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.

Trajectory/profile in human-robot cooperative tasks is investigated for real-time identification and learning. The method of three-distances and its association with specific spherical and Cartesian coordinates are presented which are invariant to rotation/translation, and insensitive to disturbance. These methods are illustrated via computer simulations.

When a cooperative task is performed jointly by a human and a robot manipulator, it is reasonable to have the human mainly making decisions and the manipulator carrying the physical load. To carry out the task successfully, the robot must be trained to possess the necessary experiences to work with the human on the assigned tasks. This goal may be achieved by real-time identification and learning of robot's position/orientation trajectories and force/moment profiles. The model of human's action, however, is also needed to help the design and analysis of the interactive system. In this paper, a variety of different cases are considered for both robot and human. Three different cases of robot's force/torque contributions are considered. An extreme case is that the robot contributes no force/moment except balancing the load so that it becomes a burden to the human. Such a situation could happen when the robot controller breaks down. Another case is that the robot furnishes enough torque/force so that the task progresses at a constant acceleration. Practically speaking, the robot contributes a nearly constant force/torque. The final case involves the real-time identification and learning of the robot's position/orientation trajectories and force/moment profiles so that they may be retrieved for future use. Five different cases are considered for the human. The first case is the open-loop approach in which his/her trajectories and profiles are preplanned. This is usually true when the human performs a daily routine after many many times. If the human cares about only the final goal position/orientation, a PD controller model suffices. A third case is to adopt a fuzzy controller model for the human. The membership function may be constructed based on the observation of the human's reaction. An interactive case may be represented by re-planning with time-delay. At each selected time instant, the human revises the actual trajectory/profile based on his/her judgement. The final case involves the simulation of the human interaction using physically the "mouse" movement. This is however restricted to the two-dimensional motion on the "mouse pad". A variety of combinations of different cases of robot and different models of human is analyzed and simulated. A comparison is made among the various combinations from which a conclusion is drawn.

In the process of human-robot interaction, effective representation and real-time learning of manipulator's trajectory/profile in response to human's motion are presented. Method of obtaining approximate solutions during the learning stage are introduced to circumvent the noise effect caused by numerical inaccuracy and computational errors. Perturbed solutions are derived as an alternative approach to overcome the noise effect. Simulation examples are given to illustrate every stage of the presentation.