Six-dimensional atmosphere entry guidance based on dual quaternion

This paper investigates the six-degree-of-freedom (6-DoF) entry guidance problem for the Human Mars exploration mission. For the Human-scale entry, powered descent, and landing mission, it is required to use aerodynamic forces to decelerate the vehicle during the entry phase. Instead of assuming the entry vehicle as a point mass, we consider both the translational and rotational dynamics. Specifically, the 6-DoF rigid body kinematics and dynamics of the entry vehicle are represented by unit dual quaternions, which reduces the non-linearity of dynamic equations comparing with the Euler angle based dynamical model. Moreover, the equivalence between the dual quaternion based and Euler angle based models is analyzed. Then, the optimal entry guidance problem is formulated to minimize the terminal speed subject to the dual quaternion based dynamics, operational and mission constraints, including heating rate and the normal load of the entry vehicle. By using a discretization technique and polynomial approximation, the optimal entry guidance problem is reformulated into a nonconvex quadratically constrained quadratic program (QCQP) problem, which is solved via a customized alternating direction method of multipliers (ADMM). The accuracy of the dual quaternion based model and the computational efficiency of the ADMM algorithm are verified via numerical simulations. © 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All Rights Reserved.