Joint torques for control of two coordinated moving robots

Tasks for two coordinated industrial robots always bring the robots in contact with a same object. Physically the three form a closed kinematic chain mechanism. When the chain is in motion, the positions and orientations of the two robots must satisfy a set of holonomic equality constraints for every time instant. To eliminate motion errors between them, one of them is assigned to carry the major part of the task. Its motion is planned accordingly. The motion of the second robot is to follow that of the first robot as specified by the relations of the joint velocities derived from the constraint conditions. Thus if any modification of the motion is needed in real time, only the motion of the first robot is modified. The modification for the second robot is done implicitly through the constraint conditions. Specifically, when the joint displacements, velocities, accelerations and torques/forces of the first robot are known for the planned or modified motion, the corresponding variables for the second robot can be determined through the constrained relations.