# Action Recognition Algorithm of Spatio-Temporal Differential LSTM Based on Feature Enhancement
## 2 Methodology  
PID control is the abbreviation of proportional integral and differential control; it has good robustness and high reliability. In the control system, the PID controller calculates the control error according to the given value and the actual output value, and then carries on proportional, integral, and differential operations on the error; finally, it combines the three operation results to obtain the control signal. Generally speaking, PID control is a linear control algorithm based on the estimation of error \"past\", \"present\", and \"future\" information. Conventional PID control has three correction links: proportional, integral and differential. Their specific functions are as follows: the proportional link reflects control error proportionally, and controls the \"present\" error of the system. The integral controller produces the control effect at the fastest speed. It reflects the rapidity of PID control. The integral link can memorize error. In view of the \"past\" error of the system, the integral controller is mainly to eliminate the steady-state error. The strength of the integral function mainly depends on the integral time constant Ti. The larger Ti, the weaker the integral action. The integral function decides the accuracy of the PID control. The differential link can reflect the trend of the error (change rate). Aiming at the \"future\" error of the system, the differential controller improves the dynamic characteristics of the closed-loop system by acting in advance, which reflects the stability of the PID control. After the analysis of the classic LSTM model, it is found that the recurrent memory network retains the results of the previous video frame \(h_{t-1}\) and inputs the information of current video frame \(x_{t}\). The network uses different weights \(w_{f}\) and \(w_{i}\) to express the relationship between them. Moreover, it is found that when \(w_{f}\) and \(w_{i}\) are positive, it is a kind of integral (I) relation; when \(w_{f}\) and \(w_{i}\) are negative, it is a kind of differential (D) relation. Due to the weight added to video frames, this is also a proportional (P) relationship. When referring to the code of the ST-LSTM on the Github, it is found that \(w_{f}\) and \(w_{i}\) are positive, so for the ST-LSTM, its internal temporal memory state and spatial memory state have a proportional (P) and integral (I) relationship. From the point of view of PID control, the differential link in the ST-LSTM is missing, so we try to add a differential (D) to the ST-LSTM. From the perspective of deep learning, adding differential is also an idea of feature enhancement. From the point of view of robot kinematics, action characteristics include posture, position, speed, etc. Taking the manipulator of a robot as an example, the action of the arm includes the translation of the center of mass and the rotation around the centroid. When the manipulator is analyzed by the Newton-Euler equation, the dynamic equation is as follows:  
\[\tau=M(\theta)\ddot{\theta}+V(\theta,\dot{\theta})+G(\theta) \tag{1}\]  
In the above formula, \(M(\theta)\) is the \(n\times n\) mass matrix of the operating arm, \(V(\theta,\dot{\theta})\) is the centrifugal force and the Gordian force vector of \(n\times 1\). \(G(\theta)\) is the gravity vector of \(n\times 1\), which depends on the position and velocity. \(M(\theta)\) and \(G(\theta)\) are complex functionsabout positions of all joints of the operating arm \(\theta\). \(\dot{\theta}\) represents the angle velocity. \(\ddot{\theta}\) represents the acceleration. Therefore, in the control theory, the control of the robot needs a differential state. The action recognition network based on deep learning pays attention to the extraction of action posture information. Enhancing the information extraction of limb speed and position changes can improve the final performance of the network. Velocity and position changes are the first-order differential of action temporal state and spatial state, respectively.