A Computation Decomposition Strategy for Optimization-Based Coordination of Automated Vehicles in Confined Sites

Journal article, 2024

Coordinating the motion profiles of fully automated vehicles in confined sites presents a challenge, particularly in avoiding conflicts in MUTually EXclusive (MUTEX) zones like intersections, merge-splits, and narrow roads. Prior methods have utilized optimization-based formulations, where the scheduling (order) of vehicles in MUTEX zones is found using a heuristic, followed by solving a nonlinear program (NLP) to determine the optimal state and control trajectories of each vehicle given the schedule. This paper presents a method that reduces the computational demand in the second step by decomposing the NLP into multiple smaller, parallelly solvable, NLPs. The method uses the confined area’s road network geometry and the vehicle positions to identify non-significant MUTEX relations and leverage results from graph theory to use this information to identify independent subproblems. We demonstrate that the solution obtained using this approach is equivalent to that obtained by solving the original NLP. Furthermore, by utilizing the dual variables connected to the MUTEX enforcing constraints, the method is capable of a further, sub-optimality-inducing, subdivision of the problem, enabling a trade-off between optimality and computation. We show how the method can be utilized, both when the plan needs to be initially computed and when there is a need for updating an existing motion plan. Simulation examples demonstrate the computational improvement with respect to the non-decomposed problem.