Skip to content

A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

Authors: Markus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli, Moritz Diehl

Published: 2017 (Conference Paper)

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

Algorithm: iLQR-GNMS

arXiv: 1711.11006

DOI: 10.1109/IROS.2018.8593840

Summary

Presents a unified family of iterative Gauss-Newton multiple-shooting methods for nonlinear optimal control, covering single and multiple shooting variants within a common framework with analysis of convergence and computational tradeoffs.

Abstract

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.

Primary

Paper arxiv.org

Standard

arXiv Abstract 1711.11006 arXiv PDF 1711.11006 arXiv HTML 1711.11006 DOI 10.1109/IROS.2018.8593840

Alternate

ieeexplore.ieee.org ieeexplore.ieee.org

Tags

  • Trajectory optimization

  • Multiple shooting

  • Gauss-Newton methods

  • Nonlinear optimal control

  • Iterative linear quadratic regulator

  • iLQR