基于能态近似法的再入轨迹优化设计

Design of Reentry Trajectory Optimization Based on Energy-State Approximation Method

针对间接法中,终端积分时间在迭代前后无法相同这一问题,介绍了能态近似法在再入飞行器三维轨迹最优化问题中的应用。首先给出了再入飞行器轨迹最优化控制问题模型,其中运动方程为三自由度模型,性能指标选为飞行器再入过程中所受的总加热量最小,控制变量则为迎角和滚转角。再入飞行过程中受到加热率、过载和动压约束,终端状态约束分别为速度、航迹倾角、高度、经度和纬度约束。文中引入了比能的概念,代替时间变量作为新的积分变量,此时末端能量只由终端速度和终端高度确定,从而解决了积分终止条件的固定问题。应用共轭梯度法和乘子法对带有约束的最优控制问题进行求解。通过仿真,计算机实时生成了一条满足终端约束条件、控制量约束条件的最优化轨迹。仿真结果表明该方法具有一定的实时性,且精度较高。仿真得到的最优轨迹能够满足飞行器自主导航对轨迹实时性的要求,具有较好的工程应用前景。

Aim. In the traditional indirect optimization method, the value of time of integral variable is no longer equal after the iterative calculations. Therefore the iterative calculations can＇t perform any more. We now propose energy-state approximation method to reduce greatly such shortcomings. In the full paper, we explain in detail how to use energy-state approximation method to solve the above-mentioned problem; in this abstract, we just add some pertinent remarks to listing the four topics of explanation： （1） description of the problem of reentry vehicle trajectory optimization; the subtopics are establishment of equations of motion （subtopic 1. 1）, selection of performance index （subtopic 1. 2） and constraint conditions （subtopic 1. 3）; in subtopic 1. 1, angle-of-attack and bank angle are selected to be control variables; in subtopic 1.2, total heat is selected to be minimized; in subtopic 1.3, we explain that, during the flight, reentry vehicle is subjected to heat rate, overload and dynamic pressure constraints and terminal state variable constraints are path inclination angle and altitude; （2） how to use energy-state approximation method; in topic （2）, the time of integral variable is substituted by energy of integral variable, therefore the iterative calculation can perform normally; （3） description of the problem of optimal control; the subtopics are disposal of state variables constraints （subtopic 3.1） and disposal of control variables constraints （subtopic 3.2） ; in subtopic 3. 1, terminal state variables constraints are dealt with the methods of multipliers; （4） how to use the conjugate gradient method. Finally we give a numerical simulation example, in which the state and control variables are selected as optimal parameters. Optimal control problem was solved using the conjugate gradient method which we found to have high convergence. The simulation results, given in Figs. 1 through 5 in the full paper, demonstrate that the energy-state approximation method is not sensitive to reentry initial conditions; they also show that the optimal solutions of trajectory optimization problem are fairly good in real-time. Therefore, the indirect method is a viable approach to the reentry vehicle trajectory optimization problem.