Self-driving cars integrate various technologies such as automatic control, computer vision, and more. These vehicles are a result of advanced developments in computer science, pattern recognition, and intelligent control systems. Vehicle localization relative to road lanes is essential for integrating autonomous vehicles into daily traffic. Vision-based lane line detection is a widely used method to solve this challenge. This work introduces a geometric approach to calculating the steering wheel angle based on lane detection and the implementation of an autonomous system. The robotic platform used is the Donkey Car with the NVIDIA Jetson Nano as an onboard computer. A camera, which is attached to the board, is placed in front of the car, providing frames to be processed. To focus on its kinematics, the car's speed is kept constant at a low value. Two techniques are tested before sending the signal to the Driver PCA9685, which manages the servo motor that controls the steering of the car. First, a weighted average filter is applied to smooth out the calculated steering angle. The second approach introduces a novel modification of the original scheme by applying a PID controller to achieve the same function as the filter while improving the car's response. An innovative geometric calculation for the robot’s position on the path is developed and applied for performance comparison. The performance index, Mean Squared Error (MSE), is used to compare the control techniques applied in this work. The track used in this study is a closed-loop oval. The car demonstrated solid performance, successfully staying on the path without deviating under fixed speed and lighting conditions. Both techniques enabled the robot to repeatedly complete the track. When comparing the results, the weighted average filter yielded an MSE index of 233.78. A reduction in MSE index was observed with the PID controller, dropping to 126.38, indicating better performance than the filter.