In this paper, we present an algorithm for decentralized control of multiple automated guided vehicles performing transportation tasks within industrial and warehousing environments. By running on each vehicle in the system, the algorithm provides vehicles with capabilities for autonomous path planning and motion co-ordination. The path planning part of the algorithm implements a free-ranging motion scheme by determining the shortest feasible paths considering nonholonomic vehicle constraints. The motion co-ordination part of the algorithm ensures safe vehicle motions by reliable detection and resolution of different conflict situations with other vehicles in the shared workspace. Conflict resolution is based on a vehicle priority scheme and results in temporary stopping or removal of the lower priority vehicles taking part in the conflict. Removal action is always performed within the vehicle's private zone, i.e., the pre-allocated local region of the workspace surrounding the vehicle. By encoding information on the vehicle size and its kinematic constraints, the introduced private zone mechanism provides the necessary physical space required for successful execution of every removal action. We also analyze the stability of the presented algorithm and discuss its deadlock-free and livelock-free properties. Algorithm performance has been validated by simulation using ten vehicles and experimentally on two different setups-a laboratory setup comprising five Pioneer 3DX vehicles and by two state-of-the-art autonomous forklifts in industrial-like operating conditions. Note to Practitioners-Efficient co-ordination of multiple material handling vehicles in warehousing operations is a complex and challenging task. The current industrial state of the art relies on a centralized controller, which dispatches transport missions to vehicles along predetermined paths. While this approach makes it easier to ensure correct system operation, it suffers from several drawbacks: the paths have to be laid out in advance, which is time-consuming and can be suboptimal; centralized planning does not scale well, as the number of vehicle increases and it includes a single point of failure into the system. In this paper, we present a decentralized approach with free-ranging vehicles, where each vehicle plans its own paths to complete assigned missions and negotiates with other vehicles for right of way in order to avoid collisions. This approach has the potential to improve system performance, as vehicles plan optimal, shortest paths to reach their goals. It also solves the scalability issues, as each vehicle makes its own plans, and negotiates for priority only with neighboring vehicles in the cases when conflicts arise. Correct system operation is ensured by introducing private zones, in which vehicles can safely perform avoidance maneuvers. In this paper, we describe and analyze our approach and present experiments that demonstrate its effectiveness in simulation, on laboratory robotic platforms and on the state-of-the-art industrial vehicles. Our algorithm performance has been verified in environments with obstacles, while operation in corridors and cluttered spaces is the subject of our ongoing research. Furthermore, extensive experiments under realistic industrial conditions need to be performed in order to fully validate the applicability and efficiency of our approach.