Constrained Differential Dynamic Programming: A primal-dual augmented Lagrangian approach

Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, different...

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Bibliographic Details
Published in:Proceedings of the ... IEEE/RSJ International Conference on Intelligent Robots and Systems pp. 13371 - 13378
Main Authors: Jallet, Wilson, Bambade, Antoine, Mansard, Nicolas, Carpentier, Justin
Format: Conference Proceeding
Language:English
Published: IEEE 23.10.2022
Subjects:
Dynamic programming
Globalization
Heuristic algorithms
Minimization
Optimal control
Robustness
Switches
ISSN:2153-0866
Online Access:Get full text
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Summary:Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, differential dynamic programming (DDP) provides an efficient approach to transcribe the optimal control problem into a finite-dimensional problem while optimally exploiting the sparsity induced by time. On the other hand, augmented Lagrangian methods make it possible to formulate efficient algorithms with advanced constraint-satisfaction strategies. In this paper, we propose to combine these two approaches into an efficient optimal control algorithm accepting both equality and inequality constraints. Based on the augmented Lagrangian literature, we first derive a generic primal-dual augmented Lagrangian strategy for nonlinear problems with equality and inequality constraints. We then apply it to the dynamic programming principle to solve the value-greedy optimization problems inherent to the backward pass of DDP, which we combine with a dedicated globalization strategy, resulting in a Newton-like algorithm for solving constrained trajectory optimization problems. Contrary to previous attempts of formu-lating an augmented Lagrangian version of DDP, our approach exhibits adequate convergence properties without any switch in strategies. We empirically demonstrate its interest with several case-studies from the robotics literature.
ISSN:2153-0866
DOI:10.1109/IROS47612.2022.9981586