Squash-Box Feasibility Driven Differential Dynamic Programming

Josep Marti-Saumell, Joan Solà, Carlos Mastalli, Angel Santamaria-Navarro

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.
Original languageEnglish
Title of host publication2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages7637 - 7644
Number of pages8
ISBN (Electronic)978-1-7281-6212-6
ISBN (Print)978-1-7281-6213-3
Publication statusPublished - 10 Feb 2021
Event2020 IEEE/RSJ International Conference on Intelligent Robots and Systems - Las Vegas, United States
Duration: 25 Oct 202029 Oct 2020

Publication series

ISSN (Print)2153-0858
ISSN (Electronic)2153-0866


Conference2020 IEEE/RSJ International Conference on Intelligent Robots and Systems
Abbreviated titleIROS 2020
CountryUnited States
CityLas Vegas
Internet address

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