A unified inverse kinematics framework for multi-offset 7-DOF manipulators based on analytical approximation and numerical correction

Inverse kinematics (IK) of multi-offset 7-DOF manipulators is challenging because structural offsets destroy geometric decoupling, making closed-form solutions difficult and reducing the efficiency and robustness of conventional numerical methods. This paper proposes a unified IK framework combining analytical approximation and numerical refinement. The original multi-offset manipulator is first simplified into an equivalent offset-free shoulder–elbow–wrist (SRS) configuration by neglecting shoulder, elbow, and wrist offsets. Approximate analytical IK solutions are then derived from the simplified geometry to provide multiple configuration-consistent initial estimates. To compensate for simplification errors, a numerical refinement strategy integrating adaptive damped Levenberg–Marquardt optimization, null-space optimization, dynamic weighting adjustment, and terminal refinement is developed. Extensive co-simulation, physical, comparative, and higher-DOF experiments validate the effectiveness of the proposed method, demonstrating high solution accuracy, robust convergence, competitive computational efficiency, and scalability to higher-dimensional redundant manipulators. By combining the efficiency of analytical initialization with the robustness of numerical optimization, the framework provides an effective IK solution for multi-offset redundant manipulators and demonstrates potential for extension to higher-dimensional and various orthogonal manipulator configurations.