This paper presents a comprehensive study on autonomous vehicle parking challenges, focusing on kinematic and reverse parking models. The research develops models for various scenarios, including turning, reverse, vertical, and parallel parking while using the minimum turning radius solution. The integration of the A* algorithm enhances trajectory optimization and obstacle avoidance. Innovative concepts like NTBPT and B-spline theory improve computational optimization. This study provides a foundation for understanding the dynamics and constraints of autonomous parking. The proposed model enhances efficiency and safety, reducing algorithm complexity and improving trajectory optimization. This research offers valuable insights and methodologies for addressing autonomous vehicle parking challenges and advocates for advancements in automated parking systems.