Handling Complex Vehicle Movements: Techniques for Finding Cross-Points and Obstaclesby@escholar

# Handling Complex Vehicle Movements: Techniques for Finding Cross-Points and Obstacles

September 3rd, 2024

This appendix outlines methods for finding cross-points between an ego vehicle and obstacles with circular and skewed motions. It involves solving polynomial equations for cross-points and transforming them based on the EV’s orientation. Additionally, it details how to identify the closest current obstacle for collision avoidance.

Authors:

(2) Markos Papageorgiou;

(3) Dimitrios Troullinos;

(4) Iasson Karafyllis;

(5) Ioannis Papamichail.

Abstract and Introduction

Vehicle Modeling

The Nonlinear Feedback Control

OD Corridors and Desired Orientations

Boundary and Safety Controllers

Simulation Results

Conclusion

Appendix A: Collision Detection

Appendix B: Transformed ISO-Distance curves

Appendix C: Local Density

Appendix D: Safety Controller Details

Appendix E: Controller Parameters

References

## APPENDIX D: SAFETY CONTROLLER DETAILS

A. Finding cross-point when EV and obstacle have circular and skewed motions, respectively

In this case, the cross-point can be found by crossing the following movement equations:

So, the cross-point’s longitudinal position is one of the roots of the following second-order polynomial that results from (46) after simplification:

B. Finding cross-point when EV and obstacle have skewed and circular motions, respectively

Following a similar procedure to the previous one, the crosspoint can be found by calculating roots of the following equation:

The found cross-points should be transformed to the coordinates aligned with the EV’s desired orientation. If they are behind the EV or obstacle or the roots are not real, they are ignored. Otherwise, the closest cross-point is considered.

C. Finding the closest current obstacle

This paper is available on arxiv under CC 4.0 license.

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