# A Multi-Objective Modified PSO for Inverse Kinematics of a 5-DOF Robotic Arm  
[PERSON]  
1 Institute of Applied Science & Technologies of Sousse, University of Sousse, Sousse 4034, Tunisia; [EMAIL_ADDRESS] (N.R. aggregates the different objectives of a problem into a single one [1; 2; 3]. The weighted sum consists of aggregating several mono-objective functions using a moderation coefficient, the weight, which is defined according to the relevance of an objective toward others. The main issue with such a strategy is how to manage those coefficients and how to define the needed aggregation rules. In reality, this approach includes a heuristic aspect, since in reality there are no rules fixing clearly how the coefficients, weights, are attributed. When all objectives obtain the same impact on optimality, we may think about equivalent equal weights, while this is very rare in reality [3], and arguing the choices of a weighting is far from being a simple issue. Multi-objective optimization tends to find a trade-off of several controversial mono-objectives satisfying a global optimality for a specific need. In Pareto-based multi-objective optimization, MO, a set of mono-objective solutions are generated, then a selection strategy using the Pareto front is used to merge the objectives and to find the solution satisfying several objectives [4]. Alternatively, and using the fuzzy or the rough representations of the controversial objectives, a rough or a fuzzy solution representing a possible trade-off may be defined using rough sets and fuzzy sets, which may be also used for the assessment of global optimality based on mono-objectives results [5]. Pareto multi-objective strategies have been investigated for mechanical system design by [PERSON] et al. since 2005, where authors applied an evolutionary multi-objective optimization to design a leg mechanism based on three objective functions [6]. In a more generic manner, a multi-objective bees algorithm (MOBA) was investigated to solve three different multi-objective engineering problems: a satellite heat pipe design problem, a space truss design, and the pressure vessel design problem. Results showed evidently that the Pareto-based approach is better than the weighted sum method, essentially for the test bed of mechanical engineering problems [7]. In industrial robotics, robotized arms are used in a large panel of applications, essentially in mass production and assembly lines, such as car assembly lines [8]. Robotics arms are also used in food manufacturing, handling operations, and smart logistics chains [9; 10]. Robotics arms may be considered as a generic tool of any industrial process; at the only condition that a specific end-effector is available or specially added to the arm, such tools may be used for painting or welding operations [11]. Whatever the industrial application of a robotic arm, a path design is needed. The path design plans the robot motions needed to perform a task [12]. To perform a task, a robot arm needs to achieve a position with respect to a suitable orientation. Such a criterion is mandatory for handling processes where a specific orientation is needed for the end-effector position to be able to grasp objects. In welding processes, the welding tool should achieve a target point with a specific orientation, making the inverse kinematics problem a real multi-objective one [11]. In robotics, inverse problems may also be addressed as multi-objective; among them, inverse dynamics and inverse kinematics, IK. IK is a typical multi-objective problem at any time the focus is not limited to the end-effector position. For inverse kinematics of robotic arms, the weighted sum is commonly used to merge position and orientation objectives of the end-effectors, and even if the proposals are presented as multi-objective, this approach is definitively closer to mono-objective rather than multi-objective. The authors in [13] proposed a knowledge-based artificial bee, k-ABC, which is an ABC with a compromise between the exploration and exploitation.