Successive Convexification for Real-Time Six-Degree-of-Freedom Powered Descent Guidance with State-Triggered Constraints

Abstract

This paper presents a real-time implementable successive convexification algorithm for a generalized free-final-time six-degree-of-freedom powered descent guidance problem. Building on our previous research, the following contributions are introduced: 1) a free-ignition-time modification that allows the algorithm to determine the optimal engine ignition time, 2) a tractable formulation of nonlinear aerodynamic lift and drag, and 3) a continuous state-triggered constraint formulation that emulates conditionally enforced constraints. In particular, contribution 3 effectively allows constraints to be enabled or disabled by if statements conditioned on the solution variables of the parent continuous optimization problem. To the best of our knowledge, this represents a novel formulation in the optimal control literature and enables a number of interesting applications in powered descent guidance, such as velocity-triggered angle-of-attack constraints. Our algorithm converts the resulting generalized powered descent guidance problem from a nonconvex free-final-time optimal control problem into a sequence of convex second-order cone programming subproblems. With the aid of virtual control and trust region modifications, these subproblems are solved iteratively until convergence is attained. Simulations demonstrate the real-time capabilities of the proposed algorithm, with a maximum solver runtime of less than 0.7 s over a multitude of problem feature combinations on a 2.2 GHz Intel processor.

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