## 1 Introduction  
The solution of inverse kinematics (IK) is one of the most critical and elemental issues in robotics. Many related research areas such as motion planning, robotic grasping, manipulation, and manufacturing are all involved in IK. The IK of a manipulator is used to find the map between the joint coordinate (\(\theta\)) and the Cartesian coordinates (\(x,y,z\)), where \(\theta\) represents the joint angles of each joint in the manipulator and (\(x,y,z\)) represent the position of the manipulator's end-effector. While most IK solutions are performed on simple manipulators, several studies focus on redundant manipulators. For a redundant robot, in addition to the basic accurate positioning, different requirements such as computation time, robustness, and minimum displacement are considered suboptimal conditions. One of these complex redundant manipulators is the multi-fingered anthropomorphic robotic hand, whose joints of fingers move simultaneously and two wrist joints are deemed as the base of the hand. To obtain the IK solution of the anthropomorphic hand, a robust algorithm is essential to solve this multiple end-effector problem. Traditionally, there are three kinds of methods used to acquire the IK solutions of a redundant manipulator, namely, the algebraic [1, 2], geometric [3], and iterative methods [4, 5, 6, 7]. Each of them has its own advantages and disadvantages. For example, the algebraic method can derive a closed-form solution from a Denavit and Hatenberg (D-H) table [8] and, thus, offers efficiency in computation. However, the algebraic method cannot guarantee a closed-form solution for all configurations of manipulators. On the other hand, the geometric method can obtain a closed-form solution, while it is usually limited in specific configurations such as sphere-revolute-sphere manipulators. Likewise, the iterative algorithm utilizes local linearization to get a linear trajectory, and it is suitable for most manipulators. Nevertheless, the iterative method may encounter a singularity problem in which it can accidentally converge to the same solution if the same initial point is given. All of these traditional methods have one point in common, i.e., high computational efficiency, but they all inevitably suffer from certain restrictions. Alternatively, thanks to the advancement of computer hardware, compute-intensive algorithms can come in handy. For these reasons, although the computation is intensive, researchers have focused on using biologically inspired optimization to solve the IK problem. Recently, many papers associated with neural networks [9; 10; 11; 12; 13] and evolutionary algorithms [14; 15; 16; 17; 18] have been published to allow obtaining the IK solution of redundant manipulators with some convincing results. [PERSON] [19] presented a hybrid approach using neural networks and the genetic algorithm (GA) to solve the IK problem under the consideration of error minimization in the end-effector. Three Elman neural networks were applied to create the floating-point initial population for the GA. The simulation experiments were performed on a six-axis serial robot and showed a critical high precision. [PERSON] et al. [20] presented an adaptive niching strategy to acquire several possible solutions to IK problem. By using the niching genetic algorithm accompanied by the quasi-Newton algorithm, the precision and resolution of the simulation results were improved dramatically. A sequential mutation genetic algorithm combined with an extreme-learning machine was presented by [PERSON] et al. [21]. In their study, the extreme-learning machine first computed the preliminary IK solution. With the use of the simple GA, the refined solution was optimized. The grasping experiments were then conducted on the 6 degree of freedoms (DOFs) Stanford MT-ARM robotic manipulator, from which an improvement in the computational time without reducing the accuracy of IK solutions was demonstrated. [PERSON] et al.