# An Artificial Plant Community Algorithm for Collision-Free Multi-Robot Aggregation
## 1 Introduction  
Due to their good mobility and fatigue resistance, various robots and unmanned aerial/ground vehicles--such as robotic arms, auto-guided vehicles (AGVs), unmanned aerial vehicles (UAVs), and unmanned surface vehicles (USVs)--have been widely used to replace humans in carrying out dangerous and complex tasks [1]. Collaboration and aggregation among multiple robots often provide advantages that cannot be achieved with a single robot [2]. However, collisions are also prone to occur during the aggregation of various robots. The collision-free multi-robot aggregation problem (CMAP) is a significant challenge that arises in many real-world applications. To address the CMAP, multiple robots must be assigned in an optimal manner to implement geographically distributed tasks collaboratively while avoiding collisions and ensuring a minimal makespan (i.e., the completion time of the last task) [3]. In many security and rescue applications, multiple robots are often required, and consideration of the CMAP can allow for optimized assignments, instructing the robots to aggregate to achieve important goals while simultaneously avoiding collisions. For example, when facing a fire, it is often necessary for a swarm of robots to aggregate and carry out firefighting tasks on important fire sources, as serious fires can cause huge losses of life and property [1,3]. However, finding the global optimal solution to the CMAP is not an easy task, making the CMAP a challenging issue. For example, the emergence of a task is random, chaotic,and unpredictable [1; 4], and it is generally impossible to know in advance where the next emergency task will appear in large-scale firefighting and disaster rescue situations. Popular methods often divide the CMAP into two sub-problems: the multi-robot aggregation problem [5] and the collision-free multi-robot problem [6]. In each sub-problem, collaboration between multiple robots allows each task to be assigned to various robots, expanding the search space to that of non-collaborative task assignment problems [7]. In a dynamic scenario, multiple robots search for the goals to complete tasks, and more robots can dynamically aggregate to execute the emergent missions. A tiny disturbance in the solution process may produce a different makespan; therefore, the CMAP is NP-hard and requires too high of a computational cost to be effectively solved in real time. To address this complicated problem, researchers have developed many methods to guide the activities of robots. Heuristic algorithms often achieve near-optimal results in a very short time and are considered promising for the execution of multi-robot system missions; such algorithms include grey wolf optimization (GWO) [2], the genetic algorithm (GA) [3], particle swarm optimization (PSO) [4], fuzzy logic (FL) [5; 6], and colony optimization (ACO) [7], deep learning (DL) [8], and reinforcement learning (RL) [9]. In the CMAP context, any delay in a task may result in a large aggregation of emergent tasks, making the solution space very rugged. The following emergent tasks are not yet detected by most robots, as they have not arrived at this point. Artificial intelligence-based approaches [10] can effectively help to allocate the task to a suitable robot through the analysis and synthesis of environmental information and task data. However, most studies focused on the CMAP have separately focused on aggregation or collision, where the aggregation and collision information are not integrated [11]. If only an optimal solution for the aggregation problem or collision problem is obtained, it may be impossible to obtain an optimal solution to the global problem [12; 13]. Additionally, traditional solution methods and heuristic algorithms cannot efficiently search for all solutions in uncertain environments [14; 15]. When an emergent task is detected, it is difficult to modify the pre-planned solution to re-assign all tasks. Our research motivation is to solve the CMAP efficiently.