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Squash-Box Feasibility Driven Differential Dynamic Programming

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

Published: 2020 (Conference Paper)

Source: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

Algorithm: Squash-Box FDDP

DOI: 10.1109/IROS45743.2020.9340883

Summary

Presents a homotopy method which progressively penalizes control action constraint violations more aggressively in an outer loop, using FDDP in the inner loop solves. Solution converges to the hard-constrained optimal trajectory. Quadratic barrier keeps decision variables (control actions) near the center of the sigmoid squashing functions, i.e. avoids a kind of "dead gradients" numerical issue.

Abstract

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.

Primary

Paper researchgate.net

Standard

DOI 10.1109/IROS45743.2020.9340883

Alternate

turing.ac.uk turing.ac.uk ieeexplore.ieee.org ieeexplore.ieee.org dl.acm.org dl.acm.org

Tags

  • Differential dynamic programming

  • Constrained optimization

  • Control limits

  • Feasibility

  • Squash-Box

  • Feasibility driven differential dynamic programming

  • FDDP