• Formation forming

As shown in Figure 14, the formation of agricultural multi-robots generally has five types: column, I-shape, linear, V-shape, and W-shape, and the circular nodes in the formation structure represent robots. Each robot is represented by RID, such as R1 and R2, and the black arrow indicates the direction of robot movement.

**Figure 14.** Multi-robot team arrangement, the arrow points to the direction of robot movement, and the circle represents the robot: (**a**) The robots of R1 to R5 formed a longitudinal linear queue. (**b**) The robots of R1 to R5 formed an I-shape queue. (**c**) The robots of R1 to R5 formed a transverse linear queue. (**d**) The robots of R1 to R5 formed a W-shape queue (**e**) The robots of R1 to R5 formed a V-shape queue.

It is necessary to achieve the desired formation by determining the formation position reference point after determining the root formation. There are usually three reference points: center, neighbors, and leading robot; as shown in Figure 15, the position of each root node is represented by PID, such as P1 and P2, and the arrows indicate the relationship between robot dependence and information transfer.

• Formation control

From the perspective of a multi-robot system control framework, formation control is divided into two types: centralized control and distributed control. The former uses a centralized control unit to make decisions, optimize robot coordination, accommodate individual robot failures, and supervise the entire group of robots. The latter does not have a unified control unit, and a single robot makes decisions based on its local information [112,113].

At present, the method of centralized formation control of agricultural multi-robots includes the virtual structure, graph-theoretic approach [114], and model predictive control [115,116]. The method of distributing the formation control of agricultural multi-robots includes leader-follower [34,41,75,117] and the artificial potential field [113].

**Figure 15.** Selection of formation reference points: (**a**) Take the green dot, in the center of P1 P2 P3, as a reference. (**b**) P1 and P3 take neighbor P2 as a reference, P2 takes the nearest neighbor P1 as a reference. (**c**) Take the leading robot P1 of P2 and P3 as a reference.

Guillet et al. in France [44] adopted the bidirectional control strategy based on the virtual structure method. As shown in Figure 16a, each robot of the whole queue is a fixed point on the virtual structure. In this structure, the queue also increases two virtual leaders' interaction with the extreme robots and carries the desired global velocity for the whole fleet. The advantage of this method is simpler communication protocols and lower communication costs; however, the reaction of the robots is slower because of different acceleration performances.

**Figure 16.** Formations of agricultural multi-robots: (**a**) the head and tail robots in the formation are used to guide UGVs in Ishape operation. And the robot in the middle of the formation plows with farming tools in the field [44]. (**b**) Leader-follower method to control the formation in V-shape operation [105]

Berman et al. in the USA adopted the graph theory approach in bee pollination [108]. When a beehive was opened, the swarm robot flew radially from a moving beacon at a constant speed. And once it encountered the edge of the graph, it flew eastward at a fixed speed. As the robot flies over the plant, it acquires at least one flower within its range through sensors and hovers over the flower with unit time probability to pollinate it and record the location of the pollinated flower, returning to the hive after pollination and starting the next flight until complete coverage of the whole field is achieved. However, this method takes a long time and the model used in the simulation is too idealized. Whether they can be used for practical production needs to be further explored.

Smith et al. in Korea adopted model predictive control (MPC) and nonlinear feedback control respectively in fish tracking (simulation) [117]. MPC is a finite-domain rolling optimal control strategy with three parts: model, prediction, and decision, sacrificing optimality to some extent [118]. The fish population location was first divided into discrete points, and the discrete points were clustered to get the vertices of fish population density, and the transition model was constructed by transforming the movement of the fish

population into the movement between the vertices. The transition model and nonlinear feedback were used to obtain the transition matrix, and the underwater robot was guided to the vertices with high fish population density according to the transition matrix. The simulation results showed that the model-based control of the underwater robot could approach the nearest point, while the feedback control made the underwater robot approach the target point. However, in practice, the underwater robot movement speed is smaller than the fish population movement speed, and the method needs further improvement when applied in practice. The leader-follower method [48,105,117,119,120] is also another classic model and widely used in the formation control of agricultural multi-robots. Japan's Zhang et al. [106] used the leader-follower method to control UGV formation. As shown in Figure 16b, the relative positional relationship between the leader and the follower is determined according to the lateral and longitudinal safety distances (l−l) between the robots first, and then the distances are dynamically adjusted with feedback linearization technology to assemble different formations. Based on the leader-follower model, Bai et al. in China also combined slide mode control with the harvester swarm [48]. The kinematic model of the farmland leader-follower harvester swarm was established first, and based on this model; the asymptotically stable path-following control law and the formationkeeping control law were designed by combining feedback linearization and sliding-mode control theory. The advantage of this leader-follower model is that the behavior of the fleets can be controlled through the determined trajectory of the leading robot. The method decouples the cooperative navigation control problem into lateral distance keeping control and longitudinal distance keeping control. The formation control is mainly accomplished by establishing the location and gesture of the following robot relative to the leading robot, such as (l−ϕ), (l−l) first, then obtaining the formation information through feedback linearization, and finally adjusting the formation according to the threshold value. The leader-follower test results show that the real paths of robots can achieve centimeter-level average error with the planned path based on the safe distance of the vehicle. But this method is only applicable for environments involving a single-tasking of agricultural production and a fixed site. The adaptability to the headland turns is not strong. The question of how to maintain robot formation in encountering static or dynamic obstacles is not considered. If the leading robot malfunctions, the formation of the fleets cannot be maintained. Once the leading robot fails, the multi-robot system is susceptible to deadlock, and the formation cannot be maintained. The "leader" replacement method was proposed [121] to overcome this shortcoming, but the method has not been applied to agricultural multi-robots.

Ju and Son in Korea adopted Ramadge-Wonham theory in supervisory control to solve the above deadlock problem [122]. Supervisory control is a feedback control theory for discrete-event systems, where the control goal is achieved by observing the occurrence of events or states and using allowable or prohibited controllable events. Finally, a time-driven system is combined with a low-level controller and an event-driven system with a highlevel controller with the criterion of satisfying the behavior specification and maximizing the allowable events. Time-driven is used when there is no fault, and once the queue encounters a fault, the control outcome is selected based on event-driven. Simulation results demonstrate that the method can be used to control complex dynamic systems, but it has not been tested in practical applications.

The characteristics and formation process of the formation control methods are shown in Table 6.

From Table 6, it can be found that more complex or hybrid control methods are mostly used in simple or simulation environments, and the application in actual agricultural production is still dominated by the leader-follower method, and the research is also mainly focused on multiple machines traveling in a straight line in a fixed column. Further research should be conducted on how to continue driving, maintain the formation, or adjust the formation after multiple robots encounter obstacles.

