© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e. a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot. This work was partially supported by the EU H2020 project GAUSS(H2020-Galileo-2017-1-776293), project EB-SLAM (DPI2017-89564-P),by the Spanish State Research Agency through the Mar ́ıa de Maeztu Sealof Excellence to IRI (MDM-2016-0656) and by the European Commissionunder the Horizon 2020 project Memory of Motion (MEMMO, projectID: 780684). Part of this research was carried out at the Jet PropulsionLaboratory, California Institute of Technology, under a contract with theNational Aeronautics and Space Administration (NASA, US Peer Reviewed