## 1 Introduction
[17] provided a continuous genetic algorithm to solve the IK problems of a 3R planar manipulator. The continuous genetic algorithm operators used in the initialization phase, crossover, and mutation were designed to smoothen the joint space while the Cartesian path was kept accurate. Although the aforementioned algorithms made a great contribution to solving the IK of redundant robots, they focused only on single kinematic chain redundant manipulators which are widely used in industry. For instance, the most common applications using GA to solve the IK problem are 6-DOFs manipulators, although there are closed-form solutions already; this can also be found in 7-DOFs manipulators, for which GA is quite applicable because it includes one redundant DOF in the joint space when the end-effector moves in the Cartesian coordinate system. Given that previous research did not consider the inverse kinematic problem of multiple manipulators such as robotic hands and dual-arm robots, further investigation on the IK problem of multiple kinematic chain manipulators is crucial. The other drawback of GA is its ignorance of an unreachable target. Specifically, GA is implemented regardless of feasibility, which is a fatal flow in solving the IK problem of a dual-arm robot. Without checking the viability in advance, it is frequently found that, when two target points are given to each arm, only one arm can reach the target point while the other one fails because of the limited range of motion. Therefore, feasibility analysis beforehand is indispensable. In this paper, a workspace-analysis-based immigration genetic algorithm (IGA) is proposed to solve the inverse kinematics of a multi-fingered anthropomorphic hand. The architecture of the proposed algorithm is divided into two stages, namely, the offline stage and the online stage. In the offline stage, workspaces of the exemplary index finger and the thumb are established by the Monte Carlo method and stored in a database for the feasibility check. In the online stage, a feasibility estimation function examines whether the IK request is out of the workspace or not. If the request is unreachable, the algorithm is suspended immediately. Conversely, with a reachable request, the feasibility function provides a better initial condition for the IGA to get high-precision IK solutions. This paper aims to solve the IK problem of multiple chain manipulators and to provide a mechanism that can avoid unnecessary computation if the target point is inappropriate. Meanwhile, the proposed mechanism can offer a superior range to variables, which improves the convergence of the IGA. The performance of this algorithm is validated through simulations, which include both reachable and unreachable IK requests. A population distribution during the evolutionary process is conducive to the understanding of the improvement in convergence. The remainder of this paper is organized as follows: in Section 2, the configuration of the anthropomorphic hand is described, and the IK problem is defined. In Section 3, the establishment of the workspace and mechanism to check the feasibility is explained. Section 4 introduces the architecture of the proposed algorithm and illustrates details of each operator in IGA, while Section 5 presents the simulation results of the proposed algorithm applied to several IK requests. Lastly, the contributions of this paper are summarized in the conclusion.