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This paper introduces a framework by which the nonlinear trajectory optimization problem is posed as a path-planning problem in a space liberated of dynamics. In this space, general state constraints for continuous and impulsive control problems are encoded as linear constraints on the native overparameterized variables. This framework is enabled by nonlinear expansion in the vicinity of a reference in terms of fundamental solutions and a minimal nonlinear basis of mixed monomials in problem initial conditions. The former can be computed using state transition tensors, differential algebra, or analytic approaches, and the latter is computed analytically. Nonlinear guidance schemes are proposed taking advantage of this framework, including a successive convex programming scheme for delta-V minimizing trajectory optimization. This work enables a stable, easy to implement, and highly rapid nonlinear guidance implementation without the need for collocation or real-time integration., Comment: 34 pages, 16 figures

A robust drift-safe rendezvous trajectory optimization tool is developed in this work, with applications to orbital rendezvous and proximity operations. The method is based on direct collocation and utilizes a sequential convex programming framework, and is extended from previous work to include passive safety constraints. The tool is then paired with a dispersion analysis framework to allow trajectories to be optimized subject to plant, navigation, and actuator uncertainties. The timing, direction, and magnitude of orbital maneuvers are optimized subject to the expected propellant usage, for a given navigation system performance. Representative trajectories are presented for the LEO flight regime, but the approach can also be applied to GEO and NRHO with minimal modification., Comment: AAS Rocky Mountain Guidance, Navigation and Control Conference, 2023