Interpretable Approximation of Optimal Trajectories for Lateral Vehicle Guidance

Solving a nonlinear optimization problem to plan an optimal trajectory is a complex task. Moreover, no convergence guarantee can be given. On the other hand, nonlinear vehicle dynamics and nonconvex environmental conditions can be considered. This paper proposes an optimization problem for lane change trajectory planning. To reduce the computational complexity, the output of the solution algorithm is approximated by an explicit function. This is applied to a kinematic model to reproduce the optimal trajectories. The interpretability of the learned function is improved by choosing a grid-based model. To fully exploit the parameters of the model, a global optimization algorithm finds an optimal input partitioning. The performance of the approach is compared to that of a grid with regular partitioning of the input space and a decision tree on a set of optimal lane change trajectories. Furthermore, the output of an optimal grid model is visualized and analyzed for plausibility.