors of commands are defined. On the discretization points with high error, the proposed method is performed to smooth the abnormal commands by commands updating equations. On the other discretization points with low error, the method is not necessary. Finally, the method is inserted into a sequential iteration algorithm to solve the original non-convex entry trajectory planning problem. In numerical simulation, the effectiveness of the proposed method is verified, and the influence of filter coefficients on convergence and accuracy is discussed.