A Hybrid ADMM for Six-Degree-of-Freedom Entry Trajectory Optimization Based on Dual Quaternions

This article investigates the six-degree-of-freedom (6-DoF) entry trajectory optimization problem in a Human-Mars entry, powered descent, and landing mission. During the entry phase, aerodynamic forces are employed to decelerate the vehicle. Instead of being treated as a point mass, both translational and rotational motions of the entry vehicle are considered. Specifically, the 6-DoF rigid body motion of the entry vehicle is modeled using the unit dual quaternion representations to avoid highly nonlinear terms in the flight dynamics expression originally based on the flight-path coordinates. Then, the entry trajectory optimization problem is to minimize the terminal speed subject to dynamical, operational, and mission constraints modeled by the new representation scheme. By applying the discretization technique and polynomial approximation, the entry trajectory optimization problem is reformulated as a nonconvex quadratically constrained quadratic programming problem, which is solved via a hybrid alternating direction method of multipliers (ADMM). The accuracy of the dual-quaternion-based model and the computational efficiency of the hybrid ADMM are validated via numerical simulations.