# Three-Dimensional Formation Control for Robot Swarms
## 2 Literature Review  
There are many papers on mobile sensor systems in 2D environments. Refs. [10; 11] considered deploying a swarm of ARs into an unknown 2D environment for achieving complete sensor coverage of the environment. The authors of [10; 11] utilized Voronoi tessellations for making all ARs evolve in time for increasing the network coverage based on local communication. Furthermore, the authors of [12] implemented their coverage controls utilizing real ARs.  
There are many papers on formation controls in 2D environments. Considering 2D environments with obstacles, [PERSON]. [13] tackled the distributed formation control of multiple robots. [PERSON]. [14] considered the problem of letting multiple nonholonomic robots follow a desired leader-follower formation under omnidirectional vision. The authors of [15] addressed distributed multi-robot formation control in the face of dynamic obstacle interference. In [16], a deep reinforcement learning (DRL)-based method was proposed to guide multiple robots through unknown complex 2D environments, where the centroid of the robot team aims to arrive at the goal while avoiding collisions and maintaining connectivity. Considering mobile ARs in 2D environments, [PERSON]. [17] proposed an online distributed algorithm based on the lattice of configurations, in order to recover the formation when a sensing failure causes the network to lose its rigidity.  
Considering 2D environments, [PERSON]. [1] discussed a decentralized algorithm for coordinating multiple ARs to spatially self-aggregate into an arbitrary shape, utilizing local communication only. The authors of [1] achieved multi-robot formation by allowing the robots to disperse inside the given 2D shape. If an AR believes that it is inside the shape, then it behaves like a gas particle with the shape as a closed container. Otherwise, the ARwanders randomly. However, random walk may lead to disconnected networks, which leads to the loss of an AR. [PERSON]. [18] presented a distributed algorithm that enables multiple robots to form arbitrary shapes and regenerate the shapes when cut.  
There are many papers on multi-agent formation control in 3D environments. Considering a fish-inspired robot swarm, [PERSON]. [19] showed that dynamic 3D collective behaviors can be achieved by measuring a robot's neighbors, without any centralized controls. The authors of [20] introduced a distributed control strategy for multiple agents, so that the agents can achieve a desired 3D formation based on local relative position measurements. Ref. [21] proposed a formation control method that enables multiple aerial robots to enclose a 3D target by generating a given geometric formation surrounding the target. The authors of [22] proposed a progressive assignment algorithm and formation control scheme that extends leader-follower formations for enabling multi-robot cooperation with minimal, one-way, local communication among agents. Ref. [23] developed a path planner for 3D robot formations and addressed how to adapt the formation shape for avoiding obstacles. Ref. [24] presented collision-free formation flight and reconfiguration for a team of autonomous helicopters. The control scheme in [24] was based on potential fields with the concept of a virtual leader. However, these papers on 3D formation controls did not consider the construction of a 3D formation for covering an arbitrary shape, as presented in our paper.  
To the best of our knowledge, the proposed multi-agent system is novel in the construction and control of a 3D formation for covering an arbitrary shape such that network connection is preserved while every AR maneuvers based on local communication. This article verifies that the proposed control scheme yields reliable accuracy against significant AR failures and movement error. MATLAB simulations are used to demonstrate the outperformance of the proposed formation controls.