Singularity-robust modular inverse kinematics for robotic gesture imitation

We present a method of computing the joint angles for an upper body humanoid robot corresponding to task space motion data from a human demonstrator. Using a divide-and-conquer approach, we group the motors into pan-tilt and spherical units, and solve the inverse kinematics in a modular fashion based on the derivative of the inverse tangent function of the relevant task space variables. For robustness to kinematic singularity, we add a regularization parameter that vanishes whenever the task variables are outside a neighborhood of zero. Simulation study on a 7 degree-of-freedom (DOF) robot arm shows a tradeoff of tracking accuracy in a neighborhood of each singularity in favor of robustness, but high accuracy is recovered outside this neighborhood. Experimental implementation of the proposed inverse kinematics on a 17-DOF upper-body humanoid robot shows that user-demonstrated gestures are well-replicated by the robot.