This paper presents the formulation and demonstration of a 6 degree-of-freedom (DoF) free-final-time guidance algorithm which solves the canonical powered descent guidance (PDG) problem. This formulation can be quickly solved as a series of second order cone program (SOCP) sub-problems making it tractable for online implementation on real-time systems using Interior Point Method (IPM) solvers. Modified Rodrigues Parameters (MRPs) are employed in this paper, which are a minimal attitude formalism derived from quaternions. This reduces the number of optimization variables and constraints that other formalisms may require. The routine can be initialized with a dynamically inconsistent trajectory as the solution is driven to meet the nonlinear dynamics more closely with each iteration. This formulation also includes typical vehicular control, environmental, and mission geometry constraints such as thrust vector gimbal angle constraints, glide-slope constraints, and attitude constraints.
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