Nonlinear Control Research Of Mobile Manipulators Based On Differential Geometry

Due to its vast workspace and flexible manipulation, a mobile manipulator has an extensive background of applications, and has attracted great attention in the international academic and industrial fields. And the mobile manipulator is time-varying, the strong coupling of nonlinear system, its course of the campaign is restricted by nonholonomic constraints. the practical control system could not exclude the influence of parameter perturbation and disturbances from the external environments or unmodelled dynamics etc,which to some extent make it difficult to control. In addition, as the complexity of its tasks increase, we need higher precision and larger scale of control. Therefore, the study of such systems and the large-scale nonlinear control issues has important theoretical and practical significance.Differential geometric method makes it possible to be realized globally by the decoupling and exact linearization control strategy based on the new theory. However, the abstract differential geometric method is lack of system theory for nonlinear system and relies on the precise of the system, which to some extent limited its application. The paper systematically summed up the methods of differential geometry and presented the nonlinear control strategy which employs the sliding mode control approach and the differential geometric method to realize trajectory tracking of the mobile manipulator. The simulation results indicate that the presented strategy has not only promoted the system to be more robust and precise, also solved the problem of constructing the nonlinear sliding surfaces. The main topics are as follows:Firstly, the paper summed up the differential geometry basic theory for the control of nonlinear system, discussed the necessary and sufficient conditions for exact linearization and decoupling control of the nonlinear system and presented the detailed steps. Next, Nonholonomic theory and a Lagrange approach are used to obtain unified mathematical model of the mobile manipulator, and analysis the system's controllable.Secondly, through the two nonlinear feedback law and diffeomorphism, realize control exact input and output decoupling for the mobile manipulator using of differential geometric method, and use zero dynamics to analyze the internal dynamic quality of the system, designed the PD tracking controller on the basis of the linear decoupling system. Next, build the substitutable simulation model using of the S-function, which is suitable for real-time dynamic simulation of the mobile manipulator control, then analyze PD tracking control and robustness of the mobile manipulator.Finally, presented the two improvement methods for problems of poor robustness and chattering, they are the improved reaching law and the dynamic integration sliding mode variable structure control based on dynamic switching functions. The simulation results show that they achieve a good performance for trajectory tracking control of the mobile manipulator, and promote the system to be more robust to the kinetic parameters perturbation +40% and external disturbances than PD tracking control. Moreover, weaken the chattering problem of the mobile manipulator.