This paper proposes collision-free optimal trajectory planning for autonomous vehicles in highway traffic, where vehicles need to deal with the interaction among each other. To address this issue, a novel optimal control framework is suggested, which couples the trajectory of surrounding vehicles with collision avoidance constraints. Additionally, we describe a trajectory optimization technique under state constraints, utilizing a planner based on Pontryagin’s Minimum Principle, capable of numerically solving collision avoidance scenarios with surrounding vehicles. Simulation results demonstrate the effectiveness of the proposed approach regarding interaction-based motion planning for different scenarios.

Since 1968, when the Golomb-Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although, there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb-Welch conjecture. Furthermore, new results on Golomb-Welch conjecture dealing with perfect Lee codes of large radii are presented. Algebraic ways of tackling the conjecture in the future are discussed as well. Finally, a brief survey of research inspired by the conjecture is given.