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 引用本文: 王培栋, 王天舒. 基于对偶四元数的多体系统动力学建模和控制. 力学学报, 2024, 56(7): 2091-2102.
Wang Peidong, Wang Tianshu. Dynamic modeling and control of multibody systems using dual quaternions. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 2091-2102.
 Citation: Wang Peidong, Wang Tianshu. Dynamic modeling and control of multibody systems using dual quaternions. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 2091-2102.

DYNAMIC MODELING AND CONTROL OF MULTIBODY SYSTEMS USING DUAL QUATERNIONS

• 摘要: 空间机械臂的在轨作业是当前空间在轨服务中应用最为广泛的技术之一, 然而, 机械臂在操作过程中漂浮基座与臂体之间的位姿耦合效应极为显著, 这给控制系统设计带来了新挑战. 针对多刚体系统的位姿一体化建模与控制问题, 文章改进了基于对偶四元数的位姿一体化建模和控制方法, 使之可以应用于多刚体系统. 该方法不仅能够精确描述复杂的力学关系, 还能够在统一的数学框架中有效地处理位姿耦合问题, 这为后续设计姿轨一体化的控制系统提供了极大的便利. 首先, 基于铰链模型建立了对偶四元数形式的铰链和臂体之间的速度和加速度递推关系, 然后, 利用铰链和臂体间力-力矩传递关系建立了递推形式的逆向动力学方程, 为了便于控制系统设计与分析, 随后推导建立了矩阵形式的位姿一体化的正向动力学方程. 然后针对推进器和控制力矩陀螺讨论了具体的执行机构的动力学建模问题, 并分别讨论了机械臂和漂浮基座的位姿一体化控制问题. 最后, 对一个6自由度机械臂和漂浮基座的组合体进行了动力学建模和控制仿真, 动力学仿真的结果证明了所提动力学建模方法的正确性, 控制仿真表明控制系统能较快地抵消机械臂运动对基座产生的干扰力和干扰力矩, 证明了所提控制方法的有效性和可行性.

Abstract: The operation of space robotic arms in orbit is one of the most extensively applied technologies in current space in-orbit services. However, the significant coupling effect of position and attitude between the floating base and the arm during operations presents new challenges for the design of control systems. To address the integrated modeling and control problems of position and attitude in multi-rigid body systems, this paper improves the dual quaternion-based integrated modeling and control method, making it applicable to multi-rigid body systems. This method not only accurately describes complex mechanical relationships but also effectively manages the coupling problems of position and attitude within a unified mathematical framework, greatly facilitating the subsequent design of integrated control systems for position and trajectory. Initially, leveraging the hinge model, the paper establishes recursive relationships for velocity and acceleration between the hinges and the arm in dual quaternion form. Then, using the force-torque transmission relationship between the hinges and the arm, a recursive form of the inverse dynamics equation is established to ease the design and analysis of control systems. Following this, a matrix form of the integrated position and attitude forward dynamics equation is derived. The paper then discusses the dynamics modeling issues related to actuators, such as thrusters and control moment gyroscopes. It addresses the integrated control problems of position and attitude for both the robotic arm and the floating base. Finally, dynamics modeling and control simulations for a composite entity comprising a six-degree-of-freedom robotic arm and a floating base are conducted. The dynamics simulation results confirm the correctness of the proposed dynamics modeling method, and the control simulation demonstrates that the control system can quickly counteract the disturbance forces and torques generated by the movement of the robotic arm on the base, proving the effectiveness and feasibility of the proposed control method.

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