| The robot is developing in the direction of high-speed,high-precision and light-weight,so that its motion includes not only a wide range of rigid body motion,but also elastic vibration caused by the deformation of flexible and lightweight links.The deformation of the flexible link will cause the system to vibrate,resulting in a decrease in the accuracy of the system's motion trajectory,and the excessive inertial force will damage or even destroy the system joints and links,reducing the service life of the system.Constructing an accurate nonlinear mathematical model of a flexible robot is a necessary means to achieve numerical solution optimization.In parallel,research on control algorithms based on precise nonlinear mathematical models can improve system control performance and reduce the complexity of intelligent control algorithms.This article takes the spatial closed-chain robot with rigid and flexible links as the research object,and conducts in-depth research on its mathematical model construction method,numerical solution algorithm and control algorithm.This main research work and results of this article are as follows:1.Aiming at the problem of inaccurate construction of the mathematical model of flexible multi-body system,a new computable model of flexible multi-body system is proposed.First,using the combination of finite element method and floating frame reference formula,a mathematical model of the flexible element considering the coupling effect is established.Secondly,according to the system constraint model,a mathematical model of the end-effector considering the small displacement is established.Finally,the rigid system model,the mathematical model of the flexible unit and the mathematical model of the end-effector can be assembled to obtain a precise and computable model of the flexible multi-body system.The model has strong versatility and can be used to construct any mathematical model of flexible multi-body system containing flexible spatial links.2.The calculable model of the flexible multi-body system is a time-varying,strongly coupled,highly nonlinear differential-algebraic equation.In order to overcome the problem of numerical divergence caused by inaccurate initial value estimation in the process of numerical solution and increase the model dimension by adding constraint equations and reduce the solution efficiency,a model reduction algorithm is proposed to transform the differential-algebraic equation problem into a pure differential problem.Solve the problem and ensure the validity of the constraint model according to Baumgarte's constraint violation stabilization methods(BSM).This solution algorithm has a simple structure and is easy to implement,can improve the solution efficiency of complex mathematical models,and ensure the accuracy of the solution.3.Based on the established nonlinear mathematical model,use the control algorithm of combining the feedforward compensation and proportion-derivative(PD)controllers,to analyze the trajectory tracking accuracy,disturbance suppression,external load in a free state(zero load)and with loads of three and five times the total mass of the components.In parallel,in order to avoid the influence of the nonlinear unknown items to the control performance in the modeling process,utilize the fuzzy control algorithm has the characteristics of approximating the nonlinear system,to have the system adaptively approximated to improve the system control performance,also to explain and analyze the design criteria,stability,solution principle and effectiveness in detail.4.Propose a new control algorithm combining neural network controller and adaptive sliding mode controller.First,utilize an adaptive sliding mode controller to ensure the accuracy of the trajectory,and then according to the performance of the neural network wireless approximated to the nonlinear system to approximate the nonlinear error and reduce the influence of unknown interference.Under the same system parameters,to compare and analyze the trajectory accuracy of the end effector under the action of adaptive sliding mode neural network control and position proportional-integral-derivative(PID)control algorithm.The results indicate that the designed adaptive sliding mode neural network controller meets the requirements of control accuracy and has better results than the position PID control algorithm,which effectively reduces the trajectory tracking error of the end effector.The new control algorithm only needs fewer hidden layer nodes,which proves that the controller has a simple structure,and facilitate the implementation and has strong versatility. |
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