Inverse kinematics framework for a 2R-3R-2R upper-limb exoskeleton using vector method

Traditional inverse kinematics (IK) methods have been primarily developed for industrial robots and focus solely on end-effector poses. However, they cannot be applied to exoskeletons owing to differences in the configuration design and the requirement for kinematic compatibility between humans and exoskeletons. The 2R-3R-2R upper-limb exoskeleton supports shoulder girdle motion and achieves a full range of upper-limb movements without causing discomfort to the users. This study proposes an IK framework for 2R-3R-2R upper-limb exoskeletons to map the vectors of the upper limb segments to the joint space using the vector method. Moreover, the framework can accommodate four task description methods, while maintaining multiple IK solutions. The proposed framework was evaluated against recently published methods, and its effectiveness was further validated through simulations. The computational times for the four task description methods were 0.033 ms, 0.43 ms, 0.76 ms, and 7.1 ms, respectively. The maximum Euler angle and maximum position error of the end-effector for the four task description methods were captured within 6×10⁻¹² rad and 1.2×10⁻⁹mm, respectively.