Modeling Of Flexible Joints Hysteresis Characteristics Of Harmonic Reducers For Collaborative Robots

With the continuous progress of robot technology,the collaborative robot(Cobot)has become the latest research direction in the development of the robot industry,being gradually applied to flexible manufacturing,disaster prevention and epidemic prevention,and medical services,et al.The multi-scene,multi-task,and complex operating conditions require not only excellent function but also higher position execution accuracy of Cobot.However,due to the harmonic reducer with a complex structure,the angle transfer accuracy of the flexible joint of Cobot will change with the load,which causes a complex hysteresis characteristic between the torsion angle and the output torque with strong nonlinearity,asymmetry,and non-smoothness,directly limiting the execution accuracy of Cobot.The high-precision flexible joint model is a prerequisite for achieving joint compensation control and improving angle transfer accuracy.Therefore,to meet the high precision requirements of Cobot,the model-based high precision control for the flexible joint of Cobot is particularly essential to the modeling for the hysteresis characteristics of the harmonic reducer in the flexible joint of Cobot.The paper examines the following.(1)An improved weighted least squares support vector machine(WLSSVM)dynamic hysteresis model based on the nonlinear auto-regressive moving average with exogenous inputs(NARMAX)structure is proposed.To make the LSSVM model with dynamic characteristics,with the aid of the NARMAX structure,the historical values of torsion angle and output torque are taken as inputs to the model in the LSSVM hysteresis model to achieve the description of the dynamic characteristics for the flexible joint.For the complex hysteresis characteristics of the joint,the PI hysteresis operator output is introduced into the input as the preprocessing of the input signal to describe the hysteresis characteristics of the joint.To address the issues that LSSVM is susceptible to the interference of model output error when solving model parameters,a modified WLSSVM is designed to solve the model by adding a regular term composed of model output error with an adaptive adjustment factor to the objective optimization function to achieve the purpose of improving the accuracy of model parameters.The proposed dynamic hysteresis model has been modeled and validated on the Franka Emika Panda Cobot platform.The experimental results show that the proposed hysteresis model has a higher model accuracy compared to the LSSVM hysteresis model and the NARMAX hysteresis model.(2)A series hysteresis model that is combined the nonlinear auto-regressive exogenous neural network(NARXNN)with the convolutional neural network(CNN)is proposed in this paper.NARXNN is directly employed to describe the complex nonlinear characteristics of the flexible joint,which will inevitably lead to large amplitude and phase lag deviations.For the sake of further improving the modeling precision of NARXNN,CNN is introduced and connected in series behind the NARXNN to construct a NARXNN-CNN combined hysteresis model.In CNN,the deviation values between the joint torsion angle history values and the NARXNN output are taken as the input of CNN to obtain the amplitude and phase features of the deviation,and at the same time to obtain the polar point features with non-smooth characteristics,which are used to solve the problem that NARXNN fails to describe the non-smooth characteristics contained in the deviation.The novel composite objective function is proposed to independently learn for two parts of the NARXNN-CNN combined hysteresis model,and thus effectively improve the learning speed.The proposed combined hysteresis model has been modeled and verified on the Franka Emika Panda Cobot platform.Compared with the NARXNN hysteresis model and the CNN-NARXNN combined hysteresis model(NARXNN connected in series behind CNN),the experimental results show that the NARXNN-CNN combined hysteresis model is of higher modeling accuracy.The two models proposed in this paper are experimentally validated to effectively describe the complex hysteresis characteristics caused by the harmonic reducer in the flexible joint of Cobot.The modeling and verifying accuracy of the NARXNN-CNN combined hysteresis model are better than the improved WLSSVM dynamic hysteresis model,and the improved WLSSVM dynamic hysteresis model,which is essentially a form of solving equations,is superior to the NARXNN-CNN combined hysteresis model in terms of computational speed.Each of them has its advantages.Depending on the different requirements for speed and accuracy,one of the models can be selected to satisfy the application scenarios with different requirements.