In this paper, a constrained space maneuver vehicles trajectory optimization problem is formulated and solved using a new three-layer-hybrid optimal control solver. To decrease the sensitivity of the initial guess and enhance the stability of the algorithm, an initial guess generator based on a specific stochastic algorithm is applied. In addition, an improved gradient-based algorithm is used as the inner solver, which can offer the user more flexibility to control the optimization process. Furthermore, in order to analyze the quality of the solution, the optimality verification conditions are derived. Numerical simulations were carried out by using the proposed hybrid solver and the results indicate that the proposed strategy can have better performance in terms of convergence speed and convergence ability when compared with other typical optimal control solvers. A Monte-Carlo simulation was performed and the results show a robust performance of the proposed algorithm in dispersed conditions.

The sensitivity of the initial guess in terms of optimizer based on an hp-adaptive pseudospectral method for solving a space maneuver vehicle's (SMV) trajectory optimization problem has long been recognized as a difficult problem. Because of the sensitivity with regard to the initial guess, it may cost the solver a large amount of time to do the Newton iteration and get the optimal solution or even the local optimal solution. In this paper, to provide the optimizer a better initial guess and solve the SMV trajectory optimization problem, an initial guess generator using a violation learning differential evolution algorithm is introduced. A new constraint-handling strategy without using penalty function is presented to modify the fitness values so that the performance of each candidate can be generalized. In addition, a learning strategy is designed to add diversity for the population in order to improve the convergency speed and avoid local optima. Several simulation results are conducted by using the combination algorithm; simulation results indicated that using limited computational efforts, the method proposed to generate initial guess can have better performance in terms of convergence ability and convergence speed compared with other approaches. By using the initial guess, the combinational method can also enhance the quality of the solution and reduce the number of Newton iteration and computational time. Therefore, the method is potentially feasible for solving the SMV trajectory optimization problem.

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In this paper, a fuzzy physical programming (FPP) method has been introduced for solving multi-objective Space Manoeuvre Vehicles (SMV) skip trajectory optimization problem based on hp-adaptive pseudospectral methods. The dynamic model of SMV is elaborated and then, by employing hp-adaptive pseudospectral methods, the problem has been transformed to nonlinear programming (NLP) problem. According to the mission requirements, the solutions were calculated for each single-objective scenario. To get a compromised solution for each target, the fuzzy physical programming (FPP) model is proposed. The preference function is established with considering the fuzzy factor of the system such that a proper compromised trajectory can be acquired. In addition, the NSGA-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the FPP solution. Simulation results indicate that the proposed method is effective and feasible in terms of dealing with the multi-objective skip trajectory optimization for the SMV.

The Space Maneuver Vehicles (SMV) [1, 2] will play an increasingly important role in the future exploration of space, since their on-orbit maneuverability can greatly increase the operational flexibility and are more difficult as a target to be tracked and intercepted. Therefore, a well-designed trajectory, particularly in skip entry phase, is a key for stable flight and for improved guidance control of the vehicle [3, 4]. Trajectory design for space vehicles can be treated as an optimal control problem. Due to the high nonlinear characteristics and strict path constraints of the problem, direct methods are usually applied to calculate the optimal trajectories, such as direct multiple shooting method [5], direct collocation method [5, 6], or hp-adaptive pseudospectral method [7, 8]. Nevertheless, all the direct methods aim to transcribe the continuous-time optimal control problems to a Nonlinear Programming Problem (NLP). The resulting NLP can be solved numerically by well-developed algorithms such as Sequential Quadratic Programming (SQP) and Interior Point method (IP) [9, 10]. SQP methods are used successfully for the solution of large scale NLPs. Each Newton iteration of the SQP requires the solution of a quadratic programming subproblem a Ph.D.