Wenbo Li

The control capability of the boost-glide vehicle models controlled by the angle of attack and sideslip angle is weak. Such vehicles' ascent trajectory optimization exhibits characteristics of strong nonlinearity and piecewise constraints of control angles. Specifically, it faces two challenges: poor convergence performance and low computation efficiency. The algorithm's convergence is sensitive to the initial guess when traditional convex approaches based on the direct linearization method are employed. The existence of the piecewise constraints of control angles increases the complexity of the problem, reducing the algorithm's computation efficiency. To effectively address the two challenges, this paper proposes the homotopy approximation function sequential convex programming (HAF-SCP) algorithm. The high-precision approximation strategy and lossless convex relaxation are proposed to improve the convergence performance first, followed by a designed approximation function to approach the piecewise constraints of control angles. Subsequently, the originally non-convex optimal control problem is reformulated into a series of convex optimization subproblems. Numerical simulations are conducted to verify the performance of the proposed algorithm in addressing the piecewise constraints of control angles. Additionally, the optimality and real-time performance are discussed through comparative simulation examples.

Solid propellant grain reverse design aims to discover optimal grain geometries by shape optimization methods to match the desired solid motor performance curves. To maximize the performance matching degree and the propellant loading fraction simultaneously, this study develops a multi-objective evolutionary neural network for the grain reverse design, where the burning surface regression calculation is efficiently employed using the fast-sweeping method. Then, grain shape feature extraction and pattern analysis are achieved through image singular value decomposition and self-organizing mapping, respectively. Finally, the design case of a dual-thrust motor and a Mars ascent vehicle show that the method can well balance the performance-matching degree and propellant loading fraction. Moreover, without any training data set, it can generate dozens of grain shape patterns, highlighting their diversity and providing new ideas for solid rocket motor designers. Our method can offer a new pathway for the research field of solid rocket motor design.

Real-time trajectory optimization is crucial for achieving autonomous guidance in powered landing. However, existing algorithms often struggle with uncertainties and are unable to handle second-order cone probability constraints, such as control magnitude and direction constraints. Additionally, the large-scale and complex nature of these optimization problems hampers real-time performance. This study addresses these shortcomings by presenting a convex formulation suitable for general second-order cone probability constraints and proposing two strategies, conservative approximation and variable reduction, to improve real-time performance. Specifically, the conservative approximation converts spectral norm constraints into second-order cone constraints, while the variable reduction reduces the number of optimization variables. Applied to a powered landing simulation scenario, the proposed approaches effectively handle second-order cone probability constraints and improve real-time performance by two to three orders of magnitude.

Space vehicles’ real-time trajectory optimization is the key to future automatic guidance. Still, the current sequential convex programming (SCP) method suffers from a low convergence rate and poor real-time performance when dealing with complex obstacle avoidance constraints (OACs). Given the above challenges, this work combines homotopy and neural network techniques with SCP to propose an innovative algorithm. Firstly, a neural network was used to fit the minimum signed distance field at obstacles’ different “growth” states to represent the OACs. Then, the network was embedded with the SCP framework, thus smoothly transforming the OACs from simple to complex. Numerical simulations showed that the proposed algorithm can efficiently deal with trajectory optimization under complex OACs such as a “maze”, and the algorithm has a high convergence rate and flexible extensibility.

The reverse design of solid propellant grain for a performance-matching goal, one of the most challenging directions of the solid rocket motor designing work, is limited by the traditional semi-empirical parameter-driven optimization methods based on some predefined grain configurations. Grain designers call for a new method that can automatically provide brand-new grain shapes beyond the traditional ones. In this work, a shape optimization method based on the evolutionary neural network is proposed to achieve the reverse design of two-dimensional (2D) grains. Firstly, the modified ellipse-form eikonal equation is solved by using the finite element method to realize the burn-back analysis of 2D grains in any shape on a fixed unstructured mesh. Then, the neural network is introduced to determine the spatial distribution of the propellant to define the grain shape. The hyperparameters of the network are continuously evolved with the aid of the genetic algorithm. Finally, the optimal grain shape that matches the performance goal most is obtained. The method is verified in different scenarios. The result shows that the design can precisely match the given pressure-time curve of star grains and slotted-tube grains. Furthermore, the method can automatically evolve a new dendritic-shaped grain that matches the given dual-thrust pressure-time curve. Since the reverse design uses the concept of shape optimization, it does not require any pre-selection of the grain shape, and the designers shall be free from defining different kinds of geometric parameters for specific grain configurations. Consequently, the method has the potential to apply in the reconstruction of an actual grain and the conceptual design of innovative grain configurations.

The real-time guidance algorithm is the key technology of the powered landing. Given the lack of real-time performance of the convex optimization algorithm with free final time, a lossless convex optimization (LCvx) algorithm based on the deep neural network (DNN) predictor is proposed. Firstly, the DNN predictor is built to map the optimal final time. Then, the LCvx algorithm is used to solve the problem of fuel-optimal powered landing with the given final time. The optimality and real-time performance of the proposed algorithm are verified by numerical examples. Finally, a closed-loop simulation framework is constructed, and the accuracy of landing under various disturbances is verified. The proposed method does not need complex iterative operations compared with the traditional algorithm with free final time. Therefore, the computational efficiency can be improved by an order of magnitude.