Terminal Trajectory Planning for the First-Stage Booster of Rocket Recovery by Parafoil System in Complex Obstacle Environments

The accurate recovery of first-stage booster of rocket is one of the most significant research issues in the aerospace field, of which parafoil system is an effective low-cost reliable roadmap. Nevertheless, as a lightweight and underactuated aircraft, the parafoil and first-stage booster combination (PFC) is extremely vulnerable to low-altitude terrain obstacles and wind turbulences, simultaneously undergoes energy consumption limitation. To guarantee flight safety and upwind landing of the PFC at low altitude environments, a terminal trajectory planning method, avoiding low-altitude static terrain obstacles and longitudinal thermal turbulences dynamic obstacles, is proposed in this paper. The method generates initial PFC trajectory by Model Predictive Static Programming (MPSP) algorithm, then obstacles-avoiding terminal PFC trajectory is planned using slack variable and sliding mode control, of which firstly transforms the obstacle-avoiding inequality constraints into equality constraints by slack variables, secondly formulate appropriate sliding mode surface to manipulate the slack variables to satisfy the safe distance between the PFC and the obstacles, thirdly plans the trajectory of safe flight and upwind landing based on MPSP algorithm. Furthermore, the trajectory optimization is done by differential dynamic programming (DDP) for least energy consumption. The numerical simulation results show that the trajectory always maintains safe distance between the PFC and the obstacles, guarantees upwind landing of PFC, and makes the control quantity more continuous and smoother. The hardware-in-the-loop experiments show that the trajectory is continuous and smooth with excellent traceability and comparatively small tracking deviation.