# Research Progress on Synergistic Technologies of Agricultural Multi-Robots
## 3 Research Progress on Synergistic Technologies of Agricultural Multi-Robots
### Formation Control
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  
Figure 16: Formations of agricultural multi-robots: (**a**) the head and tail robots in the formation are used to guide UGVs in I-shape 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]  
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. 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 [117, 119, 120, 48] is also another classic model and widely used in the formation control of agricultural multi-robots. Japan's [PERSON] 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 (I\(-\)I) 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, [PERSON] 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 formation-keeping 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 (I\(-\)\(\varphi\)), (I\(-\)I) 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.