This paper presents a new approach to obtaining the equations by the method of Newton-Euler formulation which is independent of the type of manipulator-configuration. The 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. Using this formulation, the amount of computation increases linearly as the number of joints increases while the conventional Lagrangian formulation causes the increase proportional to the quatic of the number of joints. With a program written in floating point language, it is possible to achieve an average execution time of 4.5 milli-seconds on a PDP 11/45 computer for a Stanford manipulator.
Position control of a manipulator involves the practical problem of solving for the correct input torques to apply to the joints for a set of specified positions, velocities, and accelerations. Since the manipulator is a nonlinear system whose joints are highly coupled, it is very difficult to control. This paper presents a technique which adopts the idea of "inverse problem" and extends the results of "resolved-motion-rate" controls. The method deals directly with the position and orientation of the hand. It differs from others in that accelerations are specified and that all the feedback control is done at the hand level. The control algorithm is shown to be asymptotically convergent. A PDP 11/45 computer is used as part of a controller which computes the input torques/forces at each sampling period for the control system using the Newton-Euler formulation of equations of motion. The program is written in floating point assembly language, and has an average execution time of less than 11.5 ms for a Stanford manipulator. This makes a sampling frequency of 87 Hz possible. The controller is verified by an example which includes a simulated manipulator.
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.
