Before revision:  However, these methodsare not fast enough for many robotics applications such as real-time humanoid motor control . Exploiting the sparse structure of optimal control problem , such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints.
After revision:  However, it suffers from numerical instability and, when compared to direct methods, it has limited initialization options (allows initialization of controls, but not of states) and lacks proper handling of control constraints. These limitations are due to the fact that DDP is a single shooting algorithm. In this work, we tackle these issues with a direct-indirect hybridization approach that is primarily driven by the dynamic feasibility of the optimal control problem , such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints.