Before revision: Optimal control is a widely used tool for synthesizing motions and controls for user-defined tasks under physical constraints. A common approach is to formulate it using direct multiple-shooting and then to use off-the-shelf nonlinear programming solvers that can easily handle arbitrary constraints on the controls and states .
After revision: Differential Dynamic Programming (DDP) is an indirect method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit roll-out/integration of the system dynamics .