## 5 Experimental Results
### Results  
Figure 10 shows the raw point cloud data for detected objects. Note that every object has its unique label that helps track management to associate data to each detected object (\(T1\), \(T2\), and \(T3\)). This could also help in counting the number of objects around the excavator. Figure 11 presents the operator's view to see the excavator and moving objects (\(T1\), \(T2\), and \(T3\)) around it. The box (orange color) and fan shape (purple color) in the figure represent the excavator and the operator's visible sight, respectively. The bounding boxes denote the objects around the excavator. The track IDs in Figures 10 and 11 are identical to maintain unique labels for the objects. The detailed tracking results are presented in Figure 12 that includes the information of the \(x,y\), and \(z\) coordinates of each object. These coordinates indicate the current and  
Figure 11: Object detection and tracking around the excavator in the operator’s view. Figure 10: Detected multiple objects during experiments. predicted (1 s ahead) positions of the detected objects. The tracking details were utilized for object tracking and safety evaluation. In Figure 13, the maximum and the actual working areas of the excavator are shown. It also shows the rotation angle of the excavator, the heading angle of tracked moving objects, and their current and predicted states. Figure 12: Current and predicted positions for the tracked objects. Figure 13: Multiple tracked objects and working areas of the excavator. The current area of work represented by the inner circle was obtained by conducting the kinematic analysis, while the maximum working area was achieved through a full extension of three links. The safety indices were calculated based on the actual working area. Note that \(T2\) is the static object, and thus its predicted and current positions did not change. Figure 14 shows the results of the safety evaluation results computed with the safety indices presented in Figure 8. The current states of \(T1\) and \(T3\) with a circle mark are in the warning and safe regions, respectively. However, the predicted state (1 s ahead) of \(T1\) with the \(\times\) mark indicates that it is entering the emergency region, and thus the chance of collision has highly increased. Therefore, immediate braking should be taken in 1 s to prevent a collision accident for \(T1\) since \(TTC\) is less than 1 s. All the detected static objects were far from the maximum working area in the test scenario (i.e., no potential hazard exists in this case), and thus only moving objects are included for the safety evaluation, as seen in Figure 14. Monitoring in Figure 13 and safety evaluation in Figure 14 can work synchronously (see the attached video clip). Finally, the performance of the developed safety algorithms was evaluated in terms of prediction accuracy using the same experimental data from the test scenario in Figures 13 and 14. For this evaluation, we compared the predicted positions of the moving objects \(T1\) and \(T3\) at each time frame with the actual positions 1 s after prediction. Since the minimum Euclidean distance for clustering (i.e., the minimum size of a bounding box to detect moving objects) was set as 0.4 m (average of a worker's chest size), this value was determined as a threshold to judge the success or failure of the prediction. Specifically, the prediction is recognized as'success' if the error between the predicted and actual positions at each time frame (0.1 s) per object is smaller than the threshold value. Table 1 includes evaluation results to show a successful operation (prediction) rate for each object achieved by the developed algorithms. During the considered test scenario, the successful operation rate for \(T1\) was 85.27% to indicate that the error is less than the threshold in 220 time frames out of the total, 258. The average error across all the time frames (258) was 0.29 m for \(T1\).