## 1 Introduction
### Informative Path Planning  
The developing requirements of robot monitoring have given rise to the challenge that the equipped devices are subject to limited resources, such as mission time and energy. Therefore path planning for vehicles to maximize the information gathered is of significance. In the aerial environment, many works have been done to maximize information gathering. 2D spaces were divided into several cells to find solutions for coverage paths in [9; 10]. The cells can be trapezoidal or boustrophedon [11; 12; 13]. Finding the shortest and most efficient sequence of cell visiting, and generalizing the path, was proven to be NP-hard and was formulated as a TSP problem by [PERSON] et al. [14]. [PERSON] et al. 's work [15] decomposed the environment into ranks. They solved multiple TSP problems on the ranks to minimize the number of turns taken by robots, which relates to the mission time. [PERSON] and [PERSON] reduced the problem to a generalized traveling salesman problem (GTSP). They could obtain optimal solutions in reasonable durations. They also proposed a strategy with which to recharge UAVs by UGVs during flight [16]. Their former work proved the GTSP solver GLNS performs better in terms of speed and path generation than other TSP solvers [17]. Our former studies [18; 19; 20; 21; 22; 23; 24] involved a lot of research on path planning in underwater and sea surface cases. Concerning the sea surface, [PERSON] et al. 's work [25; 26; 27] presents several algorithms for single and multiple unmanned surface vehicles. [PERSON]. [28] proposed a dive planning method to monitor underwater environments. [PERSON] et al. [29] proposed a method to efficiently inspect underwater structures using AUV, based on Bayesian active learning. [PERSON] et al. [30] presented a method to decompose the environment into several subspaces and solve the problem in two levels: sequence of subspace visiting and detailed coverage in subspaces. To efficiently grasp information from the environment, [PERSON]. et al. [31] directly planned and optimized paths via a video stream gathered by a UAV. [PERSON] et al. proposed a novel algorithm based on Octree to achieve full coverage of unknown environments [32]. In [33], [PERSON] et al. proposed a sensor-driven, two-level seabed path planning solution for AUV, which is available for any acoustic or optical sensor. In [34], [PERSON] et al. presented a method that was combined with a new concept coined branch entropy based on hexagonal cell decomposition to achieve efficient multi-objective optimization. However, the operating environment for an HAUV is simple neither underwater nor aerially. We consider the surroundings of the HAUV to be simple in 3D when few obstacles exist in the environment, and safety constraints mainly come from the terrain. Considering a multidomain mission for an HAUV, simple path planning is not sufficient. In addition, some constraints should be set according to the HAUV's motion capabilities. Considering the motion capabilities of a UAV, [PERSON] and [PERSON] developed an algorithm to minimize the fourth derivation of a position function (snap). They reduced the cost of a flight and could satisfy constraints on safety, velocity, and acceleration as well [35]. Based on the snap minimizing methods, [PERSON] set collision-free flight corridors and generated trajectories in corridors to ensure flight safety [36]. Similarly, [PERSON] et al. 's work set corridors for UAVs, but with a fast marching-based method. They also used a Bernstein polynomial to represent trajectories piecewise [37]. [PERSON] et al. [38] proposed a CIPP algorithm that optimizes a parametrized path in continuous space. All the previous works we mentioned focused on UUVs and UAVs operating with simple domain path planning. However, multidomain missions such as mapping isolated water regions and inspecting submersed structures bring challenges to such vehicles. A heterogeneous vehicle team of a UAV and a UUV is currently used to accomplish the multidomain tasks according to [39].