## 1 Introduction
Additionally, the ant colony optimization (ACO) algorithm has been used to solve the TSP [22; 23; 24], but little research has applied ACO to the CSP [25]. In the ACO, a colony of ants is dispersed into a graph to find the shortest path from the nest (start) to the food (goal). Over several iterations, the best path is exploited through a pheromone rewarding scheme [26]. ACO has been applied in several other related applications, such as vehicle routing [27], mobile robotics [28], and task scheduling [29], thus making the ACO algorithm a good starting point for solving the CSP. When a fleet of UGVs is used, an effective scheduling algorithm should be used to assign the UGVs to sub-areas. Compared to using a single UGV, fleet operations can reduce the overall travel time required and distribute the workload amongst the vehicles [30]. The scheduling algorithm is also responsible for generating the total path for all vehicles that begin at a depot (start location) and typically end at the depot or any other specified ending location. In the literature, several approaches have been proposed to schedule the vehicles, such as the GA [31; 32], and in other similar applications, tabu search (TS) [33] and simulated annealing (SA) [34]. The GA has shown great success and can effectively handle complex constraints commonly seen in scheduling problems. Other studies have had success using more trivial approaches such as assigning sub-areas to vehicles until the vehicle constraints are violated and then using zig-zag patterns within each sub-area to generate the coverage path [14]. Typically, the paths produced by any route optimization algorithm do not consider the kinematics of the vehicles. Since including the kinematic constraints in the optimization process can significantly increase the computation time, it is typically avoided. This means that the paths produced are initially infeasible and thus require further processing to modify them such that the vehicle turn radius is properly accounted for. One study uses Bezier curves to estimate a smooth centerline for UGVs to follow on roadways [35]. The problem with Bezier curves is that the curvature is difficult to control, and the paths produced by the Bezier curve in [35] are dependent on the boundary of the areas where they are generated. To gain better control of the curves, a Dubins curve can be used [36]. The Dubins curve can find the optimal path between a pair of waypoints with desired trajectories while considering a minimum turning radius. However, the UGV in the Dubins curve can only travel forward. This means that the Dubins curve often produces large turns to reach the target location and trajectory. One way to avoid such large turns is to allow forward and backward motion. The Reeds-Shepp path can be used to find the minimum cost path between a pair of points with starting and ending trajectories while considering a minimum turn radius and allowing forward and backward motions. The Reeds-Shepp path is used to enhance the feasibility of a path by modifying its waypoints with Reeds-Shepp curves [37]. However, the Reeds-Shepp path can add additional traveling when it is used to post-process a path. Due to unforeseen events, UGVs may become temporarily unavailable during operation. When this occurs, the remaining portion of the path assigned to the broken vehicle should be distributed amongst the operating vehicles. There are several different approaches explored in the literature to achieve this. In one study, a first-responder (FR) approach is proposed where the first vehicle that completes the scheduled paths can service the remainder of the broken vehicle's path [38]. However, this study does not use any optimization approaches. Therefore, it was improved in a future study by the same authors. In their subsequent study, the FR was improved by implementing the cooperative autonomy for resilience and efficiency (CARE) algorithm that uses a game-theoretic structure to reassign the path of the out-of-service vehicle amongst the fleet [39].