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

## TL;DR

This paper introduces a real-time capable numerical algorithm for 6-DOF powered descent guidance using dual quaternions, incorporating novel state-triggered range constraints for terrain navigation, and demonstrates its effectiveness through numerical case studies.

## Contribution

It develops a new trajectory optimization method using dual quaternions and state-triggered constraints, enabling real-time, constrained descent guidance for landing scenarios.

## Key findings

- The algorithm successfully incorporates line of sight constraints within specified slant ranges.
- It demonstrates robustness to initial conditions in Monte Carlo simulations.
- The method achieves real-time performance with iterative convex optimization.

## Abstract

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. Our formulation also includes a special line of sight constraints 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 the newly introduced 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. Each second-order cone program is solved using a customizable interior point method solver. Also introduced are a scaling method and a new heuristic technique that guide the convergence process towards dynamic feasibility. 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 the resulting trajectories. The second study performs a Monte Carlo analysis to assess the algorithm's robustness to initial conditions and real-time performance.