Motion Control Of A Class Of Planar Multi-link Underactuated Manipulators

The control of nonholonomic underactuated mechanical systems is an important field in nonlinear system control.This thesis studies the motion control of the planar multi-link underactuated manipulator with first-order nonholonomic constraint(planar PA^n-1 manipulator for short,where P denotes the passive link,A denotes the active link,n-1 is the number of the active links,n33).Based on the analysis of the motion characteristics of the planar PA^n-1manipulator,its end-point position control,end-link posture control and robust control are addressed.The main research results and innovations of the thesis are as follows.?1?A three-stage control strategy based on the online intelligent optimization algorithm is proposed to realize the position control objective of the planar PA^n-1manipulator.In order to simplify the complexity of the control strategy,the planar PA^n-1manipulator is first reduced to a planar virtual three-link underactuated manipulator.A two-stage control strategy is presented to realize the position control of the planar virtual three-link underactuated manipulator.In each control stage,the planar virtual three-link underactuated manipulator is reduced to a planar virtual Acrobot.The online differential evolution algorithm is used to calculate the target angles of all links of the planar virtual three-link underactuated manipulator based on the target position of the end-point and the angle constraints of two planar virtual Acrobots.The system controllers are designed for the two-stage control of planar virtual three-link underactuated manipulator respectively,and the superiority of the proposed control strategy is verified through the comparison of simulation results.?2?A two-stage control strategy based on the hybrid intelligent optimization algorithm is presented to realize the position control objective of the planar PA^n-1manipulator.While reducing the complexity of the controller design,this strategy also improves the efficiency of the motion control.In the first stage,the planar PA^n-1manipulator is directly reduced to a planar virtual Acrobot.In the second stage,the position control objective of the planar PA^n-1manipulator is achieved by utilizing the angle constraint of the planar virtual Acrobot.According to the control targets of all active links in each control stage,the system controllers for each control stage are designed,and the stability of each closed-loop system is verified based on the Lyapunov method.In order to ensure the target angles of all links,the angle of the passive link at the end of the first control stage and the initial angle of the active link of the planer virtual Acrobot meet the angle constraint of the planar virtual Acrobot,a hybrid intelligent optimization algorithm is designed to calculate the target angle of all links of the planar PA^n-1 manipulator corresponding to the target position of the end-point.Three sets of numerical simulations verify the effectiveness and efficiency of the proposed control strategy.?3?In order to realize the position-posture control objective of the planar PA^n-1manipulator,a continuous control strategy is presented based on the motion coupling relationship and intelligent optimization algorithm.By using the single controllers,the control of a class of nonholonomic systems can be achieved successfully.By further analyzing the angular velocity constraint of the planar PA^n-1manipulator,the motion coupling relationship between the active links and the passive link is found.Based on this motion coupling relationship and the control targets of all active links,the PD controllers for all active links are designed.In order to overcome the sudden change of the initial torques when applying the PD controllers,the PD controllers are improved to be the step PD controllers.The differential evolution algorithm is used to calculate the target angles of all links and the design parameters of the step PD controllers corresponding to the position-posture control objective.The superiority of the proposed control strategy is verified by comparing the results of different simulations.?4?For the robustness design problem of the position control of the planar PA^n-1manipulator,a robust control strategy based on the radial basis neural network and the online iterative correction method is proposed to overcome the influences of parameter perturbations and external disturbances on the system control performance.An uncertain model of the planar PA^n-1 manipulator with parameter perturbations and external disturbances is built.The adaptive robust controllers based on the radial basis neural network are designed for all active links.Meanwhile,these controllers are used to reduce the planar PA^n-1 manipulator to a planar virtual three-link underactuated manipulator.Based on the nominal model parameters of the planar PA^n-1 manipulator and the target position of the end-point,the target angles of all links of the planar virtual three-link underactuated manipulator are calculated by using the online differential evolution algorithm.A two-stage control method is used to control the planar virtual three-link underactuated manipulator.In each control stage,the planar virtual three-link underactuated manipulator is reduced to a plane virtual Acrobot.In order to overcome the deviation of the position control caused by the parameter perturbations,an online iterative correction method is designed to correct all link angles of the planar virtual three-link underactuated manipulator and realize the robust control objective of the planar PA^n-1 manipulator.