# Smooth 3D Dubins Curves Based Mobile Data Gathering in Sparse Underwater Sensor Networks
## 1 Introduction  
As a result of recent advances in underwater sensing, acoustic communication, and battery technologies, underwater sensor networks (USNs) have obtained considerable attention for deployment in diverse areas such as marine environment monitoring and underwater resource exploration [1]. Nevertheless, the limited bandwidth and energy-constrained characteristics of acoustic communication make it challenging to collect data in USNs. Moreover, the sparsity feature of USNs makes it hard to guarantee their entire connectivity. Additionally, the traditional multi-hop transmission of terrestrial sensor networks will lead to energy holes around the stationary sink, as underwater sensors closer to the sink deplete their energy faster, so as to cause an energy-consumption unbalance problem. To deal with disconnected routing and energy imbalances, numerous research works have adopted mobile data collection technology. For traditional wireless sensor networks, an energy-aware path-construction (EAPC) algorithm that selects an appropriate set of data collection points and constructs a data collection path was investigated in [2], two approaches including data collection using a data mulle and sensor networks with a mobile access point (SENMA) are proposed in [3], and a computationally efficient motion-planning approach to solve the joint path planning and clustering problem by using space-filling curves is proposed in [4]. Additionally, [PERSON] et al. [5] focus on low-delay and high-throughput opportunistic data collection inwireless sensor networks with mobile sinks (WSN-MSs) of general network topologies and arbitrary numbers of mobile sinks. These methods complete the data collection task of wireless sensor networks depending on either multi-hop routing or mobile sinks. For limited acoustic communication in USNs, whole network connectivity cannot be guaranteed all of the time, such that multi-hop-routing-based data collection methods do not perform well. Currently, a widely used data collection method for USNs is by the assistance of one autonomous underwater vehicle (AUV) or multiple AUVs [6]. Usually AUVs with sufficient energy are employed to collect sensory data in sparse three-dimensional (3D) USNs. Generally speaking, mobile sinks can visit underwater sensors and collect data from them while moving along a specific path, thus avoiding the long-distance energy-intensive transmission of sensory data [7; 8]. As a result, AUV-assisted USNs can efficiently improve data collection and extend the survival time of underwater sensors. Inspired by this, some energy-efficient data collection algorithms were proposed to balance the energy consumption between underwater sensor nodes. An enhanced energy-balanced data-transmission protocol was proposed to overcome energy inefficiency [9]. Also of relevance, to improve the effectiveness of mobile data collection, the mobility influence of AUVs was investigated by [PERSON] and [PERSON] [10]. A multi-hop data-gathering scheme was provided by [11] to forward data to the designated sink. An underwater acoustic sensor network with one mobile surface node to collect data from multiple underwater nodes was investigated in [12], whereby the mobile destination requests retransmission from each underwater node individually by employing the traditional automatic-repeat-request (ARQ) protocol. [PERSON] et al. [13] aimed to overcome the shortcomings of the wolf-pack algorithm (WPA) and improve three intelligent behaviors of the WPA, namely, scouting, summoning, and beleaguering. As a survey paper, [PERSON] et al. [14] studied path planning for the persistent autonomy of autonomous underwater vehicles. [PERSON] et al. [15] proposed a probabilistic neighborhood location-point covering-set-based data collection algorithm with obstacle avoidance for underwater acoustic sensor networks. However, most of this research was focused on the two-dimensional (2D) mobile data gathering (MDG) problem.