## 1 Introduction  
Distributed and networked unmanned aerial- and/or ground-based vehicles (UAVs and UGVs) for radiological contamination mapping can provide a safer and more efficient option for surveying large areas of interest. The ability to produce a timely and accurate representation of contamination is significant in applications such as nuclear emergency response, tactical mission planning, and post-event procedure development, among others [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The primary objective for mapping radiological contamination is to make an accurate measurement of the radiation in predefined areas. The aerial/ground coverage by the UAVs/UGVs and the spatial resolution of the measurements are two important aspects that determine the fidelity and efficiency of the mapping technique and motion planning procedure. Adequate coverage of a predefined area ensures that any relatively small contamination features are accounted for in the radiation map. Better spatial resolution of the calculated contamination provides a more detailed and representative map. Both coverage and spatial resolution are dependent on the detector efficiency and prescribed trajectory of the UAV/UGVs. The use of UAVs and UGVs for radiation mapping has been demonstrated in previous works where uniform survey routes are typically employed by using a raster motion trajectory throughout the area [2]. However, these uniform survey routes are unguided by real-time data, making for a less efficient survey, and are only able to produce maps in the vicinity of where the vehicles have visited previously. Other methods rely on predetermined motion paths and could be considered semi-autonomous, but require a priori knowledge on the nature of the contamination sites. The ability to implement a fully autonomous motion planning procedure that utilizes real-time sensor data would allow for the complete removal of human-in-the-loop dependencies. Table 1 summarizes the advantages and limitations of typical survey methods. The methods for coverage of an unknown environment using multi-vehicle systems relies on the ability to characterize a density function of a scalar field [12; 13; 14; 15]. The optimal solutions to the coverage control problem for unknown density functions have previously been shown; specifically, the use of Gaussian processes to describe unknown density functions of the scalar field is particularly convenient [16; 17; 18; 19]. Previous approaches relevant to this work implement Gaussian process regressions in combination with control laws based on centroidal Voronoi tessellations, where the control algorithms are governed by information entropy to reduce prediction uncertainty [17; 18; 19]. In this work, we implement Gaussian process regressions (GPR) to predict the unknown density function similar to the approaches in [16; 17; 18; 19]. However, rather than using the minimization of information entropy to govern the control laws, we propose to use the difference in successive predicted density functions. The difference in successive maps, hereafter referred to as the prediction-difference map, provides information that points toward the direction of the largest discrepancy between the current and previously predicted scalar fields to produce a convergent map. We show in simulations that the proposed motion planning procedure can offer a fully autonomous controls platform that reduces the overall survey time to reach a convergent radiation contamination map and does not require human-in-the-loop operations. Although the results shown in this work assume velocities more suitable for UAV systems, the fundamental methods can be applied to any available distributed UAV/UGV systems that have autonomous control capabilities as the technique ultimately provides optimal motion trajectories regardless of vehicle type. The paper is structured as follows: Section 2 describes the radiation transport simulations used to create datasets representing radiological contamination in large areas.