## 1 Introduction  
Sustainable development of production systems requires efficient material handling systems. Modern, smart production systems using technologies commonly referred to as Industry 4.0 open up new possibilities for automated transportation systems based on automated guided vehicles (AGVs) or autonomous mobile robots (AMRs). Such transportation systems are characterized by a high level of flexibility and reconfigurability, enabling their use in a wide range of production systems. They serve as an auxiliary system the performance of which is usually evaluated from the point of view of satisfying the following criteria [1]:  
* maximize the throughput of the system;
* minimize vehicle travel times;
* minimize the time required to complete all tasks;
* minimize total costs of movement. When considering the operation of a transportation system as an optimization task, it should be noted that constraints on various aspects of its operation play an important role in this task. These constraints also result from the specific nature of these systems, classified as discrete event systems. Transportation systems performing their tasks in a distributed production environment encounter many conflict situations, which must be solved efficiently to avoid situations such as collisions or deadlocks. It should be noted that the result of a deadlock handling method is not a specific value that can be compared with another method, but the operating state of the system without deadlocks. There are many different approaches in this area. The application of a specific approach depends on both the structure of the transportation system and the processes carried out. Methodscharacterized by adaptability to the specific nature of transportation tasks may be of particular interest. The scientific contribution of this work is a modified SOCP method [2] for collision and deadlock avoidance in multi-AGV systems, applicable in selected use cases. This approach allows for an increase in the efficiency of the transportation system based on AGVs. The efficiency of a transportation system based on AGVs depends on many factors. Various management and control issues must be carried out before and during the AGVs operation. Design and control issues of AGV systems at manufacturing, distribution, transshipment, and transportation systems are discussed by [PERSON] [1]. A broad overview of these issues may be found in the review papers by [PERSON] and [PERSON] [3] and [PERSON] et al. [4]. [PERSON] et al. [5] identify and classifies research related to the planning and control of AGVs and AMRs. They propose an agenda for future research within this field. The issues related to AGVs can be divided into two areas: transportation system design and transportation system management. The design stage includes such issues as  
* guide-path design;
* estimating the number and location of parking, pick-up, and delivery points;
* estimating the number of required vehicles. The management stage includes
* positioning of idle vehicles;
* vehicle dispatching;
* vehicle routing;
* vehicle scheduling;
* collision and deadlock handling;
* maintenance of vehicles. The very first issue is the flow path structure setting. The topology of flow path layouts could be classified into two main categories: conventional and specific (loop, mesh, square). Depending on the type of topology, an appropriate traffic control strategy must be applied. In this area, the most important factor for the transportation system operation is an appropriate method for AGV collision and deadlock handling. These control methods can be classified into three categories: static, time-window-based, and dynamic. In the conventional path topology, the transportation network can be built from unidirectional, bidirectional, and multiple lane flow paths. A bidirectional flow path network has a high throughput and a smaller number of required vehicles but appropriate control algorithms are more complicated.