Trajectory optimization via smooth regularization of bang-bang control for power braking
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 per-formance 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 con-vert 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 relia-bility,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 di-rectly solved for control.
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