## 1 Introduction
[11] proposed a variable admittance control method based on EMG signals, in which a skeletal muscle model of the upper limb containing multiple muscles was firstly built, then the best pair of antagonist muscles was filtered out, by comparing the effects of various muscles on the wrist and elbow joints, finally the end stiffness of arm was estimated by measuring the contraction level of the antagonist muscles. [PERSON] et al. [12] introduced the concept of tele-impedance to estimate the human arm stiffness in real time by measuring the EMG signals of eight muscles on the operator's arm, which was used to adjust the virtual stiffness of a robot in master-slave tele-operation task. The method had yielded good results in preliminary experiments, but its application was limited by the variability, drift and inaccuracy of EMG signals in real environments and the requirement for frequent recalibration of sensors. In summary, a lot of important achievements have been obtained in the estimation and measurement of human arm impedance, but there are still many limitations. On the one hand, these methods are difficult to apply to unstructured tasks due to the requirement of a priori motion model [13]. On the other hand, it is difficult to estimate the stiffness of each operator's arm accurately, and this approach indirectly increases the complexity of the pHRI control system due to the need for complex peripheral sensors. The neural network approach has advantages in dealing with complex model problems and can be used to recognize and predict human intentions. It should be noted that the stochastic artificial intelligence (S.A.I) does not need to fully understand the dynamic model of the controlled object, and the convergence and accuracy of the prediction results can be guaranteed by learning a large amount of data. The deterministic artificial intelligence (D.A.I) which obeys physical laws to establish the controller model can obtain high-precision performance and greatly reduce the demand for large amounts of data. [PERSON] reviewed the development of D.A.I in the control of the unmanned underwater vehicles [14], and used D.A.I to control the DC motor of the unmanned underwater vehicles to reduce the error of trajectory tracking [15]. [PERSON] et al. [16] realized the autonomous generation of control trajectory through D.A.I, which significantly reduced the average error of the trajectory. D.A.I has achieved excellent results, but the S.A.I is still the main method in the research of trajectory prediction in pHRI. [PERSON] [17] proposed a variable admittance control method for pHRI. A multilayer feedforward neural network was designed to adjust the virtual damping of the admittance controller online using the robot's velocity and operation force as inputs. [PERSON] et al. [18] proposed a variable admittance controller based on reinforcement learning for a human-robot cooperative operation task. By setting the objective of the reinforcement learning algorithm to minimize acceleration during point-to-point motion, the proposed controller can learn appropriate damping adjustment for effective collaboration without prior knowledge of the target position or other task characteristics. [PERSON] et al. [19] used RNN-LSTM network to predict the interaction force in industrial meat cutting task, and applied it in an impedance controller to enable the robot to provide assisting forces to the butcher. [PERSON] et al. [20] combined an empirical model of human motion to predict human behavior in order to estimate human intentions in pHRI. [PERSON] et al. [21] characterized the dynamics of the human arm and robot and compensated the reaction forces using human hand impedance, thus improving the transparency of the pHRI control system. [PERSON] et al. [22] investigated an admittance controller for interactive operations in a restricted task space and used an adaptive neural network to handle the trajectory tracking problem.