# Shoulder-Elbow Joint Angle Prediction Using COANN with Multi-Source Information Integration
## 2 COANN Network Optimization Algorithm Architecture
### COANN Network Optimization Algorithm
The normalization is performed in MATLAB using the map minmax function, and the min-max normalization method is used to linearly map each channel of the sEMG signal to the interval \([-1,1]\), Equation (12). :

\[x_{norm}=2\times\frac{x-x_{\min}}{x_{\max}-x_{\min}}-1, \tag{12}\]

In the above equation, \(x_{min}\) and \(x_{min}\) are the maximum and minimum values of \(x_{(i)}\), respectively. Figure 4 shows the raw signals acquired from the biceps brachii (rosy red), brachialis (ginger green), and triceps brachii (sky blue) muscles:

The sEMG signals of biceps brachii (rosy red), brachialis (ginger green), and triceps brachii (sky blue) muscles after preprocessing by the above process are shown in Figure 5 below. Figure 4: Raw electromyography signals. ### Acquisition and Processing of Shoulder and Elbow Joint Angle Signals

Stretching is a common form of upper body exercise, and this paper is a study of stretching. The position of the shoulder and elbow joint extension movement is shown in Figure 1:0

In Figure 6, 1 is the shoulder joint and 2 is the elbow joint; the angle captured by the large arm sensor is \(\alpha\), and the angle captured by the small arm sensor is \(\beta\); the rose-red sketch is for the large arm, and the blue sketch is for the small arm; and the angle of the shoulder joint is set to be A, and the angle of the elbow joint is set to be B. (Note: The initial angle of the shoulder joint is set to be \(0^{\circ}\), and the initial angle of the elbow joint is set to be \(90^{\circ}\)). Figure 1:1

Figure 1:2

The angular measurements of upper arm and forearm motion acquired by the positional sensors were computationally transformed into shoulder and elbow joint angles through Equations (11) and (12). Following data smoothing procedures, the actual kinematic profiles of shoulder and elbow joints during extension movements are demonstrated in Figure 7, which fulfilled the data quality requirements for upper-limb trajectory prediction with statistical verification (\(p<0.01\), n = 15). Figure 1:3 Preprocessed sEMG signals. Figure 1:4 Shoulder and elbow joint movement position change diagrams. ## 5 Test Procedure and Analysis

### Comparison of Prediction Effectiveness of Algorithms Under Multi-Information Fusion Inputs

This study proposes a novel COANN algorithm integrating the Cheetah Optimizer Algorithm (COA) with the Artificial Neural Network (ANN), where the COA dynamically adjusts ANN weights to replace conventional gradient descent methods, effectively addressing issues of local optima stagnation and computational latency. The COA-driven optimization framework implements phase-specific weight updates through biomimetic strategies: Rapid Tracking (Equation (4)) for global exploration, Ambush (Equation (5)) for adaptive step-size control, and Attack (Equation (6)) for precision refinement. The COANN architecture features an input layer comprising five nodes corresponding to three-channel surface electromyography (sEMG) signals (biceps brachii, brachialis, triceps brachii) and biaxial joint angles (shoulder, elbow), with the output layer generating real-time joint angle predictions. The ANN structure diagram that was used for the data analysis of upper-limb joint angle prediction is shown in Figure 1:5 This paper focuses on the prediction of multi-dimensional input and single-dimensional output. The artificial neural network input layer in the structure is 5 neurons, corresponding to three channels of 3 surface EMG signals and 2 joint angles; the hidden layer is 3 layers; the output layer is 1 layer, corresponding to 2 neurons, corresponding to the predicted 2 joint angles [19; 20]. (Note: each layer has a bias node, except for the output layer). Figure 1:6 ANN structure diagram. Figure 1:7 Actual angle of the shoulder and elbow joints during stretching exercises. In order to verify the recognition effect of the COANN, four networks--the ANN, RBF, CNN, and LSTM--are selected to compare the results obtained through multi-information sources as input [21; 22; 23; 24; 25; 26; 27; 28; 29].