# Collaborative Multi-Robot Formation Control and Global Path Optimization
## 1 Introduction
[PERSON] et al. [20] introduced key obstacle influence factors into the heuristic information, which changed the pheromone volatility rate and improved the convergence speed of the ACO. [PERSON] et al. [21] constructed the initial pheromone with unequal allocation and introduced a dynamic penalty method to improve the ACO. [PERSON] et al. [22] proposed an ACO with faster convergence and better obstacle avoidance. [PERSON] et al. [23] improved the search speed of the algorithm using multiple ant colony partitioning and a cooperative mechanism. [PERSON] and [PERSON] [24] combined GA with ACO to improve the robustness and the solution quality. [PERSON] et al. [25] proposed a new pheromone diffusion gradient formula to accelerate ACO. The above improvement strategies were optimized for the disadvantages of APF and ACO, respectively, but the trade-off between path optimization and computational cost still faced a tough choice. Some scholars started to combine the advantages of ACO and APF to find a new solution strategy. [PERSON] et al. [26] optimized the initial pheromone of ACO with an improved APF algorithm to improve the directionality of ants in the early stage of path search. [PERSON] et al. [27] combined APF and ACO to improve the convergence of the algorithm. [PERSON] et al. [28] used APF to optimize the pheromone matrix of the ACO to improve the algorithm performance and search efficiency. [PERSON] et al. [29] used the improved APF ensemble to optimize the setting of heuristic information and volatile factors of ACO to avoid the problem of falling into a local optimum. Although the above studies have improved the defects of the single algorithm to some extent, APF-ACO still has the problems of large computation and poor performance of the optimal solution due to the influence of APF and ACO's own mechanism [30]. Therefore, a new APF-ACO is proposed in this paper, which improves the convergence speed and the optimization-seeking accuracy of the basic algorithm and can solve the robot path planning problem as well. However, a single path planning algorithm does not enable robots to form effective formations and is less controllable, and multi-robot formation path planning has also attracted the attention of many scholars. Without considering information delay, [PERSON] et al. [31] investigated distributed formation control of multiple mobile robots based on graph theory and Lyapunov theories. [PERSON] et al. [32] proposed a virtual spring path planning and formation control method for multi-robot systems. [PERSON] et al. [33] investigated an observer-based approach to robot formation control. [PERSON] et al. [34] combined graph theory with ant colony algorithms and applied them to the study of path planning for robot formations. [PERSON] et al. [35] applied a third-order control protocol to implement the control of robot formations. [PERSON] et al. [36] proposed an optimization model with multi-stage consistency improvement to solve the problem of decision making in the absence of knowledge. [PERSON] and [PERSON] [37] combine algebraic graph theory with distributed control to study the robot formation framework. [PERSON] et al. [38] proposed a formation consistency control method for mixed-order systems with switching topology to improve the stability of formation control. The studies mentioned above have investigated the construction and control of robot formations using methods such as graph theory and consistency control, but relatively few studies have combined the two. In this study, we use a graph-theoretic approach for robot formation construction and a consistency control approach for maintaining the formation. In summary, this paper investigates the global path planning problem for multi-robot formations in static environments.