Solving an inverse kinematics problem for a humanoid robot\u2019s imitation of human motions using optimization

Interactions of a humanoid with a human are important, when the humanoid is requested to provide people with human-friendly services in unknown or uncertain environment. Such interactions may require more complicated and human-like behaviors from the humanoid. In this work the arm motion of a human is discussed as the early stage of human motion imitation by a humanoid. A motion capture system is used to obtain human-friendly arm motions as references for the humanoid. However the captured motions may not be applied directly to the humanoid, since the differences in geometric or dynamics aspects as length, degrees of freedom, and kinematics and dynamics capabilities exist between the humanoid and the human. To overcome this difficulty a method to adapt captured motions to a humanoid is developed. The geometric difference in the arm length is resolved by scaling the arm length of the humanoid with a constant based on a length ratio. Using the scaled geometry of the humanoid the imitation of actor’s arm motion is realized by solving an inverse kinematics problem that is formulated as an optimization problem. The errors between the captured trajectories of actor arms and the approximated trajectories of humanoid arms are minimized. Such dynamics capabilities of the joint motors as limits of joint position, velocity and acceleration are also imposed on the optimization problem. Two motions of one hand waving and performing a statement in sign language are imitated by a humanoid in dynamics simulation.