Large workspace and strong grasping force are required when a robot manipulates big and/or heavy objects. In that situation, bimanual manipulation is more useful than unimanual manipulation. However, the control of both hands to manipulate an object requires a more complex model compared to unimanual manipulation. Learning by human demonstration is a useful technique for a robot to learn a model. In this paper, we propose an imitation learning method of bimanual object manipulation by human demonstrations. For robust imitation of bimanual object manipulation, movement trajectories of two hands are encoded as a movement trajectory of the object and a force trajectory to grasp the object. The movement trajectory of the object is modeled by using the framework of dynamic movement primitives, which represent demonstrated movements with a set of goal-directed dynamic equations. The force trajectory to grasp an object is also modeled as a dynamic equation with an adjustable force term. These equations have an adjustable force term, where locally weighted regression and multiple linear regression methods are employed, to imitate complex non-linear movements of human demonstrations. In order to show the effectiveness our proposed method, a movement skill of pick-and-place in simulation environment is shown.

Measuring task complexity of movement skill is an important factor to evaluate a difficulty of learning and/or imitating a task for autonomous robots. Although many complexity-measures are proposed in research areas such as neuroscience, physics, computer science, and biology, there have been little attention on the robotic tasks. To cope with measuring complexity of robotic task, we propose an information-theoretic measure for task complexity of movement skills. By modeling proprioceptive as well as exteroceptive sensor data as multivariate Gaussian distribution, movements of a task can be modeled as probabilistic model. Additionally, complexity of temporal variations is modeled by sampling in time and modeling as individual random variables. To evaluate our proposed complexity measure, several experiments are performed on the real robotic movement tasks.