This study presents a comprehensive and standardized foundation for the mathematical modeling and control of flying-base-mounted manipulators, addressing several critical challenges in aerial robotics. The primary contributions of this study include: (1) the development of a unified framework for computing the system's generalized forces, incorporating both active motor inputs and passive constraint forces; (2) a trajectory planning method for the flying base that simultaneously accounts for both desired position and orientation; (3) an automatic and recursive methodology for deriving the system's equations of motion, ensuring that increasing the number of links in the manipulator or flying base does not introduce limitations; and (4) a motor configuration strategy that enables the flying base to achieve unrestricted motion in three-dimensional space. To address these challenges, the proposed approach systematically decomposes the robot structure—consisting of the flying base and the mounted manipulator—into a set of substructures. Each substructure, modeled as an open kinematic chain with a moving base, is analyzed using the recursive Gibbs-Appell algorithm to derive its equations of motion. These individual equations are then integrated to obtain the coupled dynamics of the complete system, capturing the mutual interactions between the flying base and the manipulator. Finally, a feedback linearization-based controller is designed to enable simultaneous trajectory tracking of both the flying base and the manipulator's end-effector. Simulation results validate the effectiveness of the proposed control strategy, demonstrating its ability to achieve precise positioning and accurate orientation tracking of the entire robotic system.
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2025 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.
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