Research On Rigid-flexible Coupling Dynamics And Control Of Parallel Robot With Flexure Hinge

In order to meet the requirements of fast response,high precision and good stability in micro positioning and tracking,it is very important to study the dynamic performance and control strategy of parallel robot.At present,in the study of parallel robot dynamics,each component is basically regarded as a rigid body,and the rigid flexible coupling relationship between the components in its working process is neglected,which result in the inaccurate dynamic model.In the study on its control,each branch of the robot is viewed as a completely independent system,and the traditional control method is used to control it separately.Also,the multivariable characteristics of the control system and the high interaction of the robot linkage are not fully considered,which affect the working performance of robots.Based on the application requirements of parallel robot in micro-positioning and tracking,a three-degree-of-freedom parallel robot model with flexible hinge is established,and its rigid-flexible coupling dynamics and optimal control strategy are analyzed.The details are as follows:Firstly,a three-degree-of-freedom parallel robot three-dimensional structure model with flexible hinge is established by using SolidWorks software,its position inverse solution is analyzed by geometric method,its position positive solution is analyzed by numerical method,and its position positive solution is calculated by MATLAB software.In order to ensure the controllability of the robot,the singularity is analyzed.The results show that the actual trajectory of the terminal centroid of the parallel robot is basically consistent with its expected trajectory,and the error is relatively small,which verifies the correctness of the built parallel robot model and provides a theoretical basis for the study of its dynamics and control strategy.Secondly,the dynamic model of the robot is constructed by the multi-body system transfer matrix method(MSTMM).By establishing the multi-body system tree model and deriving the transformation matrix between the various components,the whole transformation matrix and dynamic equation of the robot system are obtained.The dynamics and kinematics performance of rigid body model and rigid-flexible coupling model are simulated and analyzed by ADAMS software.The results show that the rigid-flexible coupling model of the parallel robot has better kinematic performance than the rigid model,The output of the rigid-flexible coupling model in the x,y and z directions has obvious changes.The displacement,velocity,and acceleration in the z direction are significantly changed,which are increased 0.4025 mm,20.8525 mm/s and 685.6229 mm/s~2 respectively.The driving force and torque of drive rod 1 in the y direction are reduced 0.0692 N and 8.5473 N-mm respectively.The parallel robot joint with flexible hinges has better flexibility,the robot motion response is faster under the simulation of rigid flexible coupling model,the driving force is relatively reduced,and the mechanical properties are closer to the engineering practice,which verifies the rationality and effectiveness of the dynamic modeling method.Then,by analyzing the state space of the robot,the state space equation is obtained.From the point of view of quantitative description of controllability and observables,the state space of the robot is reduced by using the Hankel model.Based on the reduced state space equation,the overall control scheme of the robot is established.The end pose of the robot is simulated and analyzed by LQR control and genetic algorithm-optimized LQR control methods by MATLAB software.The results show that the control effect with genetic algorithm-optimized LQR control method is more obvious.At 1 s,the robot motion has become a steady state.And the maximum displacement of the robot end in the x,y,and z directions has decreased 18.18%?17.76%and 3.07%respectively.The maximum acceleration on each leg has decreased 6.12%?6.25%and 5.88%respectively.The maximum control force on each leg has decreased 8.96%?7.32%and 9.01%respectively.The robot has higher motion accuracy,faster response,better stability and less force on the legs.Finally,based on the LQR control strategy optimized by genetic algorithm,combined with the vibration theory of multi-body system with mechanical structure,the stability of the end motion of the robot is analyzed by using MATLAB software and ADAMS software in the case of applying sinusoidal excitation to the robot fixed platform and applying load to its moving platform.The results show that the overall stability of the robot under the control method is good,and the superiority of the control method is fully verified.Moreover,the resonance frequencies at the end of the robot in the x and y directions are kept at about 5 Hz,while the resonance frequencies in the z direction have obvious backward shift phenomenon,which gradually approach to the high frequency(10 Hz),which proves the existence of high coupling in parallel robots.Through the above research,this paper provides important theoretical significance and practical reference value for further research on the dynamics and control strategy of parallel robots.