Distributed Node Deployment Algorithms in Mobile Wireless Sensor Networks: Survey and Challenges

The distributed decision-making process that leads to coordinated movement has been seen in many animal aggregations, such as bacterial colonies, insects, fish schools, bird flocks and leadership groups of mammals and crowds [5, 6, 12, 29, 79, 93, 96]. In a flock of birds, for instance, individual birds maintain a minimum distance from their neighbours while collectively forming a flocking-level behaviour [2]. In some works [39, 87, 103], the behaviour of such individual units is explored. Moreover, the observed coordinated behaviour, called collective motion in the work of Vicsek et al. [112] and Vicsek and Zafeiris [113] is defined under the “nearest neighbour rule”. Based on the nearest neighbour rule, each individual in a group goes by its own decision, but the decision of where to go is affected by its neighbours’ locations [19]. Furthermore, the behaviour of each unit is represented by a mathematical model [103]. This mathematical model can inspire its usage in other subjects where distributed decision making is the goal of moving the particles in a group. For instance, the algorithm presented in the work of Liu et al. [69] uses Lyapunov methods to maintain cohesion during mobile swarm movement that follows a leader even in the presence of sensing delays and asynchronism. Moreover, the stabilisation and control of the formation of mobile robots are discussed in elsewhere [31, 37] which employ graph-theoretic algorithms for the same purpose.

A simple discrete-time model of n moving nodes with the same speed but different angles is presented based on the animal aggregation in the work of Vicsek et al. [112]. This model updates each node’s heading based on the local rule, which is the average of the neighbouring nodes’ headings, including itself. Despite the absence of centralised coordination, by using various simulations, it has been demonstrated that all nodes move in the same direction after some timesteps [112]. Furthermore, to converge the sensor nodes’ movement to a desired direction in this model, a leader node with a fixed heading is considered in the group of sensor nodes [57].

Many studies have focused on developing a mathematical model to analyse animal aggregation behaviours. For instance, the potential function theory is used to understand flocking behaviour [63, 88]. Besides, a theory to model the motions in a fish school is presented in the work of Lopez et al. [70]. A comprehensive review of the mathematical aspects of animal aggregation behaviour is also presented in the work of Jadbabaie et al. [58].

The mathematical models of animal aggregation have inspired many distributed deployment algorithms in MSNs [1, 21, 77, 100], which are discussed in this section under the Force-based category in the Nearest Neighbour rule-based sub-category. In this article we refer to these algorithms as Triangular Blanket Coverage (TBC) [21], Decentralized Coverage Algorithm (DCA) [100] and Boundary Tracking Decentralized Control System (BTDCS) [1], for the sake of simplicity.

The area coverage algorithm, TBC, is proposed for WSNs, which is inspired by the nearest neighbour rule in animal aggregation [21]. The TBC moves the sensors into the requested area to make a triangular lattice pattern that fully covers the given 2D region between boundaries. The triangular lattice pattern is known as the best structure for sensor nodes’ placement, as theoretical analysis has proven that a triangular pattern placement can provide maximum coverage for the fewest number of sensor nodes and the least amount of energy consumption [21]. In this algorithm, the sensor movements to achieve this structure are led by a decentralised control law that is introduced in the work of Cheng and Savkin [20]. The mathematical model of animal aggregation inspires the control law that moves sensors in lines. Although the control laws result in a high coverage, the boundaries information guide the sensors’ movement and increases the coverage to full coverage. In this way, the algorithm moves every sensor in consecutive steps toward its desired place (a location on the triangular lattice) by making an average of its neighbours’ angles and coordination, and the movement calculation is also influenced by boundaries coordination. The movement of sensors at every timestep and the calculation of the next location are based on the received information from neighbouring nodes and the boundaries limitations. The complex model and the decision making, which happen in every sensor node at every timestep, make TBC a high energy consumption algorithm with high communication and computational complexity. In Figure 2, an example of the initial deployment and final deployment of sensor nodes is shown, where the area is completely covered in the final phase of the algorithm.

A more general version of the TBC algorithm, DCA, is presented in the work of Savkin et al. [100]. Unlike TBC, the RoI in DCA is not priorly known to the sensors and has an arbitrary shape. Considering the same control law as in the work of Cheng and Savkin [21], the asymptotic optimality of DCA is provided. In this algorithm, the sensor nodes know the requested boundary. However, there is no control to limit the number of sensor nodes at the area’s edges and sensors’ locations may also be outside of the boundary. Figure 3 depicts an example of DCA.

In the work of Ahmad [1], the BTDCS algorithm provides full coverage for any arbitrary shape. However, in contrast to DCA, the control laws in BTDCS omit to pass the boundaries. The restriction on surpassing the boundaries decreases the necessity of extra sensors on and above the boundaries. Therefore, the number of sensors that are needed for full coverage decreases while providing full coverage. The decreased number of sensors is resulted from discarding two sensors at every horizontal grid of the area that are not necessary. Although this process requires more energy and increases the complexity of the algorithm, the reduced number of sensors can save the deployment cost. An example of the final deployment of the BTDCS algorithm applied to the same initial arrangement of Figure 3(a) is shown in Figure 4.

The modelling of animal aggregation for mobile sensor nodes is not a simple process and has its own challenges. The main challenge is that there is no global knowledge of network topology and the decision-making process should be distributedly. In a distributed network, each node needs local data processing, data fusion and data compression because it has to be able to decide individually for its location and movements [56]. The distributed decision is also influenced by the physical constraints of mobile sensors, such as limited lifetime and communication range. Although the Nearest Neighbour rule-based algorithms provide full coverage even in intense initial deployments, the high energy consumption of every single sensor node in the network is a considerable weakness. Moreover, the single leader that converges the sensor nodes stream leads to the introduction of a single point of failure in the algorithm.

In this section, the Repulsive Force algorithms as another sub-category of the Force-based category are studied. The Repulsive Force algorithms are random localisation algorithms that do not use the nearest neighbour rule. Although some of the Repulsive Force algorithms are inspired by the same natural phenomena as the Nearest Neighbour rule-based algorithms, the modelling of these algorithms is different. In this section, the Swarm-Based algorithm [77] is discussed, followed by the Distributed Self-Spreading Algorithm (DSSA) [53], Smart Self-organization Node Deployment (SSND) [42] and the Virtual Force Algorithm Inspired by Spring Force (VFA-SF) [30].

The schooling behaviour of fish influenced the Swarm-Based algorithm [77]. The local rules in the school of fish are interpreted as different forces to provide coverage in this algorithm. Every sensor node considers three forces: (1) a separation force that moves the sensor node away from its neighbouring nodes to increase the size of the swarm, (2) a cohesion force that controls the swarm’s connectivity, and (3) an alignment force that holds the sensor node aligned to its neighbouring nodes and speeds up the relocation to existing holes. Although the Swarm-Based algorithm and Nearest Neighbour rule-based algorithms [1, 21, 100] are inspired by animal aggregation, the mathematical model in the Swarm-Based algorithm is not the same as the Nearest Neighbour rule-based category and, hence, it falls under the Repulsive Force category. Unlike the Nearest Neighbour rule-based algorithms [1, 21, 100]. the Swarm-Based algorithm is a random algorithm and not a deterministic algorithm (i.e., sensors have fixed locations to move and full coverage is guaranteed). In random localisation algorithms, full coverage is not always achievable; however, the total distance that sensor nodes take and the energy that is used are much less than those of the deterministic algorithms.

DSSA is another Repulsive Force algorithm that is inspired by the equilibrium of molecules [53]. The uniform distribution of molecules when they are in their lowest energy with almost the same distance from each other in the stable status, known as the equilibrium of molecules, has motivated DSSA to replicate the same behaviour to cover a required area. In DSSA, the force between any two neighbouring nodes that follows Coulomb’s law is called partial force. Every sensor node moves to its desired location by partial forces at every timestep, independent N sensor nodes’ movement whether they are involved in its neighbouring nodes or not. The partial force is calculated based on the current location of the sensor, the distance between the sensor and its neighbouring nodes, and the local density (i.e., the number of neighbouring nodes). Therefore, for every sensor node at each timestep, the total force is a cumulative entered force of all neighbouring nodes in its one-hop neighbourhood. As long as the condition for terminating the algorithm execution is not met, the partial force calculation procedure is carried out. In Figure 5, an example of the partial forces between \(s_1\) and its neighbouring sensor nodes is demonstrated.

The obtained coverage of DSSA and the nature of the distributed partial force used in the algorithm make DSSA a leading approach to provide blanket coverage. However, many of the assumptions in DSSA are not feasible in realistic applications. The two major challenges of DSSA are recognised as high energy cost and latency. These are due to the fact that almost all sensor nodes move at every timestep, even if it is not necessary. Moreover, every sensor node receives obsolete location information from its neighbouring node as they report their current location while they are still moving at the same time as the report.

SSND is another proposed algorithm under the Repulsive Force sub-category, which is inspired by the equilibrium of molecules [42]. The SSND algorithm elects a prior sensor node in each neighbourhood to avoid the unnecessary movement of all sensor nodes at each timestep. Therefore, at each timestep, only a selected number of sensor nodes move to improve the coverage.

The SSND procedure calls an eligibility function that returns an eligibility value. The eligibility value along with location and some other information are exchanged among one-hop neighbouring nodes. Afterwards, the received information composes the final entered force between the neighbouring node, as shown in Figure 5, and identifies the sensor node with the highest eligibility value in the neighbourhood. The most eligible sensor node moves to the desired location at each timestep while other sensor nodes remain in their locations. The movement of only one sensor node in each neighbourhood at every timestep ultimately distributes the sensor nodes uniformly while normalising the local density in every neighbourhood.

The SSND algorithm has developed the final percentage of coverage while reducing energy consumption. This clarifies the fact that moving only necessary sensor nodes in each neighbourhood provides not only the accurate location of the neighbouring sensor but also sufficient sensor movement to improve the coverage. However, SSND consumes more energy than those under Geometrical algorithms due to a lack of environmental information.

In the work of Mathews et al. [77], a virtual spring force algorithm and an improved virtual spring force algorithm together with a performance evaluation method for sensor deployment algorithms in a large-scale MSN are presented. The virtual spring force moves sensor nodes based on their relative position to neighbouring nodes and the presence of an event [124]. The goal of the proposed algorithms is to create a hexagonal structure (i.e., a triangular pattern) of the sensor node’s locations in the network, which is a known solution, as mentioned earlier. In some sub-regions, the process of calculating spring virtual forces resulted in the prior creation of a stable hexagonal structure [77]. These sub-regions are still connected with sensor nodes as a hexagon with no exact number. However, in a large-scale network, a hollow or distorted balance is created, which is unavoidable.

VFA-SP became applicable in large-scale networks by enhancing the algorithm through adding an external force that starts from the centre of the target area. As central areas are more important to be covered than the edges of the area, the external force is added to the sensor nodes that are at the corners. The applied external force to these sensors encourages the formation of a hexagonal structure while avoiding the formation of unusual structures or holes at the early stages of the algorithm. The presented simulation results confirm the legitimacy of the algorithm’s assertation and creation of a complete hexagonal structure. However, the provided coverage is highly dependent on the precise reported locations of sensor nodes, and failure in detecting the precise location hugely affects the performance of the algorithm. Moreover, sensor nodes need to wait for an update of their neighbours’ locations before approaching the estimated location, which causes some delay in the process. Finally, different environment requirements need different initial parameters for the algorithm that are neither specified values nor relevant to previous conditions.

In summary, the Force-based deployment algorithms are costly in terms of consumed energy. However, the deployment algorithms in the Nearest Neighbour rule-based sub-category guarantee full coverage if there is no failure in the system due to the existence of a single leadership cluster in the network. In the Repulsive Force sub-category, unlike the Nearest Neighbour group, sensor nodes can freely move in the area with less energy consumption while being more robust to system failure due to losing one or more sensor nodes.