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In this paper, a convex optimization algorithm is proposed to solve the online trajectory optimization problem of boost back of vertical take-off/vertical landing reusable launch vehicles. To achieve high-precision landing of launch vehicles, trajectory optimization of the boost-back flight phase considering the accuracy of entry is carried out, especially in emergencies. The trajectory optimization problem is formulated as an optimal control problem with minimum fuel consumption, and then it is transformed into a series of convex optimization subproblems, which can be solved by primal-dual interior-point method accurately and rapidly. During the transformation, flip-Radau pseudospectral discretization method, lossless convexification and successive convexification technology are applied. To drive the vehicle to predetermined entry points at the expected velocity, terminal constraints are expressed as orbital constraints of the endpoint in the boost-back flight phase. Considering the influence of Earth's rotation, the right ascension of the ascending node of the target orbit is updated according to the time and true anomaly at the end of the boost-back flight phase. Furthermore, the homotopy method is applied to the situation where there is no good initial guess when emergency happens. The algorithm presented in this paper performs well upon the simulation experiments of mission change and thrust decline. With good accuracy, high computational efficiency, and excellent robustness, the convex approach proposed has a great potential for onboard application in reusable launch vehicles and other space vehicles. [ABSTRACT FROM AUTHOR]

This brief presents an integrated trajectory planning and attitude control framework for six-degree-of-freedom (6-DOF) hypersonic vehicle (HV) reentry flight. The proposed framework utilizes a bilevel structure incorporating desensitized trajectory optimization and deep neural network (DNN)-based control. In the upper level, a trajectory data set containing optimal system control and state trajectories is generated, while in the lower level control system, DNNs are constructed and trained using the pregenerated trajectory ensemble in order to represent the functional relationship between the optimized system states and controls. These well-trained networks are then used to produce optimal feedback actions online. A detailed simulation analysis was performed to validate the real-time applicability and the optimality of the designed bilevel framework. Moreover, a comparative analysis was also carried out between the proposed DNN-driven controller and other optimization-based techniques existing in related works. Our results verify the reliability of using the proposed bilevel design for the control of HV reentry flight in real time. [ABSTRACT FROM AUTHOR]

Based on the analytical solutions of T-H equations and its state transition matrix form, the open-loop control method of spacecraft impulsive relative hovering was studied， which is promising for practical engineering use. The true anomaly intervals of the hovering impulse were optimized by the nonlinear mathematical programming. Based on the calculation of collision probability, the method of safety analysis and risk management was proposed. The numerical simulations show that the introduced relative hovering method can be used for circular and elliptical reference orbits hovering. Furthermore, the local optimal solution can be obtained by applying the true anomaly intervals optimization method. The maximum collision probability and the minimum relative distance nearly appear at the same time. And, the smaller the relative distance is, the larger the collision probability. [ABSTRACT FROM AUTHOR]

A new concept of dynamic reentry footprint was presented to ensure the reentry of the spacecraft safely and accurately. Concerned with all the given flight states and the constraint conditions of the spacecraft during the whole reentry flight process, the maximum reachable area on the earth surface can be calculated by the given numerical algorithm. Combined with the dynamic reentry numerical algorithm, the modified genetic algorithm was applied to optimize the reentry flight trajectories, and all the qualified trajectories which constitute the landing footprint can be calculated. Through a series of reentry flight numerical simulations, the characteristics of dynamic reentry footprint was summarized, which can be used to optimize the guidance and flight trajectory. [ABSTRACT FROM AUTHOR]

To satisfy the requirement of long-term on-orbit displaced spacecraft for specific tasks, a hybrid propulsion technology, consisting of solar electric propulsion (SEP) and solar sail, was studied for the displaced geostationary orbit. The relation between the sail attitude angles and the SEP acceleration for hybrid propulsion system was firstly deduced. A single variable extremum problem obtained from the first-order optimality condition was solved to minimize the SEP acceleration and acquire the control law of solar sail attitude angles. Numerical simulations show that the hybrid propulsion approach can save about 57% of fuel consumption per year compared with the SEP method. The hybrid propulsion approach achieves the goal of improving the lifetime of spacecraft and meets the requirements of the displaced geostationary orbits. [ABSTRACT FROM AUTHOR]

The minimum-fuel, multi-pulse and time-fixed rendezvous problem is investigated, and a population entropy based particle swarm optimization (EPSO) algorithm is proposed to optimize the rendezvous trajectory. The relative motion of two spacecrafts between two near circular orbits is described by the linearized C-W equations, and taking the minimum energy as a control object, the optimal transfer trajectory based on continuous impulse is got to determine the pulse point location. For the engineering practicability, a multi-pulse control method is used. The location parameters of the pulse point are used to establish the optimization object function of taking the time interval between two pulse-points as the decision variable, and it is solved using the EPSO algorithm. In EPSO, the population entropy is used to describe the particles' location confusion degree, and the search space is determined by using the previous population entropy, thus reducing the waste of search space, and improving the searching speed and accuracy of convergence. Simulation results demonstrate the algorithm has better optimization performance, and it is suitable for the spacecraft trajectory optimization. [ABSTRACT FROM AUTHOR]

To realize the trajectory optimization of the lunar module in ascent stage, the dynamical model of the lunar module was established and nondimensionalized to construct the optimal control-oriented model. Based on Pontryagin's minimal principle and taking the fuel consumption as the optimizing index, the optimal problem was converted into a time free two>point boundary value problem(TPBVP). Using one of initial value hypothesizing methods, combined with the forward sweep algorithm, the TPBVP was solved and the optimized trajectory was obtained. Numerical simulation was conducted. The simulation results justify the rapid convergence rate and high reliability of the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at planning the vehicle's entry trajectory for Mars Pin-Point Landing, a new method based on hp-Radau pseudospectral algorithm is proposed. The vehicle's dynamics, state constraints during Mars Entry phase and vehicle' s mobility and safety constraints are taken into consideration synthetically. By combining the properties of collocation points of hp-Radau pseudospectral algorithm, the problem of trajectory optimization can be converted into a large-scale parameters optimization problem with multi-constraints, thus a solving framework of trajectory optimization is obtained. Also, the analytical form of Jacbian matrix of performance index and constraint equations is derived in order to improve the method's efficiency. The simulation result indicates that; (1) the hp-Radau pseudospectral algorithm can be used to solve the trajectory optimization problem during Mars Entry ,and has more efficient performance compared with the radau pseudospectral algorithm; (2) Compared with the numeric difference method, the analytical form of Jacbian matrix could substantially increase the method's efficiency and time-consuming stability by 58.75% and 85.58% respectively. [ABSTRACT FROM AUTHOR]

Trajectory optimization for spacecraft proximity maneuver with vision guidance path constraints is studied in this paper. At the beginning, the model of spacecraft proximity orbit maneuver for elliptic orbit optimization problem with path constraints is built. After that, the optimal problem is transformed into a Nonlinear Programming problem (NLP) by using gauss pseudospectral method. The state variables and control variables are selected as optimization parameters at all collocation nodes. Then, the resulting NLP is solved by using MATLAB software package SNOPT. Finally, simulation results verify that the proposed method is valid and robust. [ABSTRACT FROM AUTHOR]

The global optimal 4-D trajectory (t, x, y, z) for a spacecraft controlled by low thrust and launched from the Earth to fly around the Sun is proposed in this paper. To optimize the 4-D trajectory of the spacecraft, a set of numerical algorithm, including a searching algorithm and a 4-D trajectory optimization algorithm is presented. The searching algorithm is used for finding as many as possible asteroids near the 4-D trajectory of the Earth chosen from all the 248997 asteroids in the whole Sun system. The performance index of optimal trajectory is to maximize the number of asteroids met with the spacecraft and the rendezvous times with them, and also maximize the final mass. The 4-D trajectory optimization algorithm is composed of improved dynamic programming algorithm, conjugate gradient algorithms based on optimal control theory and static parameter optimization algorithm. Based on a great deal of numerical flight simulation by using this combined algorithm, the 4-D optimal trajectory of the spacecraft is obtained, the spacecraft passes by 12 asteroids among the 248997 asteroids in the whole Sun system within one year. [ABSTRACT FROM AUTHOR]

A high efficient hybrid algorithm based on support vector machine (SVM) and genetic algorithm (GA) is proposed for near space vehicle trajectory optimization with multiple constraints. The mathematical model for trajectory optimization is derived and the trajectory optimization problem is converted into a parameter optimization problem through parameterization and penalty function approach. The parameter optimization problem is solved by a hybrid trajectory optimization algorithm, in which SVM is used to classify chromosomes generated during GA operation in order to eliminate unfitted chromosomes and accelerate optimization speed An example used for downrange optimization in the proposed algorithm is presented, and simulation results show that the proposed approach is more efficient than the approach based on basic GA. [ABSTRACT FROM AUTHOR]