基于bang-bang控制平滑正则化的动力制动轨迹优化

Trajectory optimization via smooth regularization of bang-bang control for power braking

针对行星定点软着陆实时在线制导的任务需求,结合行星着陆轨迹优化技术在动力学特征、约束条件、不确定环境方面的特点,以燃料最优为性能指标,提出了一种平滑正则化处理不连续切换点的方法。而以燃料最优为性能指标的着陆问题,其推力或推力加速度大小为最多切换两次的bang-bang控制,用间接法将其转化为一个两点边值问题会带来对初值敏感、算法复杂度高且依赖于导数的数值算法无法求解的问题。为此,对比了以末端高度为性能指标的气动制动和以燃料最优为性能指标的动力制动,对动力制动中的推力bang-bang控制问题,通过对切换函数的分析将其控制形式分解为3种情形,进而引入偏差参数,对bang-bang控制的不连续切换点进行平滑处理,使其转化为可以直接用数值算法求解的连续可导函数,并通过数值仿真验证了该方法的可靠性、快速性和精确性。结果表明:相较于直接法中的伪谱法,该方法对初始值不敏感,降低了算法复杂度,收敛性好且终端误差较小,解决了模型对初始值敏感、数值算法无法直接求解bang-bang控制的难题。

For the task requirements of real-time online guidance for planetary pinpoint soft landing,combined with the characteristics of the planetary landing trajectory optimization technology in terms of dynamic features,constraints,and uncertain environments,a smooth regularization method to deal with discontinuous switching points of bang-bang control was proposed,with optimal fuel as the performance index.For the landing problem with optimal fuel as the performance index,the thrust or thrust acceleration is bang-bang control that switches twice at most.Using the indirect method to convert it into a two-point boundary value problem will bring disadvantages of sensitivity to the initial guess,the high complexity of the algorithm,and the inability to be solved by numerical algorithms that rely on derivatives.Therefore,A comparison was made between aerodynamic braking with the terminal height as the performance index and power braking with the optimal fuel as the performance index.For the thrust bang-bang control problem in power braking,the control form was divided into three cases by analyzing the switching function.The switching point of the discontinuous bang-bang control was then smoothed by introducing a bias parameter,resulting in a continuously differentiable function that can be directly solved by numerical algorithms.Numerical simulations verified the reliability,speed and accuracy of the proposed method.The results of the study show that compared with the pseudo spectral method,the proposed method is less sensitive to the initial guess and reduces the complexity of the algorithm,converges faster and has smaller terminal errors.So,the method can solve the problem that the model is sensitive to the initial value and the numerical value cannot be directly solved for control.