Managing uncertainty is a fundamental problem in entry guidance. Knowledge of atmospheric density, winds, vehicle attitude, and position are all imperfect -- especially at planetary bodies like mars…

This federal contract award was granted by the National Aeronautics and Space Administration (NASA) to Stanford University, a private research university located in Stanford, California. The $264,284.63 grant is for research focused on improving entry guidance systems for future NASA missions that seek to land larger payloads on planetary bodies like Mars. The research aims to develop a unified framework for modeling, trajectory design, and control that explicitly addresses the challenges of managing uncertainty in factors such as atmospheric density, winds, vehicle attitude, and position. The project will leverage high-fidelity flight dynamics models, rigorous uncertainty quantification, and robust verification methods to enhance the performance, robustness, and safety of entry guidance systems. This award does not have a set-aside designation and was provided to Stanford as the prime contractor, without mention of any subcontractors. The research supports NASA's ongoing efforts to improve the precision and reliability of landing systems for future exploration missions.

Managing uncertainty is a fundamental problem in entry guidance. Knowledge of atmospheric density, winds, vehicle attitude, and position are all imperfect -- especially at planetary bodies like mars that have not been as well-characterized as earth. As future NASA missions seek to land larger payloads with vehicles that have lower ballistic coefficients and rely on supersonic retropropulsion, modeling and reasoning about uncertainty will become even more crucial to achieving robust high-precision entry guidance. To meet this challenge, we propose a unified framework for modelling, trajectory design, and control that explicitly deals with uncertainty at every stage in the process to enhance performance and safety. Most entry guidance methods used in practice are based on apollo-heritage bank-angle control. While simple and effective, these methods typically result in position errors of many kilometers. More recent work has focused on onboard trajectory planning with numerical predictor-corrector methods or online convex optimization. These techniques offer improved system performance in the nominal case, but do not provide any guarantees on closed-loop performance under realistic disturbances and uncertainty. That sort of insight is typically only gained through exhaustive monte carlo simulations. We propose a new approach to entry guidance that is fully general and is based on three main pillars: high-fidelity flight dynamics models, rigorous uncertainty quantification, and use of sumof- squares robust verification methods. High-fidelity models that capture the full six-degree-of-freedom flight dynamics of the entry vehicle are essential for achieving high performance and generality. By making no simplifying assumptions, our approach can fully exploit the capabilities of any vehicle configuration. A full dynamics model also enables the second pillar of our approach: rigorous uncertainty quantification. In order to understand how atmospheric density, winds, and state-estimation errors affect the error ellipse for a vehicle, they must all be modeled. Robust verification methods have been developed over the past decade in the robotic motion planning community. They make use of ideas from SUM-of-squares optimization to compute "invariant funnels" -- tubes around reference trajectories that bound the state of the closed-loop system in the presence of disturbances. Funnels can be computed using modern convex optimization tools and enable calculation of error ellipsoids without monte carlo simulations. Integrating funnels with trajectory optimization will allow reference trajectories to be designed that achieve the smallest-possible error ellipsoid, or ensure that worst-case disturbances do not cause the system to violate constraints. By combining robust verification methods with models that accurately capture flight dynamics, uncertainties, and disturbances, we anticipate making significant improvements over current state-of-the-art entry guidance methods in performance, robustness, and safety.