A Pedestrian Dynamics Based Approach to Autonomous Movement Control of Automatic Guided Vehicles

These days, production and logistics systems become more and more automated to achieve a higher cost-efficiency of the manufacturing and delivery processes. For a robust operation of individual production units, the absence of substantial perturbations and the simultaneous availability of all necessary resources such as raw material, tools, and energy are typical requirements. These idealized requirements are, however, often not completely met in reality because of the presence of unpredictable factors such as machine failures or human interference. In order to better cope with such problems, recent work has concentrated on elaborating the potentials of autonomous control approaches in various areas of application [1, 2] which promise higher flexibility and robustness in the presence of unexpected situations than traditional centralized control approaches.

Many real-world examples for material handling and storage systems (for example, container terminals) are characterized by a high number of individual transportation tasks each requiring a significant amount of time. In such cases the utilization of automated transfer cars can provide a feasible solution to keep the internal transportation costs as low as possible. Specifically, the installation and operation costs of modern, complex technical solutions need to be over-compensated by a reduction of labor costs and an overall increase of transportation efficiency in the mid- to long-term.

Automatic guided vehicles (AGVs) are already widely used in intralogistics or ports of transshipment. Their practical operation is challenged by two mutually interdependent problems for planning and control: task allocation to the entire set of available vehicles (scheduling) and routing of the individual AGVs. The latter aspect can be realized by either prescribing a fixed route the vehicle has to follow exactly, or utilizing autonomous control concepts allowing the vehicle to move freely in space in a cost-efficient and safe way. This contribution exclusively focuses on the latter aspect. Specifically, the potentials of pedestrian dynamics-based self-organization concepts are studied. Conversely, it is not the aim of this work to provide a thorough and complete review of existing alternative solutions or to discuss the closely related problem of job scheduling.

At present, AGVs are still often subject to a centralized movement control allowing for the anticipation and thus preventation of potential collisions or deadlock situations [3, 4]. One corresponding strategy is that the individual vehicles have to pass certain checkpoints allowing for a forecast of possible conflicts. In addition, gridding of the available space simplifies the distribution of priorities and permissions for entering specific areas: if the next checkpoint or the next grid cell cannot be reached (for example, due to an occupation by another transfer car) a vehicle remains at rest until the blocking situation is resolved. Alternatively, the network of possible transportation routes can be decomposed into paths that can be reserved for usage by individual vehicles. The latter strategy typically requires a central control unit with complete on-line coverage information of the entire network. Furthermore, the paths can be divided into sections allowing for a forecast of the future occupation and, hence, for possible preventive actions [5, 6].

As an alternative to such centralized approaches, efforts have been reported recently to design and practically realize a fully decentralized control strategy for AGVs in intralogistics applications,¹ where the availability of physical space is a crucial restriction to all transportation processes [7, 8]. As a basic condition, one has to require that such an approach must (i) adequately substitute the advantages of existing priority and permission assignment strategies by means of an intelligent control algorithm and (ii) avoid collisions and deadlock situations as far as possible. Specifically, individual vehicles shall freely move in space without any external actions and react autonomously and flexibly in the presence of possible conflicts. While the corresponding problem has already been widely studied in the field of robotics, this contribution discusses an alternative conceptual approach that is based on some fundamental self-organization principles realized in nature.

A paradigmatic example for successfully operating autonomous units are groups of human individuals. In the last decades, numerous efforts have been reported for mathematically modelling the dynamics of pedestrians and their mutual interactions on the microscopic (individual-based) level (i.e., as a multi-agent system [9]), including cellular automaton [10, 11, 12] and interaction force models [13, 14, 15]. The latter class of models postulates the existence of a repulsive short-range potential resulting in the avoidance of too close encounters between individuals. As a particularly useful and widely applicable approach, the social force model [14, 16, 17] has attracted great interest for appropriately describing the behavior of groups of human individuals in various situations. Meanwhile, it is being applied for simulating pedestrian dynamics in sophisticated state-of-the-art traffic simulators such as PTV VISWALK [18].

This contribution is intended to provide a first conceptual study of the potentials and practical limitations of a pedestrian dynamics-based strategy to establishing an autonomous movement control for AGVs. Specifically, the basic ingredients of the social force model are used for implementing corresponding control mechanisms that allow single AGVs to individually choose their trajectory according to a prescribed transportation task and gradually re-evaluate and adapt their motion to the presence of static as well as dynamic obstacles in real-time. By studying generic scenarios, possible limitations of this approach are identified, which call for modifications and extensions of the simple behavioral rules of the underlying pedestrian dynamics model to be applicable for the purposes of industrial logistics. In Sect. 2, the theoretical foundations of the social force model of pedestrian dynamics are briefly reviewed, with a particular emphasis on how to translate its basic ingredients for an autonomous movement control of AGVs. Section 3 describes some practical challenges for establishing such a control in the presence of real-world problems such as static and dynamic obstacles and high vehicle densities at specific sources or sinks in a logistics system. Possible solutions of these problems are discussed. Finally, the main findings of the presented work are briefly summarized and put into context.

In order to better understand the dynamics of AGVs subject to a social force based autonomous control, different scenarios have been studied including such with either exclusively static or dynamic obstacles (i.e., only one AGV in a geometry with prescribed boundaries or several AGVs moving freely without external boundaries, respectively) as well as settings with fixed boundaries and a set of source and sink locations. In the following, some exemplary results taken from a more detailed simulation study [24] are discussed that highlight relevant points where clarifications or modifications of the basic social force model for pedestrian dynamics are necessary to achieve an industrially applicable solution for an autonomous movement control of AGVs. In order to keep the number of parameters in all simulations as low as possible, the following simplifying assumptions are made: First, the area usable for transportation processes has a flat profile. Second, all AGVs have the same physical properties, particularly the same size, mass and maximum acceleration. Third, the dynamics is considered as an ideal motion without friction losses. Finally, all accelerations and decelerations take place instantaneously without any reaction times.

3.2 Avoidance of Deadlocks and Related Problems

Especially in case of a high vehicle density, the combined procedure of braking and eluding as described above can trigger the emergence of a deadlock situation. Specifically, due to the superposition of different mutually independent force components, units can reach a steady state or livelock (i.e., a situation where individual units alternate between different states in a periodic way) where no effective further motion is possible (see Fig. 1). Therefore, the affected units need to be released after undershooting a certain minimum speed (except for loading and unloading processes at the respective sources and sinks) to enable further movement. As a possible solution, deadlocks or livelocks can be detected by a simple logic comparing the instantaneous and preceding positions of each vehicle. If such a situation occurs, the unit has to be forced to calculate a new route, e.g., by making use of a prescribed set of checkpoints (see below).

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The two-dimensional autonomous movement of an AGV can only be realized with a detailed knowledge of the available space. Figure 2 presents an example of a situation where a vehicle is forced by an oncoming unit to give way such that it fails to pass a static obstacle at the correct side. In order to avoid such problems and thus ensure an efficient operation, one possible solution is to specify distinct checkpoints that need to be passed on the way between the unit’s origin and final destination. According to these prescribed checkpoints, a new route can be interactively recalculated onboard in case of an arising deadlock or livelock. For this calculation, it is necessary that each unit has access to full information on the positions of all static obstacles.

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Another possible example for the emergence of deadlock situations are frequently used transportation relations where multiple vehicles have the same destination. For example, one could think of a machine which has to be continuously supplied with raw materials by AGVs (sink), or continuously produces semi-finished goods that need to be transported by AGVs to the next processing stage (source). If there is (intermittently or permanently) more transportation capacity (i.e., more AGVs) concentrated in the ultimate vicinity of this source or sink than necessary to serve the actual demand (which is determined by the production capacity and the time necessary for loading or unloading the transportation units) this can result in the mutual blocking of individual vehicles (see Fig. 3). Note that this is mainly a problem of properly designing the surroundings of sources and sinks in terms of available space in combination with a feasible job scheduling. However, given that a corresponding problem actually occurs due to whatever reasons, there are different possibilities to circumvent the resulting conflicts and avoid a deadlock. One simple approach is defining a certain area in the direct vicinity of the respective source or sink which all AGVs can only access after receiving an individual permission. In this case, the units have to communicate to receive this permission. This can be realized either centrally (by communication between the AGVs and some control entity representing the destination) or decentrally (by pairwise communication between the concerned AGVs). In the latter case, one could for example adopt the social goods concept [25, 26] to enforce individual AGVs to give way to others if they have a transportation job with lower priority (e.g., a later due date). A further possible improvement is the separate definition of incoming and outgoing routes by disjoint sets of checkpoints. As a final (although typically less severe) problem, one has to examine the behavior of subsequent AGVs sharing the same route. Specifically, if two successive vehicles have the same trajectory, the repulsive force from the former would decelerate the latter. In order to avoid unnecessary braking and acceleration demands, adaptive methods should be used for adjusting the velocity of the second AGV according to the velocity and direction of motion of the first one.

This work presented a first conceptual study on the applicability of pedestrian dynamics based models for establishing an autonomous movement control of AGVs in intralogistics or container terminals. In particular, the case of free motion in a two-dimensional physical space has been considered which is more frequent and more flexibly applicable than the alternative of track-based vehicles.

The empirical, partially simulation-based considerations described in this contribution indicate that in combination with additional procedures ensuring the avoidance of collisions, deadlocks, and livelock situations, the social force concept provides a prospective foundation for the designated purpose. In particular, the proposed approach is applicable in the case of moderate to high vehicle densities [24]. However, without the discussed modifications the basic social force model is not directly applicable. Potential problems especially emerge in areas with particularly high vehicle density and/or few available space, such as bottlenecks in the given spatial geometry of the working area or around frequently visited sources and sinks. Most of these problems are practically avoided by introducing checkpoints at bottlenecks or diverges of different possible routes, as well as by establishing local permission strategies based on individual priorities. While the latter can be practically realized by means of a centralized control unit within a restricted spatial domain or sophisticated self-organisation concepts [25, 26], the major part of the transportation process is still subject to a fully autonomous movement control that is realized according to an on-line evaluation of the positions of static and dynamic obstacles.

In summary, the proposed pedestrian dynamics-based approach appears suitable and interesting for potential industrial applications. However, further research is necessary to fully explore its corresponding potentials and limitations in more detail.