# Comparison Study of the PSO and SBPSO on Universal Robot Trajectory Planning
## 1 Introduction  
Using robots in manipulation tasks had a significant growth in the context of industrial production in recent years [1]. The aforementioned diffusion of robots in an industrial environment provided, over the years, that various methods were developed in order to monitor and control manipulator and mobile robots [2]. With this, they acquired the ability to operate in dangerous environments for humans, for example, beyond Earth's atmosphere, in aquatic explorations, and in the transport of materials [3]. The purpose of this paper is to present the simulation of article Swarm Optimization (PSO) and the Serendipity-Based PSO (SBPSO) algorithm to modify APF approach, in order to generate free trajectory of collision of a UR5 universal manipulator robot. These metaheuristics will be used to optimize the repulsion constants of the potential field of the starting point and obstacles and the attraction constant of the end point, which are directly related to the intensity of the force resulting from the potential field. Particle Swarm Optimization (PSO) is a heuristic algorithm dependent on social behavior of a flock of birds. The method was recommended by [PERSON] and [PERSON] in 1995 [4]. They had an objective to seek the optimal solution, in a space of search, by exchanging information between individuals of a population to determine which trajectory they should take in the search space. In this paper, the PSO was used because it has a number of advantages including rapid convergence and ease of implementation, but often faces a problem where their particles get \"stuck\" in great places. This problem is called premature convergence [5]. In this algorithm, individuals called particles function as a set of birds searching for a flight shape and considering the position of each particle withinspace; this is due to a curve of evolution within society or set of particles. Each particle will have its success defined by the general trend of the population [5]. Many engineering problems are common to study types of its behavior process, as a rule, such as a dynamic system which can been modeled by a set of equations that consider the same variables and is subjected to a certain evolution over time. A set of techniques which has been applied to this kind of problem is succussed on what it involves and is known as bio-inspired computing techniques [6]. These techniques applied to the different domains such as: prediction systems [7; 8], power systems [9; 10], telecommunications [11; 12], intrusion detection systems [13; 14], and others. In the context of bio-inspired computing, Swarm Intelligence consists of a set of metaheuristics based on some living beings whose behavior emergencies can result in an ability to resolve. It is important to mention that the work of the PSO and SBPSO algorithm is to enhance the artificial potential field approach in order to obstacle avoidance collision. In order to enhance work of the PSO by delaying premature convergence, the serendipity concept will be used. Serendipity is a term used to describe a fortunate situation that happens by chance. Recommendation systems are developed as a solution to the problem of information overload. The accuracy of the recommendations has been the focus of recommendation system research [15; 16]. Accuracy, on the other hand, resulted in a problem known as overspecialization. This happens when the system only refers to items connected to the user's profile. Serendipity is a strategy that can be used to resolve overspecialization. According to [17], a recommendation system provides products based on the user's interest profile and converges on recommendations when these items do not meet the real expectations of the user. A metaheuristic algorithm converges to a place without considering other more suitable solutions in order to suggest items that may be more suitable. It is possible to observe the correlation between overspecialization and premature convergence.