## 4 Results and Discussion
The exceptional performance of CBF-QP can be attributed to its suitability for real-time, safety-critical applications, such as obstacle avoidance in dynamic environments. By leveraging control barrier functions (CBFs), the CBF-QP approach enforces rigorous safety constraints, ensuring that the system operates within predefined safe limits. This is particularly advantageous in scenarios where real-time adaptability and safety are paramount, such as agricultural fields or autonomous navigation in unpredictable terrains. The ability of CBF-QP to provide real-time safety guarantees while minimizing control effort makes it an ideal choice for applications requiring robust and efficient collision avoidance. In contrast, AMPC is better suited for applications that prioritize optimal long-term planning and adaptability to changing conditions. AMPC optimizes control inputs over a finite horizon, providing globally optimal or near-optimal solutions for trajectory planning. This makes it highly effective in scenarios where computational resources are available, and the primary challenge is to achieve optimal performance over extended periods. However, the computational complexity of AMPC can be a limiting factor in real-time applications, particularly those with strict timing requirements or limited processing capabilities. The choice between CBF-QP and AMPC ultimately depends on the specific requirements of the application. For safety-critical tasks in dynamic environments, such as obstacle avoidance or real-time navigation, CBF-QP offers a more efficient and reliable solution. On the other hand, for applications requiring long-term planning and adaptability to changing conditions, AMPC provides a robust framework for achieving optimal performance. In some cases, a hybrid approach that combines the strengths of both methods could be highly beneficial. For instance, integrating CBF-QP for real-time safety enforcement with AMPC for long-term trajectory optimization could yield a comprehensive solution that addresses both safety and optimality. The performance improvements demonstrated by CBF-QP, as highlighted in Table 2, reflect its ability to achieve faster response times, higher precision, and reduced energy consumption compared to AMPC. These advantages are particularly critical in applications where real-time decision-making and safety are paramount. By providing a systematic framework for enforcing safety constraints and optimizing control inputs, CBF-QP enhances the reliability and efficiency of WMRs in dynamic and complex environments. In summary, the CBF-QP approach offers a robust and efficient solution for enhancing the performance of WMRs in safety-critical applications, while AMPC excels in scenarios requiring long-term planning and adaptability. The choice between these methods should be guided by the specific requirements of the application, such as the need for real-time safety, computational efficiency, or optimal performance. In some cases, a hybrid approach that leverages the strengths of both CBF-QP and AMPC could provide a comprehensive solution, enabling WMRs to operate safely and efficiently in a wide range of environments.