## 1 Introduction and Motivation
The approaches in the field of trajectory planning are possible ways to formulate the problem of autonomous vehicle motion in intersections. The actual methods and the future challenges in path planning are summarized in [28]. Some similarities between the path planning and the problem of autonomous vehicles in intersections motivated the use of Bezier-based methods in the problem. For example, in [29] a Bezier curve optimization method was proposed to cope with these constraints, and autonomous vehicles were considered that were equipped with all the necessary sensors for obstacle detection. In this way, the obstacle avoidance problem was transformed into an optimization problem under equality constraints. Another method with the use of Bezier curves was found in [30], which presents a novel method to resolve the obstacle avoidance and overtaking problems named Hybrid Planning. An MPC-based solution to track the lane centerline while avoiding collisions with obstacles was found in [31]. Further relevant works in the topic of path planning are as follows. [PERSON] et al. [32] presented a real-time dynamic path planning method; i.e., an optimal path with appropriate acceleration and velocity profiles is the result. A graph-based planning method to generate an actionable set of multiple drivable trajectories for race vehicles, is found in [33]. For road vehicles, [PERSON] et al. [34] proposed an optimal trajectory generation method, with which velocity maintenance, merging, following, stopping and a reactive collision avoidance functionality were achieved. In [35] a real-time safe stop trajectory planning algorithm, based on selection from a precomputed set of trajectories has been developed. Several papers deal with the selection of the velocity of autonomous vehicles, which has relevance in the problem of intersection scenarios. For example, [PERSON] et al. [36] proposed an optimization-based velocity planner using the multi-parametric sequential quadratic problem, with which a spatially and temporally varying friction coefficient, and a race-focused energy strategy for the road can be handled. In [37] a solution to the mathematical problem behind the trajectory design problems has been provided; i.e., a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers is proposed. Moreover, in [38] a real-time velocity optimization algorithm for fixed paths was developed and implemented. Another important group of efficient solutions on the problem contains the learning-based approaches, especially reinforcement learning (RL) [39; 40; 41; 42]. The advantage of this method is its model-free property, which can provide solutions to the problem of constraint formulation. Moreover, the training of the control agent through a high number of epochs is carried out, which can lead to improved performances. A deep RL method was applied to unsignaled intersections in [39]. It also provided an analysis to explore the ability of the system to learn active sensing behaviors and safe navigation in the case of occlusions. [PERSON] and [PERSON] [43] also presented a deep RL-based model that considers the effectiveness of leading autonomous vehicles in mixed-autonomy traffic at a non-signalized intersection. [PERSON] et al. [44] offered a new approach to training the intelligent agent that simulatesthe behavior of an unmanned vehicle, based on the integration of reinforcement learning and computer vision. Using full visual information about the road intersection obtained from aerial photographs, they studied through automatic detection the relative positions of all road agents with various architectures of deep neural networks. In spite of promising achievements, the resulting neural-network-based agents cannot provide a guarantee of collision avoidance for the vehicles. That short review of the existing literature showed that several efficient solutions exist, but there are challenges for achieving a reliable control method.