An Iterative LQR Method for Addressing Model Uncertainty in the Mars Entry Problem

Abstract

Since the moon landing in 1969 sounded the proverbial shotgun inciting efforts to expand the frontiers of space exploration, there has been unparalleled effort to enhance the technologies for doing so. While human presence in Earth orbit has boomed over the past decade, crewed planetary missions have yet to reach desired goals. Set by NASA as the future destinations beyond Earth orbit, Mars presents significant challenges to the entry, landing and descent sequence. Missions including sample return and human exploration require precise landing accuracy. Additionally, entry vehicle dynamics and atmospheric parameters at time of flight are hard to predict. This along with the advancement of mission objectives invoke the need for a reliable, robust, and computationally reasonable method with certifiable guarantees of safe landing.

Therefore, this paper presents a closed-loop trajectory optimizer capable of incorporating the atmospheric models and navigational data uncertainty for the nonlinear dynamics of hypersonic entry by applying an iterative Linear-Quadradic-Regulator (iLQR). iLQR is an efficient and powerful method for trajectory optimization derived from Differential Dynamic Programming (DDP) principles, which have been applied successfully in cases of robotic movement to locally improve upon a single trajectory through second-order convergence for a local optimal trajectory. iLQR takes this method a step further by iteratively linearizing the system dynamics, converging to determine an optimal trajectory by minimizing the performance cost and the uncertainty in the dynamics model.

To demonstrate its effectiveness, the algorithm will be tested against a series of realistic simulations to test the model performance against mission requirements, such as high altitude and precision landing. Results show an efficient data-driven algorithm capable of learning how to successfully control a 40 ton crewed-scale spacecraft for Mars entry under dynamical uncertainties in the state model. Additionally, given system performance parameters, the covariance, or landing accuracy, of the final position can be determined from the algorithm and the results can be used to determine safe parameter ranges that achieve the desired accuracy