## 4 Results and Discussion
When a double-wheeled mobile robot (DWMR) encounters an impact, it actively employs collision avoidance strategies, as illustrated in Figure 9. In this scenario, the environment is characterized by asymmetry, with two obstacles strategically positioned within the agricultural area. The black circles represent potential obstructions, while the red line depicts the trajectory of the DWMR, guided by advanced control algorithms. Both the horizontal and vertical axes are clearly labeled, providing a precise spatial representation of the scenario and highlighting the robot's ability to navigate complex environments. The development and integration of control barrier functions (CBFs) have revolutionized the implementation of safety constraints in robotic systems. Unlike traditional methods, which often rely on overly conservative constraints, CBFs enable a less restrictive and more flexible approach to ensuring safety. This adaptability is particularly crucial in dynamic environments, where the system must respond to unpredictable changes while maintaining robust safety guarantees. By enforcing specific state constraints, CBFs ensure that the system operates within predefined safe bounds, significantly reducing the risk of collisions even in highly nonlinear and uncertain scenarios. The effectiveness of CBFs lies in their ability to provide real-time safety guarantees without compromising the system's performance. For instance, in the case of the DWMR, the control algorithms dynamically adjust the robot's trajectory to avoid obstacles while  
Figure 9: Wheeled mobile robotic collision avoidance at double obstacle. minimizing deviations from the desired path. This is achieved by continuously evaluating the system's state and applying corrective actions to satisfy the CBF constraints. The result is a highly adaptive and resilient system capable of operating safely in complex and asymmetric environments, such as agricultural fields with uneven terrain and dynamic obstacles. Moreover, the use of CBFs enhances the scalability of multi-robot systems, where multiple DWMRs must navigate shared spaces without interfering with one another. By ensuring that each robot adheres to its safety constraints, CBFs enable efficient coordination and collision-free operation, even in densely populated environments. This capability is particularly valuable in agricultural applications, where multiple robots may be deployed simultaneously to perform tasks such as planting, harvesting, or monitoring. In summary, the integration of CBFs into the control framework of DWMRs represents a significant advancement in robotic safety and autonomy. By providing a flexible and robust mechanism for enforcing safety constraints, CBFs enable robots to navigate dynamic and asymmetric environments with confidence, significantly reducing the risk of collisions and enhancing overall system performance. This approach not only improves the reliability of robotic systems in agriculture but also paves the way for their broader adoption in other safety-critical applications. Figure 10 presents the simulation results of a wheeled mobile robot (WMR) navigating a scenario with double obstacles. The results reveal distinct recovery patterns for the WMR's velocity and position states: the velocity state exhibits a nonlinear recovery, while the position state is restored linearly. As depicted in Figure 9, the control effort demonstrates a rapid decline for velocity regulation but decreases more gradually for position stabilization. This difference highlights the varying energy requirements for controlling different states of the system. Notably, the controller barrier gains exhibit significant variations, with the first barrier requiring substantial energy to restore the WMR to its initial position and velocity. This underscores the dynamic nature of the control system and its ability to adapt to complex scenarios.