Customized Real-Time First-Order Methods for Onboard Dual Quaternion-based 6-Dof Powered-Descent Guidance

The dual quaternion-based 6-DoF powered-descent guidance algorithm (DQG) was selected as the candidate 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 the utmost importance in terms of enabling technologies such as terrain relative navigation (TRN). 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. This framework is entirely devoid of matrix factorizations/inversions, making it suitable for safety-critical applications. Under the hood, the SeCO framework leverages a first-order primal-dual conic optimization solver, based on the proportional-integral projected gradient method (PIPG), that combines the ideas of projected gradient descent and proportional-integral feedback of constraint violation. Unlike other conic optimization solvers, PIPG effectively exploits the sparsity and geometric structure of the constraints, avoids expensive equation solving, and is suitable for both real-time and large-scale applications. We describe the implementation of this solver, and develop customizable first-order methods, including an analytical preconditioning algorithm, to solve the nonconvex DQG optimal control problem in real-time. Strategies such as warm-starting and extrapolation are leveraged to further accelerate convergence. We show that the DQG-customized solver is able to solve the problem significantly faster than other state-of-the-art convex optimization solvers, and thus demonstrate the viability of SeCO for real-time, mission-critical applications onboard computationally constrained flight hardware.