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Introduction
It is difficult and complicated to implement the closed-loop endo-atmospheric guidance of launch vehicles, due to the presences of the aerodynamic forces, engine thrust, earth gravity, winds and flight constraints. So the classical atmospheric ascent guidance is open-loop (Hanson et al., 1995). In such an approach, the nominal trajectory is designed off-line and then tables of attitude commands, shown as a function of time, altitude or velocity, are given. The guidance commands are achieved by the tables during the flight. The open-loop approach cannot handle emergency launching and aborts adaptively and is one cause of costly launch delays. Moreover, the open-loop guidance has poor anti-disturbance ability and low guidance accuracy. A rapid trajectory planning algorithm could overcome all of the above problems of open-loop guidance scheme. The algorithm can give an optimal and feasible trajectory with path constraints and final condition constraints in a short time, according to the initial state conditions of launch vehicles. It could observably shorten the consuming time of designing nominal trajectory and effectively improve the adaptability of designing tasks. Furthermore, if the real-time requirement is met, the algorithm can be applied to on-line trajectory planning and closed-loop guidance, where the initial state is given by the on-board navigation system. The scheme of closed-loop atmospheric guidance can obtain high guidance precision and implement automatic trajectory design of abort or engine-out situations.
In view of numerous potential applications, the rapid atmospheric ascent trajectory planning methods are being widely studied. Calise et al. develop a hybrid analytic/numerical approach (Calise et al., 1998, 2004), which combines the analytical solution of the optimal vacuum flight and numerical collocation for atmospheric portion base on regular perturbation method. The approach is near-optimal and suitable for real-time guidance applications, demonstrated by numerical simulations. Ding et al. propose a Gauss pseudo-spectral method for atmospheric trajectory optimization and fast-reconstruction of suborbital launch vehicles (Ding et al., 2009). The approach is one of the direct methods for optimal control problems, which transforms the optimal ascent problem into a nonlinear programming problem. Simulation results show that the method has high precision and is possible to generate optimal trajectory in 2-10 s. In addition, an on-line trajectory planning and closed-loop guidance approach based on the indirect method are widely...