Figure 6
The illustration consists of four plots. Top left plot (a), “Paths of 10 robots”: The horizontal axis is labeled “X,” ranging from 0 to 100 with an interval of 20. The vertical axis is labeled “Y,” ranging from 20 to 70 with an interval of 10. It displays the trajectories of ten robots as blue dashed lines with arrow markers and numeric labels 1-10, all navigating within a winding corridor on the X-Y coordinate grid. The corridor is outlined by two polygonal boundary lines, one black and one red, surrounding the paths. The robots’ paths follow the corridor’s turns and remain close together. The paths of robots start from (0, 0), follow closely the path of each other by passing through (30, negative 20), (40, 29.2), (80, negative 13.3), and (92, 50), and end at (0, 60). Top right plot (b), “Paths of robots in safe and danger areas”: The horizontal axis is labeled “X,” ranging from 0 to 100 with an interval of 20. The vertical axis is labeled “Y,” ranging from 20 to 70 with an interval of 10. The corridor contains an interior safe region shaded in gray and a surrounding red-shaded band indicating danger areas. Each robot’s path remains mostly within the central safe region as the lines curve and turn together along the corridor. The corridor starts from (0, 0), passes through (20, negative 20), (40, 30), (80, negative 15), and (92, 50), and ends at (0, 60). Bottom left plot (c), “Curves of shortest and longest distances among all robots”: The horizontal axis is labeled “Time (second),” ranging from 0 to 350 with an interval of 50. The vertical axis is labeled “Collision Distance (meter),” ranging from 0 to 25 with an interval of 5. The plot features a blue-shaded region stretching between two fluctuating lines: the upper line varies from around 12 to 22 meters, while the lower line remains just above zero. The shaded area between lines visually represents the spread between the shortest and longest collision distances over time. Bottom right plot (d), “Curve of minimal collision time for all the robots”: The horizontal axis is labeled “Time (second),” ranging from 0 to 350 with an interval of 50. The vertical axis is labeled “Collision Time (meter per second),” ranging from 0 to 5 with an interval of 1. The black line is dense and spiky, showing rapid, frequent changes throughout the time period, with collision time often reaching the maximum value of 5. Gaps appear where there is no collision time recorded. Note: All the numerical data values are approximated.Robot path following. Note that collision times longer than 5 s are omitted. Source: This study