Application of Optimal Control Techniques to the Parafoil Flight of Space Rider

The design of reusable aerospace vehicles is a challenge that the aerospace industry has been pursuing for several years in order to reduce the cost of access to space and the environmental impact also in terms of orbital debris. The Space Rider programme of the European Space Agency (ESA) falls within the framework of such initiatives. Among the greatest challenges for this type of mission is the design of the Guidance, Navigation & Control (GNC) subsystem for the atmospheric re-entry phase. This subsystem is responsible for collecting and processing data from onboard sensors so that the state of the spacecraft can be used to generate a feasible trajectory in compliance with mission requirements. The requirements for this kind of mission are generally expressed in terms of landing accuracy and touchdown velocity with further possible constraints related, for instance, to the presence of no-fly zones. The final descent and landing phase of the Space Rider mission consists of an autonomous flight under parafoil that must guarantee a smooth and precise landing. The GNC subsystem plays a key role in ensuring adequate performance for a safe landing that does not result in damage to the vehicle and allows it to be reused for subsequent launches. This task is quite challenging due to the limited control authority provided by the parafoil and the high sensitivity to environmental conditions. In particular, a medium-large parafoil is characterized by an airspeed of 10-20 m/s, which may be of the same order of magnitude as the windspeed generating high uncertainty in trajectory generation and tracking. In addition, typically, no thrusters are envisaged for flight under parafoil, so the actuation is based exclusively on the asymmetric and symmetric brake deflection used for lateral and vertical control respectively. A further major limitation for trajectory generation is the very slow dynamics of the parafoil in the latero-directional plane, which results in a very low maximum turning speed that for large parafoils can be in the order of 5-10 deg/s. Considering the numerous constraints that characterize parafoil re-entry, one of the most critical stage is what is commonly referred to as the Terminal Guidance (TERGUID) phase. This is the final part of the descent where the vehicle performs the final approach to the designated landing point (LP) trying to counterbalance the unknown effect of the wind. The study presented in this thesis was developed at the AOCS/GNC department of SENER Aeroespacial (Madrid, Spain) and the objective is to design a complete solution for managing the Terminal Guidance phase of a Space Rider type case. This includes a guidance algorithm to generate an optimal solution for the TERGUID trajectory, a path tracking procedure and a guidance logic that allows for a correct implementation within the whole GNC software. For trajectory generation, the approach presented by Yakimenko and Slegers was selected. The authors apply a direct method based on inverse dynamics in the virtual domain to select the optimal trajectory given a specific two-point boundary-value problem (TPBVP). This study proposes several modifications to the aforementioned method to adapt the algorithm to the specific case of Space Rider.