{"title":"Constrained Trajectory Optimization on Matrix Lie Groups via Lie-Algebraic Differential Dynamic Programming","authors":"Gokhan Alcan , Fares J. Abu-Dakka , Ville Kyrki","doi":"10.1016/j.sysconle.2025.106220","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106220"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125002026","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.