DYNAMIC MODELING AND CONTROL OF MULTIBODY SYSTEMS USING DUAL QUATERNIONS

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.