Workspace-Intersection-Based Inverse Kinematics Solution for a Two-Segment Variable-Length Continuum Manipulator

This paper proposes an improved inverse kinematics solution for a two-segment continuum manipulator actuated by pneumatic artificial muscles (PAMs). A contraction model of PAMs is incorporated to construct a dynamic workspace volume, thereby overcoming the limitations of conventional geometric approaches that rely on the constant-length assumption. A K-Dimensional Tree (KD-tree) algorithm is employed to accelerate the search for candidate intersections between workspace volumes. The resulting candidate set is then refined through a weighted nonlinear least-squares optimization. This step improves the accuracy of the intermediate point estimation while balancing position and orientation errors. To ensure the uniqueness and physical consistency of the inverse solution, a stiffness-oriented maximum energy principle is further introduced, selecting the configuration that maximizes Rigid. Simulation studies demonstrate higher accuracy, faster convergence, and improved robustness compared with traditional Jacobian-based iterative approaches. Physical experiments on a PAM-driven prototype further confirm the feasibility and effectiveness of the method. These results highlight the potential of the proposed solution for real-time control of soft continuum manipulators with significant flexibility, nonlinearity, and variable-length actuation.