Analytical Closed-Form Joint Solution of Quaternion-Based Inverse Kinematics for Humanoid Robots

To better emulate human motions, humanoid robots need to move with their knees stretched out. In this case, there is a singularity problem in solving the Inverse Kinematics problem. In this paper, a novel analytical closed-form joint solution for the Inverse Kinematics is proposed to overcome the problem of singularity. First, Forward and Inverse Kinematics equations are derived based on the quaternion and the Kinematic transform matrices. Then, the analytical closed-form joint solution has been derived for a common joint configuration used in humanoid robots. Finally, computer simulation and validation has been done for a 3-D human-like walking pattern with toe-off and heel-strike phases.