# Multi-Robot Formation Control Based on CVT Algorithm and Health Optimization Management
## 4 Experiment and Simulation
### Simulation of Formation Health Optimization Management
#### 4.2.1 All Robots Are Healthy  
Figure 10(a),b describes the results of the first case, where each robot is initialized with the same health level, and the health of each robot decreases normally with its movement. Figure 10(a) depicts the health of each robot during formation control without health optimization management. When all the robots reach the final configuration, the health of robot 1 drops more than the rest, reaching the final configuration when \(h_{i}(t)=0.26\). In Figure 10(b), with optimized health management, the same robot extends its lifespan and does not reach the final configuration until \(h_{i}(t)=0.48\), increasing the lifespan by 22%. Figure 11: Comparison before and after adding HOM in the first scenario: (**a**) \(h_{i}(t)\) of the robot under normal conditions; (**b**) \(h_{i}(t)\) of the robot under HOM; (**c**) \(e_{i}(t)\) under normal conditions; (**d**) \(e_{i}(t)\) under HOM. It can be seen from Figure 11c that if there is no health optimization management, the differences in robot health will diverge over time, while in Figure 11d, the differences are bounded. 2.2 The Initial Power of a Single Robot Is Lower than That of Other Robots, Resulting in a Decrease in Battery Life  
Figure 12a,b describes the results in the second case, where each robot is initialized with the same health level. Figure 12a depicts the health of each robot during formation control without health optimization management. When all the robots reach the final configuration, the health of robot 4 drops more than the rest, reaching the final configuration when \(h_{i}(t)=0.04\). In Figure 12b, with optimized health management, the same robot extends its lifespan and does not reach the final configuration until \(h_{i}(t)=0.38\), increasing the lifespan by 34%. As can be seen from Figure 12c, if there is no health optimization management, the differences in robot health diverge greatly with the passage of time, while in Figure 12d, the difference is small. 2.3 The Failure of a Single Robot Component Caused by the External Environment, Such as a Damaged Wheel That Causes a Sharp Deterioration in the Health of the Robot  
Figure 13a,b describes the results of the third case, where each robot is initialized with the same health level. Figure 13a depicts the health of each robot during formation control without health optimization management. When all the robots reach the final configuration, the health of robot 4 drops more than the rest, reaching the final configuration when \(h_{i}(t)=0.15\). In Figure 13b, with optimized health management, the same robot extends its lifespan and does not reach the final configuration until \(h_{i}(t)=0.4\), increasing the lifespan by 25%. Figure 12: Comparison before and after adding HOM in the second scenario: (**a**) \(h_{i}(t)\) of the robot under normal conditions; (**b**) \(h_{i}(t)\) of the robot under HOM; (**c**) \(e_{i}(t)\) under normal conditions; (**d**) \(e_{i}(t)\) under HOM. As can be seen from Figure 13c, if there is no health optimization management, the differences in robot health diverge with time and are large compared with the average value, while in Figure 13d, the differences are small. 2.4 Due to the Abnormal Fault of the Motor of a Single Robot, the Power Consumption Rate of the Robot Increases  
Figure 14a,b describes the results of the fourth case, in which each robot is initialized with the same health level. Figure 14a depicts the health of each robot during formation control without health optimization management. When all robots reach the final configuration, the health of robot 4 decreases more than the rest, reaching the final configuration at \(h_{i}(t)=0.02\). In Figure 14b, with health optimization management, the same robot extends its life and does not reach the final configuration until \(h_{i}(t)=0.3\), increasing its life by 28%. As can be seen from Figure 13c, if there is no health optimization management the differences in robot health will diverge greatly with the passage of time, while in Figure 13d, the differences are small.