-Industry 4.0 is a promising solution for the management of manufacturing processes, due to its potential to increase both energy saving and optimized production. Within this context, in this paper we propose the use of automated connected vehicles fleets for the autonomous handling of products among workstations in manufacturing processes. Numerical results confirm its effectiveness w.r.t a typical production process.
In the last decades, Industry 4.0 has raised an emerging interest from researchers, device developers and industries, since it allows to increase energy saving, contributes to cost reductions and increases an optimized production. The industry and society have gradually developed the idea of Industry 4.0 [1], smart factories [2], networking manufacturing [3] and to this aim several architectures have been recently proposed [4]– [6]. In the meantime, new information and communication technologies (ICTs), as the industrial cloud [7], [8], industrial internet of things [9] and high performance embedded system [10] have been recently proposed as key tools for manufacturing industry with the aim of combining the higher productivity demands, energy savings and flexibility market. In particular, industrial wireless networks (IWNs) are the most promising technologies for rapid achievement of Industry 4.0 advantages. In this regard, IWNs have been rapidly entering in manufacturing concept and are becoming a fundamental issue for the achievement of smart factories and the architecture of Industry 4.0 [11].
In order to achieve a smart and flexible production, it is necessary to increase the deployment of autonomous products handling, during the different production steps, within the factory. For this aim, several approaches for trajectories optimization to track within the manufacturing area and the use of autonomous driving of vehicles fleets have been proposed [12]. Both the vehicles fleet size and the scheduling/dispatching have influence on the system throughput and, hence, they have been examined in the recent technical literature (e.g., see [13], [14] and references therein). However, research activities usually do Fig. 1. Example of resources dispatching path in manufacturing process [21] not focus on the design of cooperative control strategies for the deployment of autonomous fleets of connected vehicles in the manufacturing area, while classical attempts usually focus on fleet assignment in order to obtain the fleet operation cost minimization [15], [16], or on planning upkeep tasks in order to minimize the maintenance cost [17]. Therefore, scheduling and re-scheduling fleet assignment and maintenance planning are implemented in task-dedicated decision support systems [18].
In this context, the conjunction of the new tools for automated mobility developed in Smart City Initiatives with the concept of Industry 4.0 can increase the flexibility in the manufacturing processes by exploiting autonomous vehicles fleets that share information through IWNs [19], [20]. Following this paradigm, the paper proposes a cooperative control strategy for the management of a fleet of automated connected vehicles handling products among workstations in manufacturing processes. The paper is organized as follows. In Section II the problem statement is provided and the novel distributed control approach is presented. In Section III stability analysis of the multi-vehicle control strategy is provided. While, in Section IV is presented the simulation results, confirming the efficiency of the proposed control approach. Finally, conclusion and future work are drawn in Section V.
II.
AUTOMATED VEHICLES IN INDUSTRY 4.0
Automated vehicles can be used for material handling within a flexible manufacturing system, and for proving asynchronous movement of product pallets through a network of guide paths between the workstations. Each work station is connected to the guide path network by a pick-up/delivery station where pallets are transferred to/from the automated vehicles [21].
In this paper it is considered a manufacturing system (see for example Figure 1) consisting in M workstations and r kind of resources to be dispatched following p different paths (chosen according to specific optimization algorithm [12]). For resources dispatching we exploit for each p-th path a fleet of N vehicles travelling together with a constant speed and maintaining a prefixed spacing policy. Each vehicle within the fleet supplies the M -th station present in the path with a specific resource r. Moreover, each vehicle has to stop at the workstations along the specific p-th path, for the necessary time of resource manufacturing, i.e. Tw. Note that, in this preliminary work we assume the manufacturing time equal for each of the M workstations along the p-th path, while the distance among vehicles i and j within the fleet has to be equal to the distance between two different workstation, i.e. k and l at which the vehicles are parked. To realize the vehicles fleet, vehicles are organized as a string, with vehicles following one another along the p-th path and sharing their state information (e.g., the absolute position, the velocity, and the acceleration) with all other agents communicating through a V2V communication paradigm, as described in [22], [23]. Vehicles are equipped with on-board units that are configured as receiving and transmitting hosts. The reference motion is provided by the first vehicle of the fleet that acts as a leader. Within our framework, the behavior of the generic i-th vehicle (i = 1; : : : ; N ) in the fleet is mathematically described by a simple linear model that was possibly obtained by applying inputoutput feedback linearization to simplify the complexity of the model describing the longitudinal vehicle dynamics, and without considering parasitic time delays and lags as follows: r_i(t) = vi(t) v_i(t) =
ui(t);
1
mi
(
To achieve the control objective each vehicle exploit their own state information and the information sent by other vehicles in its communication range. On the basis of these information, each vehicle computes the desired acceleration that guarantees the fleet formation. Since vehicles share information through a wireless communication channel (V2V communication paradigm), it happens that information can be received by each vehicle with a different time-varying delay, whose current value depends on the actual network conditions [24]. This implies that the control strategy has to be based on these the delayed information traveling on the vehicular network.
Hence, the control strategy, that embeds the V2V communication delays, is chosen as: ui(t) = b [vi(t) 1 PN i j=1 kij ij [ri(t) v?(t)] + rj (t ij (t)) ij (t)v0 where kij > 0 and b > 0 are the stiffness and damping coefficients to be appropriately tuned to regulate the mutual behavior among neighboring vehicles (i.e., the decentralized controller parameters); ij mimic the presence/absence of a communication link between vehicles i and j; i is the degree of the vehicle i and represents the number of vehicles communicating with vehicle i; di?j is the desired distance among vehicle i and vehicle j that is equal to distance between the workstation at which the vehicles has to stop; ij (t) is the aggregate delay computed by vehicle i using the time stamps sent by its neighboring vehicles. Indeed, focusing on the p-th path segment close to the receiver vehicle, delay time ij (t) can be assumed bounded between a maximum constant value and a minimal constant value, e.g., min ij (t) max [25].
III. STABILITY ANALYSIS OF MULTI-VEHICLE CONTROL
STRATEGY
To derive the fleet dynamics under the action of the
collaborative strategy in (
?
di0
Re-writing the control action ui(t) (see (
Lemma 2: [23] Let F be the matrix defined in (
Theorem 1: [29] Consider the vehicular network in (
S1(1 . .
.
Sq(1
d1) < 0 ;
dq) < 0 ;
lim x(t) = 0
t!1
then the closed loop system (
Sketch of the proof: The above statement can be proved by using the Lyapunov-Krasovskii theory [26].
In what follows we provide, for the sake of brevity, a sketch of the proof that is based on the following steps [29]: i) Consider the following Lyapunov-Krasovskii function for system in (13):
V (x(t)) = x>(t)P x(t) + Pq=1 Rtt (t) x>(s)S x(s)ds; (22) where P = P > > 0 2 R2N 2N and S > 0 2 R2N 2N ( = 1; : : : ; m) are appropriately chosen; ii) Differentiate the functional in (22) along the trajectories of the system (13); iii) Select the control gains kij , b according to lemma 1, lemma 2 iv) Satisfy the following inequalities:
Q +
q q X S + X =1 8 > < > :
?
In this section, we show numerical results obtained via the software Matlab/Simulink, in which we consider considered a fleet of four automated vehicles plus a leader moving among six workstations. The reference behaviour is imposed by infrastructure with a trapezoidal velocity profile, with the aim of moving each vehicle among different workstations. Once each vehicle reaches the next workstation, the reference behavior ensures that it remains there for a time Tw that is required for manufacturing process. Without loss of generality, we consider the case a maximum velocity of 10 [m/s] with Tw = 10 [s], as depicted in fig. 2-a and fig. 3-a.
Moreover, each vehicle has mass mi = 1000[kg], while, at 0.4 0.2 0 -0.2 -0.4
0 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 the initial instant, is supposed to be stopped (vi(0) = 0; i = 1; : : : ; 4) at different workstation, i.e. p0 = 85, fp1(0) = 65 [m], p2(0) = 45[m], p3(0) = 25[m], p4(0) = 5[m]. Communication delays are modeled as stochastic variables with a uniform discrete distribution, i.e., i(t) ?; i(t) 2 [ min; max], with min = 0 [s], and max ? = 10:9 10 2[s], where the theoretical upper bound is within the average end-to-end communication delay that is typical of IEEE 802:11 vehicular networks [30]. As illustrated in fig. 2-a and fig. 3-a, and as expected from the theoretical analysis in section III, the strategy presented in this manuscript guarantees the tracking of the reference behaviour, while the position and speed errors converge toward zero, as reported in fig. 2-b and fig. 3-b respectively.
The paper presents a seminal work aimed to shows how automatic mobility concepts can increase flexibility in manufacturing industry. In particular, it illustrates the performance of a cooperative control protocol that allows the autonomous motion of fleets of conneced vehilces for products handling among different workstation. As future work we will consider the case in which the manufacturing time is different for each workstation and the desired trajectories of vehicles fleets can intersect among themselves.
The authors would like to thank Eng. E. Napoletano, Ph.D. student at Department of Information Technology and Electrical Engineering, University of Naples Federico II and Silverso Vespoli, Master Grad Student at University of Naples Federico II, for their valuable contribution.