Successive Convexification for 6-DoF Powered Descent Guidance with Compound State-Triggered Constraints

Abstract

This paper introduces a continuous formulation for compound state-triggered constraints, which are generalizations of the recently introduced state-triggered constraints. Statetriggered constraints are different from ordinary constraints found in optimal control in that they use a state-dependent trigger condition to enable or disable a constraint condition, and can be expressed as continuous functions that are readily handled by successive convexification. Compound state-triggered constraints go a step further, giving designers the ability to compose trigger and constraint conditions using Boolean and and or operations. Simulations of the 6-degree-of-freedom (DoF) powered descent guidance problem obtained using successive convexification are presented to illustrate the utility of state-triggered and compound state-triggered constraints. The examples employ a velocity-triggered angle of attack constraint to alleviate aerodynamic loads, and a collision avoidance constraint to avoid large geological formations. In particular, the velocity-triggered angle of attack constraint demonstrates the ability of state-triggered constraints to introduce new constraint phases to the solution without resorting to combinatorial techniques.

Fast Trajectory Optimization via Successive Convexification for Spacecraft Rendezvous with Integer Constraints

“…An alternative approach to incorporating (20) is to use continuous variables to formulate a logically equivalent constraint. Recent work [13,14] has shown the following equivalence to hold. Proof.…”

“…Moreover, we demonstrate the use of continuous optimization techniques (no integer variables) that can be solved fast enough to facilitate rapid trade studies and trajectory design. By using the newly introduced state-triggered constraints [13,14], we show how to model the MIB constraint within a continuous optimization problem, effectively solving the problem identified (but not solved) in [6]. Moreover, plume impingement constraints that restrict the directions in which thrusters may be fired are enforced.…”

“…Although the duration t f is fixed, an optimal value of t f can be searched for via a line search method. A free-final time formulation can also be used, which has been studied in previous work on successive convexification [13,14]. We use a cost which minimizes the cumulative thruster firing time and is a proxy for total fuel usage [18, Section 4.3.4.1.2]:…”

“…Definition 1. The successive approximation (22) locks when g(z(t)) < 0 implies g(z(t)) < 0. In this situation, c(z(t)) ≤ 0 will always hold at time t for all subsequent iterations of successive convexification.…”

“…Like most non-linear optimization routines, the algorithm requires an initial trajectory guess. However, successive convexification is known to be very flexible in the quality of the initial guess that it is given [13,14,34]. As a result, we propose a constant-velocity linearly interpolated initial trajectory between the initial and final states:…”