Industrial robots are mechanical manipulators whose dynamic characteristics are highly nonlinear. To control a manipulator which carries a variable or unknown load and moves along a planned path, it is required to compute the forces and torques needed to drive all its joints accurately and frequently at an adequate sampling frequency (no less than 60 Hz for the arm considered). This paper presents a new approach of computation based on the method of Newton-Euler formulation which is independent of the type of manipulator-configuration. This method involves the successive transformation of velocities and accelerations from the base of the manipulator out to the gripper, link by link, using the relationships of moving coordinate systems. Forces are then transformed back from the gripper to the base to obtain the joint torques. Theoretically the mathematical model is "exact. "A program has been written in floating point assembly language which has an average execution time of 4.5 milliseconds on a.PDP 11/45 computer for a Stanford manipulator. This allows an on-line computation within control systems with a sampling frequency no lower than 60 Hz. A further advantage of using this method is that the amount of computation increases linearly with the number of links whereas the conventional method based on Lagrangian formulation increases as the quartic of the number of links.

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Tasks for two coordinated industrial robots always bring the robots in contact with the 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 canstraints for every time instant. To eliminate motion errors between them, we assign one of them 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, and accelerations of the first robot are known for the planned or modified motion, the corresponding variables for the second robot and the forces/torques can be determined through the constrained relations.

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