Optimal Covariance Steering on Lie Groups for Precision Powered Descent

that directly controls uncertainty and provides a theoretical guarantee of solution optimality. The current 6-DOF PDG algorithms such as Penalized Trust Region lack both capabilities. First, they are modeled deterministically and rely on extensive Monte Carlo simulation to validate robustness under uncertainty. In contrast, my proposed algorithm will employ the theory of covariance steering to compute a fuel-optimal trajectory while simultaneously exerting closed-loop control over the entire covariance evolution. Second, current 6-DOF PDG algorithms heavily rely on linearization and heuristics to convert non-convex problems into conic problems that can be efficiently solved by classical optimization algorithms. This convexification process is not lossless and can lead to divergent or infeasible solutions. Since rigid-body dynamics represented by dual quaternions live on a Lie group instead of a Euclidean space, our best chance of proving theoretical guarantees is to adopt a generalized convex optimization framework called g-convex optimization. Moreover, the current covariance steering theory is only developed for linear systems; it remains to make the theories of covariance steering and g-convex optimization compatible with each other. Thus, a major effort in the proposed research is to generalize the theory of covariance steering to Lie groups. The generalized theory will guarantee that the proposed algorithm converges to a fuel-optimal solution that is simultaneously robust under uncertainty. My proposed research directly addresses the civil space shortfall "advanced algorithms and computing for precision landing". I believe that we need to boldly go beyond linear methods in order to consistently meet the increasingly stringent human-class precision landing requirements. By exploiting advanced mathematics, my proposed research will deliver robust, theoretically guaranteed precision landing capabilities for the Artemis program and the Moon to Mars Architecture.

This is a mature technology (TRL 7+) — the realistic path in is usually NASA's Technology Transfer Program: licensing an existing NASA patent, or a Space Act Agreement to use NASA facilities/expertise directly. NASA also runs a startup licensing program with no upfront fee for companies formed to commercialize a specific NASA technology.

None of these are guaranteed paths for this specific project — TechPort itself doesn't have an "apply" button. Reaching out to the contact(s) above with a specific question is usually the fastest way to find out what's actually open.