Constrained RLV guidance via pseudospectral model predictive convex programming and predefined-height sliding mode approach

Online trajectory generation and tracking for the Terminal Area Energy Management (TAEM) phase of a Reusable Launch Vehicle (RLV) is one of the core technologies for achieving a soft landing. The processing of complex non-convex path constraints significantly reduces the real-time performance of guidance methods. In addition, the terminal full-element state constraints are difficult to satisfy due to the coupling of longitudinal and lateral motion of RLV. To address these issues, a high-precision constrained guidance method for RLV is proposed in this paper. The analytical sensitivity relationships among the terminal states, non-convex path constraints, and control profile are rapidly constructed via multi-interval pseudospectral discretization. The repeated recursive calculation of sensitivity matrix is avoided by linearizing the non-convex constraints at state output points and expanding the sensitivity matrix sequentially, which reduces the time consumption of constraint processing. Furthermore, a model-based prediction-correction process is introduced to eliminate deviation iteratively and constraints are handled using homotopy to improve convergence. Meanwhile, a robust parallel guidance method is presented to overcome numerical instability issues. The guidance commands obtained by trajectory online generation are prioritized executed, while the tracking commands are calculated in parallel to enhance the guidance feasibility. Instead of tracking a fixed reference trajectory, a predefined height-convergent sliding mode surface is designed and tracked online, which can guarantee that the RLV states converge to the desired values at a preset height, even under various uncertainties. Finally, Monte Carlo simulations are conducted to demonstrate the effectiveness and robustness of the proposed method.