# A Multi-Objective Modified PSO for Inverse Kinematics of a 5-DOF Robotic Arm
The k-ABC was applied to solve the inverse kinematics of a 5-degree of freedom, 5-DOF, robotic arm, by merging the error fitness and the orientation into a single mono-objective formulation with application which minimizes the position and the orientation Euclidean distance toward a couple of target values. The proposal showed its effectiveness in drawing a circular path. In [14], a particle swarm optimization inverse kinematics solver, Ik-PSO, is investigated for the 6-DOF industrial KUKA KR 6 r900, with position and orientation objectives, and where the multi-objective strategy was based on a weighted sum of position and orientation errors. A similar approach was proposed with application to a 5-DOFindustrial robot, the Kuka Youbot manipulator [15], where authors used the inertia weight PSO with an exponentially decreasing inertia weight, cognitive, and social coefficients. A swarm approach with behavior moderation based on Gaussian-like distributions was also proposed in [16], where a beta function was introduced to distinguish two types of swarm behaviors: one for search phase and one for exploitation phase with application to inverse kinematics. The beta salp swarm algorithm, beta SSA, was proposed in [16] for general optimization and inverse kinematics. The beta SSA is an SSA where search and explore phases are managed using beta profiles. Multi-objective approaches of articulated systems and robotic arms are not popular, while they are more effective and more suitable to handle the difference in dimensions between position and orientation. [PERSON] et al. (2016) developed an MO strategy for inverse kinematics for a 6-DOF robotic arm based on The Fast and Elitists Non-Dominated Sorting Genetic Algorithm and the Bacterial Chemotaxis Multi-Objective Algorithm [17]. The multi-objective inverse kinematics, MO-IK, solver was used to optimize a couple of objective functions for position and orientation of the end-effector. A multi-objective PSO (MO-PSO)-based method for inverse kinematics was proposed in [18], where authors used MO-PSO to minimize the error position as well as the angular elongation between initial and final poses. An evolutionary multi-objective approach for inverse kinematics was proposed in [19] for the grasping problem of the humanoid robots; the proposal showed that such an approach can find accurate solutions in real time when compared to classical IK solvers. In this paper, a new modified behavior PSO variant is proposed, m-PSO, which stands for a fitness-oriented PSO where the swarm particles evolve differently according to their fitness. A multi-objective optimization approach is then proposed based on m-PSO, the MO-M-PSO, which is applied to solve the inverse kinematics of a 5-DOF robotic arm, which is a 3D-printed educational robot. The arm inverse kinematics problem is formulated as a multi-objective problem assessing end-effector position and orientation as two separate objectives. A Pareto front strategy is then used to find out the best compromise between those objectives. The remainder of this paper is organized as follows: Section 2, presents the multi-objective optimization concepts and challenges, then in Section 3, a multi-objective modified PSO, MO-m-PSO, is presented and detailed. Section 4 is dedicated to experimental investigations, which include a single-point IK solution as well as circular path planning for the 5-DOF robotic arm. The proposed method is compared to recent state-of-the-art contributions in Section 5. Finally, conclusion and perspectives are developed in Section 6.