翼伞系统最优归航轨迹设计的敏感度分析方法

Optimal homing trajectory design for parafoil systems using sensitivity analysis approach

本文对三自由度翼伞系统归航轨迹优化问题进行了研究,采用控制变量参数化与时间尺度变换相结合的优化算法对翼伞系统的最优控制问题进行数值求解.该方法是基于灵敏度分析的优化算法,将控制量以及控制量转换时间转化为一系列参数优化问题同时进行求解.仿真结果表明,相对于基于两端边值优化算法而言,灵敏度分析法只需要正向积分进行求解,因而具有计算简单、耗时短等优点,其控制效果良好,距离偏差和方向偏差均满足实际需求,有效地提高了翼伞系统的着陆精度,验证了该优化算法的可行性.

We investigate the control problem with three degrees-of-freedom（3DOF） for the parafoil system in the optimal homing trajectory design. The control parameterization and time-scaling techniques are employed to generate numerical solutions. The method is based on an optimization algorithm of sensitivity analysis in which control variables and their transform time are converted to an optimization problem of a series of parameters for simultaneous solving.Simulation results demonstrate the effectiveness of our computational optimal control algorithm. Instead of solving the two-point boundary value problem（TBVP） from the Pontryagin maximum principle（PMP）, we propose a method that requires only the integration of the state ODE and the sensitivity system with known initial conditions for all the equations,making the computational cost much less than that in solving the TBVP. Although the dimension of the sensitivity system is higher than that of the adjoint equation of the TBVP, it still can reduce the computational cost significantly. This method can effectively improve the accuracy in landing a parafoil system and reduce the control energy consumption, showing the feasibility of the proposed optimization algorithm.