Interactions and motions in human-robot coordination

In human-robot cooperative tasks, the robot is required to memorize different trajectories for different assignments, and retrieve a proper one from them in real-time for the robot to follow when an assignment is repeated. A three-point representation of the space curves is translation/rotation/scaling invariant. Schemes of matching positions by vectors, and orientations by matrices are efficient in that computing time is short enough for real-time implementations. Physical experiments are performed to illustrate and verify the analytical results