Dynamic motion imitation of two articulated systems using nonlinear time scaling of joint trajectories

This paper proposes the analysis of two strategies for motion imitation of articulated systems with balance constraint. The two systems have different dynamic characteristics and their respective motions are restricted to the sagittal plane. The first strategy is based on nonlinear time scaling of joint trajectories ensuring that the balance of the imitating system is maintained through the motion. With this approach, the imitating system tracks the input reference trajectory without modifying the task to be accomplished by compromising on acceleration of the motion to ensure the condition for the balance is satisfied. As a consequence of reducing acceleration, there exists a delay between the reference system and the imitating system. However, we have ascertained that the joint angles are accelerated for the delay created to catch up with the reference motion. In contrary, the second strategy modifies directly the joint angle trajectories to ensure balance. This approach is the traditional approach in motion imitation used in human to humanoid motion transposition. We have formulated both strategies as an optimization problem in order to obtain feasible joint trajectories for the imitator. This work is a preliminary study for the imitation of a human being by a humanoid robot.