A Closed-Form Inverse Kinematic Analytical Method for a Humanoid Seven-DOF Redundant Manipulator

Humanoid manipulators with kinematic redundancy offer enhanced dexterity and adaptability to complex environments. Solving their inverse kinematics (IK) is fundamental to trajectory tracking, motion planning, and real−time control. Conventional Jacobian−based iterative methods are widely used, but they are often sensitive to the initial guess, computationally expensive, and less effective in handling strict constraints. Arm−angle−based analytical parameterization reduces redundancy resolution to a single parameter. However, joint limits may lead to multiple disconnected feasible arm−angle intervals. Many existing methods still depend on a numerical search or intelligent optimization to select the arm angle. This lowers computational efficiency and provides less explicit control over branch and configuration selection. To address these issues, this paper extends the arm−angle analytical IK framework. It introduces global configuration parameters to explicitly control the shoulder−elbow−wrist configuration. It also completes the analytical derivation of the rotational relationships of the first three joints in the reference plane. In addition, a feasibility determination and modeling scheme for the arm−angle domain is established, which covers disconnected feasible intervals. The IK problem is then reformulated as a one−dimensional optimization over the feasible domain. An efficient interval−based search is employed to determine the optimal arm angle. Experimental results demonstrate high accuracy and interference−free trajectory tracking. Comparative tests on randomly sampled target poses are also performed. The results show more concentrated error distributions, shorter average computation time, and higher success rates. These results confirm the advantages of the proposed method in accuracy, robustness, and real−time performance.