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Because the structures of robotic manipulators vary, they have distinct kinematic models. As a result, these models are linked to a variety of mathematical functions to determine the relationship between joint angles and their positions. In most cases, the joints are connected in series and are controlled by actuators such as motors. The gripper is commonly used at the end of a series of connected links. The position of the robotic arm in the three-dimensional coordinate system is defined by this. The estimated problem for robotic models is divided into two categories: 1) forward kinematics and 2) inverse kinematics. Forward kinematics (Saha, 2014) is derived from equations that derive relationships between the location of the gripper and the joints. Inverse kinematics is the process of estimating joint angles from end position information.
The transformation matrices are utilized to establish the relationship between this angle position data. The rotational and translational relations defined by the transformation matrices cannot be generalized a priori for all sorts of robots. Because each robot has its own joint spaces and limitations, a mathematical model must be developed to determine the relationship between joint angles and position. Although fuzzy-based tactics have been shown to be effective for such estimates (Jamwal et al., 2010), they cannot be applied to all robots. Machine Learning (ML) models can be used to discover such correlations, which may overcome the hampered generalization problem (Craig, 2009). Several machine learning algorithms addressing the generalization of robotic manipulators to anticipate robot position have been suggested in the last decade. The Fuzzy Logic methodology is used to study the path planning of a 6R robot, and it has been proven that the Gaussian membership function produces superior results than other membership functions (Sahu & Choudhury, 2018).
Various optimization approaches are compared for the inverse kinematics problem of a serial robot manipulator (Ayyıldız & Çetinkaya, 2016). An optimized approach for a redundant serial robotic manipulator is presented (Kivela et al., 2017). The optimization approaches are also found helpful in estimating the position information for 2-DOF using genetic programming (Arellano & Rivera, 2019). The hybrid algorithm comprising fuzzy system, genetic algorithm and immune algorithm has been proposed for solving the forward kinematics problem of the stewart platform (Sheng et al., 2006). Also, joint space and orientation representations for the forward kinematics estimation is presented (Grassmann & Burgner-Kahrs, 2019). Optimum design parameters of the robotic gripper have been obtained by using various meta-heuristics techniques like ABC, FA, TLBO, ACO, and PSO algorithm (Mahanta et al., 2019). In this article, a two-step methodology such as geometric modeling followed by the formulation of objective functions is adopted to solve the problem.
The Particle Swarm Optimization (PSO) approach used for various forward and inverse kinematic estimation can be found in (Jahandideh & Namvar, 2012) (Durmus et al., 2011) (Huang et al., 2012) (Li et al., 2007) (Zhang & Gao, 2012). For inverse kinematics, a new quantum-behavioured particle swarm algorithm has been proposed recently (Dereli & Köker, 2020). A Meta-Heuristic Paradigm for solving the Forward Kinematics of 6-6 General Parallel Manipulator (Chandra et al., 2009). Also, inverse kinematics problems have been solved using the Firefly Algorithm (Rokbani et al., 2015). A series of meta-heuristic approaches applicable to robotics can be found in (Erdogmus & Toz, 2012). Other than PSO, the forward kinematics of parallel manipulators have been solved with the Genetic Algorithm (Boudreau & Turkkan, 1996). The inverse kinematics for arm movements of robots is presented in the article (Cavdar et al., 2013). Various meta-heuristic methods like ACO, PSO, FA, FOA, FWA and ABC swarm intelligent optimization algorithms are employed to optimize the global and local path planning of mobile robots (Lei et al., 2019).