Polar Coordinates for Accurate Iso-Distance Curve Alignment in Vehicle Simulations

Authors: (1) Mehdi Naderi; (2) Markos Papageorgiou; (3) Dimitrios Troullinos; (4) Iasson Karafyllis; (5) Ioannis Papamichail. Table of Links 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 B: TRANSFORMED ISO-DISTANCE CURVES For the iso-distance curve transformation to align with the desired orientation, new polar coordinates are defined whose origin is found by crossing two lines perpendicular to the vehicles’ rear axles, while having the ego vehicle’s desired deviation from the circular angle. This implies that the coordinates are different for each pair of vehicles. The lines’ equations, according to Fig. 20, can be written as Note that each vehicle projects other vehicles on its own coordinates; therefore, in both equations of (42), the desired orientation of vehicle i is taken into account. Intersecting above equations gives the centre of new coordinates as Then, the radius and angle of each vehicle in the new coordinates is calculated by Furthermore, the distance in the new coordinates is This paper is available on arxiv under CC 4.0 license. Authors: (1) Mehdi Naderi; (2) Markos Papageorgiou; (3) Dimitrios Troullinos; (4) Iasson Karafyllis; (5) Ioannis Papamichail. Authors: Authors: (1) Mehdi Naderi; (2) Markos Papageorgiou; (3) Dimitrios Troullinos; (4) Iasson Karafyllis; (5) Ioannis Papamichail. Table of Links Abstract and Introduction Abstract and Introduction Vehicle Modeling Vehicle Modeling The Nonlinear Feedback Control The Nonlinear Feedback Control OD Corridors and Desired Orientations OD Corridors and Desired Orientations Boundary and Safety Controllers Boundary and Safety Controllers Simulation Results Simulation Results Conclusion Conclusion Appendix A: Collision Detection Appendix A: Collision Detection Appendix B: Transformed ISO-Distance curves Appendix B: Transformed ISO-Distance curves Appendix C: Local Density Appendix C: Local Density Appendix D: Safety Controller Details Appendix D: Safety Controller Details Appendix E: Controller Parameters Appendix E: Controller Parameters References References APPENDIX B: TRANSFORMED ISO-DISTANCE CURVES For the iso-distance curve transformation to align with the desired orientation, new polar coordinates are defined whose origin is found by crossing two lines perpendicular to the vehicles’ rear axles, while having the ego vehicle’s desired deviation from the circular angle. This implies that the coordinates are different for each pair of vehicles. The lines’ equations, according to Fig. 20, can be written as Note that each vehicle projects other vehicles on its own coordinates; therefore, in both equations of (42), the desired orientation of vehicle i is taken into account. Intersecting above i equations gives the centre of new coordinates as Then, the radius and angle of each vehicle in the new coordinates is calculated by Furthermore, the distance in the new coordinates is This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv