## 1 Introduction  
Manipulator robots, known for their unparalleled precision, efficiency, and safety, are revolutionizing industries across the globe. These versatile machines are pivotal in space applications, where they service satellites, remove orbital debris, and construct and maintain orbital assets, ensuring the sustainability of our extraterrestrial endeavors [1]. In the automotive industry, robotic manipulators excel in welding tasks, utilizing an electric arc and shielding gas to enhance manufacturing processes [2]. The healthcare sector has also benefited immensely, with robotic arms enabling minimally invasive surgeries that surpass traditional open surgery methods in terms of precision and recovery time [3]. By performing repetitive and hazardous tasks with consistent accuracy, these robotic systems not only improve operational efficiency but also ensure worker safety. Central to their functionality is the complex challenge of solving the inverse kinematics (IK) of the robotic manipulator, a crucial aspect that underpins their application in these diverse fields. The inverse kinematics problem entails determining the joint variable configuration that corresponds to a specific position and orientation of the end-effector. This task is generally more complex than solving the forward kinematics problem for several reasons [4]:  
* Equations to solve are generally non-linear, making it not always possible to find a closed-form solution. * Multiple solutions may exist. * Infinite solutions may exist. * There might be no admissible solutions. Conventional numerical methods based on differential kinematics rely on the Jacobian matrix to determine the relationship between joint variables and end-effector positions [5]. However, these methods encounter significant problems due to singularities in the Jacobian matrix, which can lead to undefined or infinite solutions [4; 6]. Closed-form methods such as algebraic or geometric methods are commonly used for manipulators with simple geometric structures [7]. Due to these drawbacks, artificial intelligence methods are increasingly utilized to solve the inverse kinematics problem. In recent years, although to a limited extent, the solution of inverse kinematics has been explored using Artificial Neural Networks (ANNs). Typically, the input to the network is the desired position and orientation of the end-effector and the output is the vector of generalized coordinates, representing the robot's joint configurations. However, this method faces challenges in generalizing across different kinematic structures or manipulators, as it requires a unique dataset for each specific manipulator. Due to the complexity of the problem, research has been limited to solving it within the three-dimensional Cartesian plane, with the additional necessity of identifying singularity zones [8; 9]. Additionally, approaches that account for both position and rotation demand very large datasets and an optimization process for the candidate solution, often utilizing numerical methods such as the Newton-Raphson method [10]. For these reasons, this paper proposes solving the inverse kinematics problem using metaheuristic algorithms. In the past decade, metaheuristic algorithms have emerged as a viable alternative for addressing various challenges in robotics. These algorithms are particularly useful for solving problems that are difficult to tackle with conventional methods or for which no exact solution method exists [11]. In the literature we can find examples of the application of metaheuristic algorithms, such as their use for hyperparameter tuning in both machine learning algorithms and deep neural networks [12], and trajectory tracking optimization [13], as well as in robotic navigation [14].