Research On Immersion & Invariance Control Algorithm Of Space Manipulator With Joint Flexibility

Space manipulator plays a very important role in the establishment,maintenance of space station and many other space missions,and its control problem has always been a research hotspot both at home and abroad.Because of the influence of emission weight,geometrical configuration and so on,the general space manipulator has light weight,large span,low rigidity and large flexibility such that its model is very complicated.Thus,studying the order-reduced control method of space manipulator is necessary.In this paper we mainly study the control problem of space manipulator with joint flexibility based on Immersion and Invariance(I&I)theory.I&I theory is a geometric order-reduced method,of which the basic idea is to dynamically immerse the object system into a low-order target system and require it with desired dynamic performance.First find a mapping such that the actual object system and the target system are linked and accordingly construct a constant manifold,and then design the controller to make the manifold attractive and the track bounded.The main contents of this paper are as follows:First of all,based on the linear torsion spring model of flexible joint proposed by Spong,the dynamic model of a 3-DOF flexible-joint space manipulator is established by Lagrangian equations.Then,according to the basic idea of I&I theory the simplified rigid manipulator model is selected as the target system and the controller is designed based on the passivity-based control theory such that the target system can achieve the desired performance.Simulink simulation shows that the closed-loop system can track the reference trajectory signal well and has good robustness and ati-interference performance.Finally,for the simplified flexible-joint space manipulator model of which the coupling items are removed and for the complete model two different I&I controllers are designed.Simulink simulation shows that both controllers can make the closed-loop system track the reference trajectory signal but the tracking error of the former is relatively smaller while the controller form of the latter is more concise.From the controller design and simulation it can be found that the application of I&I control theory is very flexible and it can make it possible that the complex high-order model can be asymptotically immersed into the simplified low-order model such that the complex system can have similar dynamic performance with the simplified system.So it can make a great advantage in the order-reduced control of space manipulator with complex model.