# Robotic Coverage Path Planning for Ultrasonic Inspection
## 2 Related Work  
Most existing work on coverage path planning relates to problems where a robot moves in 2D space. This is interesting for applications such as lawn mowers, vacuum robots, and harvesting machines. In the literature, recent surveys on coverage path planning have limited focus on 3D coverage [2; 3]. Many classical approaches, such as cellular decomposition [4], and grid-based [5] and graph-based [6] methods, are difficult to extend to 3D cases. In general, the computational complexity tends to increase massively with the transition from 2D to 3D. Many coverage planning algorithms address the problem of a mobile robot that is required to visit all locations in the region of interest. The region of interest is discretized so that it is represented by a finite number of points or grid elements [7; 8]. Depending on the application, additionally, the orientation of inspection positions needs to be considered. This enlarges the space of possible solutions, leading to increased computational complexity. For on-machine inspection with a 5-axis system, a method was proposed that considers multiple orientations per inspected point [9]. Subsequently, the points with different orientations are connected by solving a traveling salesman problem. Robotic inspection using ultrasound is relevant for multiple quality control applications in industry. An example for robotic UT is the inspection of components of a thermonuclear reactor [10]. Even in the medical field, ultrasonic scanning by a robot is an interesting topic. A recent method [11] is based on force-feedback during the scanning process. In the context of robotic scanning, recent work involves in-line dimensional inspection via spatio-temporal adaptive sampling (STAS) [12]. This method estimates deviations of the whole part based on partial measurement of a free form surface. In addition, the method adaptively selects the next region to be measured in each step. An interesting extension of coverage path planning deals with multi-robot environments [13; 14]. For most applications, this requires some kind of synchronization of robots. Although there could be some potential of using our method in a multi-robot environment, we do not further address this scenario. As computational complexity is often high in the context of 3D surface inspection, some papers propose heuristics that iteratively grow the inspected region. One method uses a geometric random tree to sample possible future configurations [15]. This was shown to provide good scaling properties with respect to the complexity of scenarios. In general, the concept of iteratively growing the covered area with influence from control theory is referred to as receding horizon. A recent work [16] deployed this concept for online path planning to adaptively acquire information from the surface. Information already acquired is inserted into a manifold Gaussian process and influences the progressive calculation of the path. A problem that is related to coverage path planning is classical point-to-point robot path planning. Robot path planning addresses the problem of finding a valid sequence of configurations or states by which a robot moves from some start position to a target position. Depending on the space of possible states, this can have different levels of complexity. There are well-known algorithms available, e.g., rapidly exploring random trees (RRT) [17]), that solve the point-to-point path planning problem. In the following, we deploy standard solutions for point-to-point robot motion planning. This is mainly relevant for situations where sub-paths that cover separate regions need to be connected. The main intention of such a connecting motion is not to increase coverage but to perform a transition from one region or robot configuration to another. An adequate definition of coverage is an important topic for CPP algorithms. Definitions of coverage can be very diverse, ranging from point-wise coverage [13] to drones that spray disinfectants [18].