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Figure 2. (a) Parametric symbols related to vehicle size and kinematics. (b) Parallel parking scenario diagrams. In which <i>SL>0</i> indicates the parking space length, <i>SW>0</i> indicates the parking space width and <i>CL>0</i> is the line width. The <i>y=CL</i> and <i>y=-SW</i> functions determine the borders between acceptable parking spaces.

Figure 3. Ego vehicle model.

Figure 4. (a) Routing using rapidly-exploring random tree. (b) Designing the parking space and ego vehicle. (c) Automated parking process with the rapidly-exploring random tree method with the nonlinear model predictive control controller. (d) Automated parking simulation process with the nonlinear model predictive control controller.

Figure 5. Nonlinear model predictive control diagram block.

Figure 6. Stages of line detection.

Figure 7. (a) Input film. (b) Output of the processed film.

Figure 8. The<b> </b>nonlinear model predictive control controller graphs. (a) velocity, (b) streeing. Comparison the results of RRT and NLMPC for (c) y position, (d) x position, and (e) yaw angle.

Figure 9. Loss mask in several steps.

Figure 10. Mask accuracy in several steps.

Figure 11. The result of masking process.