Minimum-time lane changing problem of vehicle handling inverse dynamics based on adaptive mesh refinement and collocation optimization method

In order to solve the problems of multiple constraints, many different calculations of nonlinear equations which lead to major errors in the process of vehicle lane changing with minimum time, an adaptive mesh refinement and collocation optimization method is proposed. Firstly, the problem of vehicle lane changing with minimum time has been divided into nonlinear programming problems in different grids. The Lagrange interpolation polynomial was used to approximate the solution of the optimization problem in the grid, and the absolute and relative errors were resolved. Then, a mesh was determined for the unsmooth part according to the curvature of the trajectory, and the location and number of meshes were further determined according to the relationship between the maximum relative error and the allowable error. At the same time, the solution accuracy was improved by adding an adaptive calculation to the smooth interval which does not meet the tolerance error. Finally, the simulation example of comparison with the traditional optimization method was proposed. The results showed that the algorithm presented in the paper had a higher solution efficiency under the same calculation accuracy.