Onboard Dual Quaternion Guidance for Rocket Landing

Abstract: The dual quaternion guidance (DQG) algorithm was selected as the candidate 6-DoF powered-descent guidance algorithm for NASA's Safe and Precise Landing -- Integrated Capabilities Evolution (SPLICE) project. DQG is capable of handling state-triggered constraints that are of utmost importance in terms of enabling technologies such as terrain relative navigation. In this work, we develop a custom solver for DQG to enable onboard implementation for future rocket landing missions. We describe the design and implementation of a real-time-capable optimization framework, called sequential conic optimization (SeCO), that blends together sequential convex programming and first-order conic optimization to solve difficult nonconvex trajectory optimization problems, such as DQG, in real-time. A key feature of SeCO is that it leverages a first-order primal-dual conic optimization solver, based on the proportional-integral projected gradient method (PIPG). We describe the implementation of this solver, develop customizable first-order methods, and leverage convergence-accelerating strategies such as warm-starting and extrapolation, to solve the nonconvex DQG optimal control problem in real-time. Finally, in preparation for an upcoming closed-loop flight test campaign, we test our custom solver onboard the NASA SPLICE Descent and Landing Computer in a hardware-in-the-loop setting. We observe that our algorithm is significantly faster than previously reported solve-times using the flight-tested interior point method-based subproblem solver, BSOCP. Furthermore, our custom solver meets (and exceeds) NASA's autonomous precision rocket-landing guidance update-rate requirements for the first time, thus demonstrating the viability of SeCO for real-time, mission-critical applications onboard computationally-constrained flight hardware.