This is the MATLAB code for the article
@ainproceedings{zhou2024homotopic,
title={Homotopic Optimization for Autonomous Vehicle Maneuvering},
author={Jian Zhou, Arvind Balachandran, Bj\"orn Olofsson, Lars Nielsen, and Erik Frisk},
booktitle={2024 35th IEEE Intelligent Vehicles Symposium (IV)},
year={2024},
pages={}}
which has been accepted for publication at the 35th IEEE Intelligent Vehicles Conference (IEEE IV).
The authors are from the Department of Electrical Engineering, Linköping University, Sweden, and the Department of Automatic Control, Lund University, Sweden.
Contact: Jian Zhou (jian.zhou@liu.se).
To run the code you need to install:
CasADi: https://web.casadi.org/
HSL Solver: https://licences.stfc.ac.uk/product/coin-hsl
Note: Installing the HSL package can be a bit comprehensive, but the solvers just speed up the solutions. You can comment out the places where the HSL solver is used, i.e., options.ipopt.linear_solver = 'ma57', and just use the default linear solver of CasADi.
The article includes three case studies. The implementation details of the code are given below.
In the folder case_1_change_homotopy_iteration_n:
(1) The file MinTimeCoGDoubleTrackInitialization.m defines the optimization problem for initializing the homotopic optimization.
(2) The file MinTimeCoGDoubleTrack.m defines the optimization problem during the homotopy iterations.
(3) The file parameters_define.m defines the static parameters.
(4) The files main_1.m to main_11.m contain the cases for implementing the homotopic optimization with different iterations main_1.m,
(5) To implement the method, first run parameters_define.m, then you can choose any case from main_1.m to main_11.m to get the results with different
In the folder case_2_different_road_velocity_conditions:
(1) The file MinTimeCoGDoubleTrackInitialization.m defines the optimization problem for initializing the homotopic optimization.
(2) The file MinTimeCoGDoubleTrack.m defines the optimization problem during the homotopy iterations.
(3) The files parameters_define_D.m, parameters_define_W.m, and parameters_define_S.m define the static parameters on the dry, wet, and snow roads, respectively. The files parameters_define_H.m, parameters_define_M.m, and parameters_define_L.m define the static parameters with high initial speed, middle initial speed, and low initial speed, respectively.
(4) The files main_D.m... main_L.m implement the homotopic optimization method corresponding to the parameters defined in parameters_define_D.m...parameters_define_L.m. For example, main_D.m implements the problem subject to the dry road with the static parameters defined in parameters_define_D.m.
(5) To implement the method, first run the file parameters_define_X.m to define the parameters, then run the main file main_X.m.
In the folder case_3_compare_with_stepwise_initialization:
(1) It contains three sub-folders, corresponding to the implementation of the stepwise initialization for the three problems listed in Table III of the paper.
(2) For instance, in the sub-folder problem 1, the implementation of Problem 1 in Table III of the paper by the stepwise initialization is provided, where the file MinTimeCoGDoubleTrackInitialization.m defines the optimization problem for initializing the optimization. The file MinTimeCoGDoubleTrack.m defines the optimization problem for solving the maneuvering problem, where the initial guess is obtained stepwisely. The file parameters_define.m defines the static parameters, and main.m is the main file for running the method. Normally, the stepwise initialization does not get convergence for this problem. The files in another two sub-folders are interpreted in the same way.
(3) To implement the method, first run parameters_define.m, then run main.m.
In the folder case_4_compare_with_driver_model_initialization: (1) It contains three sub-folders, corresponding to the implementation of the driver-model-based initialization for the three problems listed in Table III of the paper.
(2) For instance, in the sub-folder problem 1, the implementation of Problem 1 in Table III of the paper by the driver-model-based initialization is provided. The file MinTimeCoGDoubleTrack.m defines the optimization problem for solving the maneuvering problem, where the initial guess is obtained by the driver model. The file parameters_define.m defines the static parameters, and main.m is the main file for running the method. The files SplinePath.m, generate_circle_points.m, and DriverModel.m together find the initial guess of the problem by the driver model. Normally, the driver-model-based initialization does not get convergence for this problem. The files in another two sub-folders are interpreted in the same way.
(3) To implement the method, first run parameters_define.m, then run main.m.