Constrained Differential Dynamic Programming Revisited

Authors: Yuichiro Aoyama, George Boutselis, Akash Patel, Evangelos A. Theodorou

Published: 2020 (Conference Paper)

Source: IEEE International Conference on Robotics and Automation (ICRA)

Algorithm: AL-DDP

arXiv: 2005.00985

DOI: 10.1109/ICRA48506.2021.9561530

Summary

Revisits constrained DDP with augmented Lagrangian methods, improving constraint handling within the DDP backward-forward pass framework. Contemporary with ALTRO, but from a different group with a different perspective on convergence.

Abstract

Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls, however, a widely successful constrained version of the algorithm has yet to be developed. This paper builds upon penalty methods and active-set approaches towards designing a Dynamic Programming-based methodology for constrained optimal control. Regarding the former, our derivation employs a constrained version of Bellman's principle of optimality, by introducing a set of auxiliary slack variables in the backward pass. In parallel, we show how Augmented Lagrangian methods can be naturally incorporated within DDP, by utilizing a particular set of penalty-Lagrangian functions that preserve second-order differentiability. We demonstrate experimentally that our extensions (individually and combinations thereof) enhance significantly the convergence properties of the algorithm, and outperform previous approaches on a large number of simulated scenarios.

Links

Primary

Paper arxiv.org

Standard

arXiv Abstract 2005.00985 arXiv PDF 2005.00985 arXiv HTML 2005.00985 DOI 10.1109/ICRA48506.2021.9561530

Alternate

ieeexplore.ieee.org ieeexplore.ieee.org

Tags

• Differential dynamic programming

• Constrained optimization

• Augmented Lagrangian

• Trajectory optimization