Lagrange-Poincaré-Kepler Equations of Disturbed Space-Manipulator Systems in Orbit

2025-10-16

AI Summary

Modeling spacecraft–manipulator systems in non-inertial orbital reference frames remains challenging due to strong couplings among spacecraft attitude, orbital motion, and manipulator deformation dynamics. Method: This paper proposes the Lagrange–Poincaré–Kepler (LPK) framework—a novel geometric formulation that integrates Keplerian orbital dynamics and exponential joint parameterization into the Lagrange–Poincaré theory. Built upon the Lagrange–d’Alembert principle on principal bundles, it yields closed-form structural matrices explicitly incorporating orbital perturbations and external symmetry-breaking torques. Contribution/Results: The LPK framework ensures both geometric rigor and computational tractability, enabling hardware-in-the-loop simulation and autonomous control integration. Validation via a 7-DOF manipulator demonstrates significantly improved dynamical fidelity and numerical efficiency under orbital conditions compared with conventional approaches—providing a high-fidelity, computationally efficient dynamical foundation for on-orbit autonomous operations.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This article presents an extension of the Lagrange-Poincare Equations (LPE) to model the dynamics of spacecraft-manipulator systems operating within a non-inertial orbital reference frame. Building upon prior formulations of LPE for vehicle-manipulator systems, the proposed framework, termed the Lagrange-Poincare-Kepler Equations (LPKE), incorporates the coupling between spacecraft attitude dynamics, orbital motion, and manipulator kinematics. The formalism combines the Euler-Poincare equations for the base spacecraft, Keplerian orbital dynamics for the reference frame, and reduced Euler-Lagrange equations for the manipulator's shape space, using an exponential joint parametrization. Leveraging the Lagrange-d'Alembert principle on principal bundles, we derive novel closed-form structural matrices that explicitly capture the effects of orbital disturbances and their dynamic coupling with the manipulator system. The LPKE framework also systematically includes externally applied, symmetry-breaking wrenches, allowing for immediate integration into hardware-in-the-loop simulations and model-based control architectures for autonomous robotic operations in the orbital environment. To illustrate the effectiveness of the proposed model and its numerical superiority, we present a simulation study analyzing orbital effects on a 7-degree-of-freedom manipulator mounted on a spacecraft.

Problem

• Extending Lagrange-Poincaré equations for spacecraft-manipulator systems in orbit
• Modeling coupling between spacecraft attitude, orbital motion, and manipulator kinematics
• Capturing orbital disturbances and their dynamic coupling with manipulator systems

Innovation

• Extended Lagrange-Poincare Equations for orbital systems
• Combined spacecraft attitude, orbital motion, and manipulator kinematics
• Derived closed-form structural matrices capturing orbital disturbances