| With the rapid development of modern industry,industrial robots have become the core technology equipment of intelligent manufacturing.Industrial robots are used in the highend manufacturing of complex processes,and the performance and execution accuracy of industrial robots are increasingly high because of more complicated task requirements.As indispensable precision transmission equipment in industrial robots,reducers can determine the performance of industrial robots.As a newly developed industrial robot,the application of cooperative robot is expanding,while the harmonic reducer is the key to the hysteresis of joints for the cooperative robot.The complex hysteresis will inevitably affect the motion accuracy of the robot and limit the application of the industrial robot in the precision field.The hysteresis model is established according to the hysteresis characteristics,and the control algorithm is designed based on the hysteresis model to realize the high-precision control of industrial robot,which will become one of the research directions of the control method of industrial robot.In view of the complex hysteresis characteristics of the flexible joints for industrial robots,such as multi-value correspondence,asymmetry and difference between main loop and sub-loop,two modeling methods were proposed in this paper:(1)Neural network hysteresis model for describing the asymmetrical characteristic.Aiming at the asymmetrical hysteresis characteristics of flexible joints for industrial robots,based on the structure of symmetric Play operator in PI model,the linear part of Play operator is replaced by nonlinear function: Two transformed Sigmoid functions were combined to construct a new function close to the contour of the hysteresis curve as an asymmetric nonlinear hysteresis operator.With this as the activation function,a neural network hysteresis model was constructed by referring the framework of PI model to model the complex hysteresis characteristics of flexible joints.(2)A hybrid hysteresis model for describing the characteristics of main loop and subloop.Since the sub-loop of hysteresis curve has different variation characteristics from the main loop,a hysteresis model is designed for the sub-loop according to its characteristics.It is found that the variation trend of the sub-loop part is similar to that of the ellipse,so an appropriate ellipse model is used for modeling the sub-loop part.To establish the quasielliptic hysteresis model,ellipse parameters are obtained by fitting ellipse with direct least square method.To model the complex hysteresis characteristics with asymmetry and differences between main loop and sub-loop,a hybrid hysteresis model is constructed by combining the neural network hysteresis model with the quasi-elliptic hysteresis model.The strongly nonlinear hysteresis characteristics which are asymmetrical,and in which the feature of sub-loop varies from main loop of flexible joint for industrial robot are studied in this paper.In order to achieve high precision modeling of complex hysteresis characteristics,by improving the PI model,neural network hysteresis model is constructed.And the asymmetric and nonlinear operator improved the degree of nonlinear for the hysteresis model,besides,the outline of the hysteresis operator similar to the hysteresis curve enables the hysteresis model to satisfy the variation law of hysteresis characteristics.To verify the model,the results show that compared with PI model,neural network hysteresis model has higher prediction accuracy and generalization ability.The model was further validated with artificially interference,the experimental results show that the hysteresis model of neural network has better anti-interference ability.According to the time change trend and pattern characteristics of the sub-loop,the quasi-elliptic model was proposed,which use the global properties of ellipse to approach the local properties of sub-loop part.In view of the quasi-elliptic model for the sub-loop part,compared with the neural network hysteresis model for the main loop part,it can keep in the same order of magnitude on the maximum error,and has slightly lower value of number on the root-mean-square-error(RMSE)than neural network hysteresis model.To model the complex hysteresis characteristics of flexible joints for industrial robots,the hybrid hysteresis model composed of the neural network hysteresis model and the quasi-elliptic model was proposed to synthetically describe the properties of main loop and sub-loop.The verification results indicate that the hybrid hysteresis model can accurately describe the hysteresis characteristics of flexible joints for industrial robots. |
