Constrained Differential Dynamic Programming Revisited
Constrained Differential Dynamic Programming Revisited
复制标题
重温约束微分动态规划
DOI：
10.1109/icra48506.2021.9561530
复制
发表时间：
2020
期刊：
影响因子：
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通讯作者：
Evangelos A. Theodorou
中科院分区：
文献类型：
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作者：
Yuichiro Aoyama;George I. Boutselis;Akash Patel;Evangelos A. Theodorou
微分动态规划(DDP)已成为一种成熟的无约束轨迹优化方法。然而，尽管它在机器人学和控制中有几个应用，但该算法的一个广泛成功的受限版本尚未开发出来。本文在惩罚方法和有效集方法的基础上，设计了一种基于动态规划的约束最优控制方法。对于前者，我们的推导采用了Bellman最优原理的约束版本，在后向传递中引入了一组辅助松弛变量。同时，我们展示了如何通过利用一组保持二阶可微性的惩罚拉格朗日函数，将增广拉格朗日方法自然地结合到DDP中。实验证明，我们的扩展(单独和组合)显著增强了算法的收敛特性，并且在大量模拟场景中的性能优于以前的方法。
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.