基于Lie-代数微分动态规划的矩阵李群约束轨迹优化

IF 2.5 3区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS
Gokhan Alcan , Fares J. Abu-Dakka , Ville Kyrki
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引用次数: 0

摘要

矩阵李群是一类重要的流形,常用于控制和机器人领域,在这些流形上优化控制策略是一个基本问题。在这项工作中,我们提出了一种新的基于增广拉格朗日的约束微分动态规划(DDP)方法,专门用于矩阵李群上的轨迹优化。该方法在误差状态空间中构造优化问题,在逆向传递过程中采用自动微分,在正向传递过程中通过离散时间李群积分保证流形一致性。与以往仅限于特定流形类的方法不同,我们的方法鲁棒地处理了任意矩阵李群的一般非线性约束,并在训练过程中表现出对约束违反的弹性。我们通过大量的实验来评估提出的DDP算法,证明了它在SE(3)上管理刚体机械系统约束方面的有效性,与现有优化求解器相比,它的计算优势,在外部干扰下作为lie -代数反馈控制器的鲁棒性,以及在轨迹优化任务中的有效性,包括现实四旋翼场景作为欠驱动系统和变形物体,其变形动力学在SL(2)中表示。实验结果验证了该方法的通用性、稳定性和计算效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Constrained Trajectory Optimization on Matrix Lie Groups via Lie-Algebraic Differential Dynamic Programming

Constrained Trajectory Optimization on Matrix Lie Groups via Lie-Algebraic Differential Dynamic Programming
Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel augmented Lagrangian-based constrained Differential Dynamic Programming (DDP) approach specifically designed for trajectory optimization on matrix Lie groups. Our method formulates the optimization problem in the error-state space, employs automatic differentiation during the backward pass, and ensures manifold consistency through discrete-time Lie-group integration during the forward pass. Unlike previous methods limited to specific manifold classes, our approach robustly handles generic nonlinear constraints across arbitrary matrix Lie groups and exhibits resilience to constraint violations during training. We evaluate the proposed DDP algorithm through extensive experiments, demonstrating its efficacy in managing constraints within a rigid-body mechanical system on SE(3), its computational superiority compared to existing optimization solvers, robustness under external disturbances as a Lie-algebraic feedback controller, and effectiveness in trajectory optimization tasks including realistic quadrotor scenarios as underactuated systems and deformable objects whose deformation dynamics are represented in SL(2). The experimental results validate the generality, stability, and computational efficiency of our proposed method.
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来源期刊
Systems & Control Letters
Systems & Control Letters 工程技术-运筹学与管理科学
CiteScore
4.60
自引率
3.80%
发文量
144
审稿时长
6 months
期刊介绍: Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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