## 1 Introduction  
Sensor networks can perform various autonomous tasks in dangerous and harsh environments. In the case where each sensor has mobility, sensor network can perform environmental monitoring [1, 2, 3], area coverage [4, 5, 6, 7], formation control [8, 9, 10], target tracking [11, 12], or intruder detection [13, 14, 15, 16]. This article solves the coverage problem using multiple mobile sensors in an underwater cluttered environment. A mobile sensor needs to avoid underwater obstacles while it moves, since we consider 3D underwater environments with many obstacles. Underwater mobile sensors are deployed in the workspace, to perform collaborative monitoring and data collection tasks. For complete monitoring of the cluttered workspace, it is required to build sensor networks such that no sensing hole exists in the workspace. In underwater environments, optic, electromagnetic, or acoustic sensors have been used for wireless communication [17, 18]. But, building sensor networks in underwater environments is difficult, since communication range is rather short [19, 20, 21]. As a method to build underwater sensor networks autonomously, this article considers surface ships dropping underwater robots into the underwater 3D workspace. Here, each robot can move and has sensing/communication abilities. Since Global Positioning Systems (GPS) cannot be used to localize an underwater robot, this article introduces network building approaches to generate underwater sensor networks, while localizing every robots in the networks. As a ship arrives at the sea surface of the designated workspace, it begins dropping underwater robots while not moving at the site. Once multiple robots are dropped, they autonomously move into the unknown 3D cluttered workspace until no sensing hole existsin the workspace. As a robot moves in a cluttered workspace, it needs to avoid obstacles while maintaining the network connectivity with other robots. Many papers handled how to make multiple robots perform area coverage in 2D environments [4; 5; 8; 22; 23]. To build a sensor network in an unknown 2D workspace, the reference [2] made a single robot explore the workspace while deploying static sensor nodes. One restriction of this approach is that the robot must be large enough to carry all sensor nodes. Also, the robot must have enough power to explore the 2D workspace completely, since a sensor node has no mobility. the references [6; 7] used Voronoi tessellations to make all robots spread in order to increase network coverage based on distributed information from their neighbors. The authors of [8] considered deploying a swarm of robots into an unknown 2D environment to remove all sensing holes in the environment. The authors of [8] handled the case where each robot has bearing-only sensors measuring the bearing to its neighbor in its local coordinate frame. Cluttered environments were not considered in the papers addressed in this paragraph. Our paper is distinct from other papers addressed in the previous paragraph, since our paper considers the coverage problem in 3D workspace with many obstacles. Since a robot moves in a cluttered workspace, it needs to avoid obstacles while building the sensor network. As far as we know, only a few papers handled coverage path planning for 3D space. In [24], different deployment strategies for 2D and 3D communication architectures for UnderWater Acoustic Sensor Networks (UW-ASNs) were proposed. For deploying underwater sensors, the reference [24] introduced a sensor which is anchored to the sea bottom and is equipped with a floating buoy that can be inflated by a pump. The buoy pulls the sensor towards the ocean surface. The depth of the sensor can then be regulated by adjusting the length of the wire that connects the sensor to the anchor. However, this deployment approach cannot be used for covering a deep sea. Also, collection of these sensors is not trivial, since a sensor is anchored to the sea bottom.