  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.
