It is undeniable that along with any type of industrial application there is an associated monitoring task. This is essential to avoid accidents, sabotage, or theft that could disrupt normal operation and, in the worst case, lead the industry to bankruptcy. For this reason, for decades a part of the personnel of companies has been dedicated to surveillance and control tasks. However, with recent advances in mobile robotics and optimization algorithms, it is possible to increase the efficiency of such tasks, reducing human errors and improving performance, quality, and monitoring.

In order to design a procedure capable of improving the quality of these tasks beyond human capabilities, it is imperative to address all the challenges that this implies. Specifically, within the scope of trajectory optimization, efficient route planning for autonomous vehicles is essential to minimize labor time while providing comprehensive spatial surveillance in the most efficient way possible.

In the current market there are robots that receive orders to navigate freely to a specific point (usually called free navigation) or to navigate following predefined trajectories. Both approaches allow the creation of paths that run through a given space, facilitating the implementation of surveillance applications. However, waypoints must be chosen judiciously to maximize efficiency, that is, to cover the maximum area in the shortest possible time ^[1].

2. Path Optimization for a Surveillance Robot

The need for safety in both outdoor and indoor environments has led to growth in the development of mobile robots with the ability to explore surfaces. Surveillance robots are used to monitor the behavior, activities, and other changing information for the general purpose of managing, directing, or protecting one’s assets or position [4]^[2]. Mobile robots assigned the task of surveillance play a crucial role in different sectors: security, health, rescue, agriculture, institutions, etc. [5]^[3]. As an example of this variety of uses, an application of surveillance of engine rooms in a ship by autonomous mobile robots to detect fire is presented in [6]^[4]. A map of the engine room was created using an autonomous robot, and when a destination was set on the map, a path was found and the engine room was surveilled autonomously. The paper by Zhang et al., reviews the latest research on AGVs and AMRs, and discusses visual tracking control technologies in civil engineering applications [7]^[5]. Security robots are commonly used to protect and safeguard a location, some valuable assets, or personal property against danger, damage, loss, and crime. Most of the works found in the literature on this specific application of mobile robots work with aerial vehicles (UAVs). The papers by Stolfi et al., present a surveillance system for early detection of individuals using a swarm mobility model, in the first paper, and a swarm of unmanned aerial vehicles with a Competitive Coevolutionary GA that aims to maximize intruder detection in the second reference [8,9]^[6][7]. Sun et al. designed a two-mode monitoring systems for industrial facilities and their adjacent territories based on the application of unmanned aerial vehicle (UAV), Internet of Things (IoT), and digital twin (DT) technologies [10]^[8]. Prykhodchenko et al. present a single-robot solution for the surveillance of buildings [11]^[9]. The robot operates with a combination of different people detection techniques for detecting and tracking humans. The paper by Lee and Shih proposes an autonomous robotic system based on a convolutional neural network to perform visual perception and control tasks [12]^[10]. The visual perception aims to identify all objects moving in the scene and to verify whether the target is an authorized person. There are different systems for security and surveillance which are currently available in the market. According to [13]^[11], conventional patrolling lacks an integrated multi-sensing system that coordinates various technologies for surveillance and detection of human intruder movement in the different scenarios. They usually are equipped with cameras. Some of them are controlled remotely [14]^[12]. Nevertheless, Light Detection and Ranging (LiDAR) sensors are affordable in terms of the acquisition price and processing requirements. Examples of applications of this sensor can be found in [15]^[13], where the authors describe a mobile robot that operates in an indoor environment and it is capable of tracking pairs of legs in a cluttered environment using a 2D LiDAR scanner. The already mentioned paper by Kim and Bae creates a map of the engine room using LiDAR technology [6]^[4]. The authors in [16]^[14] systematically review and analyze in mobile robotics the use 3D ToF LiDARs in research and industrial applications. In [17]^[15], a multimodal sensor module for multiple fixed and mobile agents in outdoor environments is proposed. It has a vision sensor and four-channel sound that are synchronized and integrates them using a 3D LiDAR and a calibration method. This sensor equipment enables integrated data collection for a 24 h monitoring of the outdoor surveillance area. A graph theoretic approach including heuristic algorithms for optimal point-to-point navigation using a LiDAR sensor is presented in [18]^[16], ensuring total workspace coverage and minimization of action performed by an indoor robot. Path planning is the core task for the AGV system, and it generates the path from origin to destination. However, the implementation of path planning and trajectory tracking by autonomous robots generates a series of optimization problems that can be dealt with using various techniques [19]^[17]. In Ayvali et al., stochastic trajectory optimization methods are used. The authors introduce the ergodicity metric as an objective in a sampling-based stochastic trajectory optimization framework for a mobile robot. In their approach, they construct a probability distribution over feasible trajectories and search for the optimal trajectory using the cross-entropy method [20]^[18]. A different approach consists of addressing these challenges with heuristic optimization techniques. GAs are computer programs that mimic the processes of biological evolution (selection, crossover, mutation) to solve problems and model evolutionary systems [21]^[19]. This feature makes them suitable for solving optimization problems that require an adaptive computer program. In the case of path planning, they allow researchers to easily introduce a fitness function with more than one objective that also maintains several possible solutions at the same time. In PSO, a group of simple entities called “particles” are positioned within the search space of a given problem or function. Each particle evaluates the objective function at its current location and determines its path through the search space by fusing certain aspects of its individual history, the location that has the best fitness, and those of one or more peers within the swarm [22]^[20]. The search approach used by this method is particularly suitable for the problem of optimizing a trajectory in a complex environment since it leads to the rapid identification of a solution, as shown in the results obtained in this problem. PS is an effective technique for exploring the minima of a function, even when that function is not differentiable, exhibits stochastic behavior, or is not necessarily continuous [23]^[21]. The PS algorithm explores a set of points surrounding the current location and actively searches for a point within this set where the value of the fitness function is less than at the current point. This feature makes this method suitable for finding routes as long as the initial route is close to a good solution. This suggests that this method will work effectively in small environments with few obstacles. Some other works have explored these techniques. For instance, the work in [24]^[22] proposes an hybrid PSO-SA algorithm for the optimization of AGV path planning. In [25]^[23], a comprehensive review of methodologies for path planning and optimization of mobile robots is provided. It includes not only the classic but state-of-the-art techniques such as artificial potential fields, GA, swarm intelligence, and machine learning-based methods. The paper by Xiao et al. focuses on the indoor AGV path-planning problem in large-scale, complex environments and proposes an efficient path-planning algorithm (IACO-DWA) that incorporates the ant colony algorithm (ACO) and dynamic window approach (DWA) to achieve multi-objective path optimization [26]^[24]. First, an improved ant colony algorithm (IACO) is proposed to plan a global path for AGVs that satisfies a shorter path and fewer turns. Then, local optimization is performed between adjacent key nodes by improving and extending the evaluation function of the traditional dynamic window method (IDWA), which further improves path security and smoothness. An overview of navigation strategies for mobile robots that utilize three classical approaches, roadmap (RM), cell decomposition (CD), and artificial potential fields (APF), in addition to eleven heuristic approaches, including GA, ACO, artificial bee colony (ABC), gray wolf optimization (GWO), etc., which may be used in various environmental situations is presented in [27]^[25].