Dual Quaternion-Based Powered Descent Guidance with State-Triggered Constraints

What is it about?

This paper presents a numerical algorithm for computing 6-degree-of-freedom free-final-time powered descent guidance trajectories. The trajectory generation problem is formulated using a unit dual quaternion representation of the rigid body dynamics, and several standard path constraints. We introduce a special line of sight constraint that is enforced only within a specified band of slant ranges relative to the landing site, a novel feature that is especially relevant to Terrain and Hazard Relative Navigation. We use state-triggered constraints to formulate these range constraints in a manner that is amenable to real-time implementations. The resulting (non-convex) optimal control problem is solved iteratively as a sequence of convex second-order cone programs that locally approximate the non-convex problem. Key aspects of a real-time implementation are discussed, including the use of a customizable solver and scaling techniques. To demonstrate the capabilities of our algorithm, two numerical case studies are presented. The first studies the effect of including a slant-range-triggered line of sight constraint on powered descent trajectories. The second study performs a Monte Carlo analysis to assess the algorithm's robustness to initial conditions and real-time performance.

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