  For optimal control problems that involve planning and following a
trajectory, two degree of freedom (2DOF) controllers are a ubiquitously used
control architecture that decomposes the problem into a trajectory generation
layer and a feedback control layer. However, despite the broad use and
practical success of this layered control architecture, it remains a design
choice that must be imposed $a\ priori$ on the control policy. To address this
gap, this paper seeks to initiate a principled study of the design of layered
control architectures, with an initial focus on the 2DOF controller. We show
that applying the Alternating Direction Method of Multipliers (ADMM) algorithm
to solve a strategically rewritten optimal control problem results in solutions
that are naturally layered, and composed of a trajectory generation layer and a
feedback control layer. Furthermore, these layers are coupled via Lagrange
multipliers that ensure dynamic feasibility of the planned trajectory. We
instantiate this framework in the context of deterministic and stochastic
linear optimal control problems, and show how our approach automatically yields
a feedforward/feedback-based control policy that exactly solves the original
problem. We then show that the simplicity of the resulting controller structure
suggests natural heuristic algorithms for approximately solving nonlinear
optimal control problems. We empirically demonstrate improved performance of
these layered nonlinear optimal controllers as compared to iLQR, and highlight
their flexibility by incorporating both convex and nonconvex constraints.
