Discrete-Time Differential Dynamic Programming on Lie Groups: Derivation, Convergence Analysis, and Numerical Results

• 成果类型: Article
• 署名作者: Boutselis, George, I; Theodorou, Evangelos
• 署名单位: University System of Georgia; Georgia Institute of Technology; General Electric
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3034206
• 发表日期: 2021
• 页码: 4636-4651
• 关键词: Discrete optimal control; dynamic programming; geometric control; Lie groups

摘要

We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our article generalizes the original differential dynamic programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A key element lies, specifically, in the use of quadratic expansion schemes for cost functions and dynamics defined on Lie groups. The obtained algorithm iteratively optimizes local approximations of the control problem, until reaching a (sub)optimal solution. On the theoretical side, we also study the conditions under which convergence is attained. Details about the behavior and implementation of our method are provided through a simulated example on TSO(3)(.)