Discrete-Time Control of Fast Non-Linear Motion of Robot Manipulators with Ideal Actuators

Non-linear and coupled dynamic equations of motion automatically generated by computer in algebraic form are piecewise linearized and discretized to form a set of state difference equations by which a mathematical basis is provided for computer control, numerical integration and simulations. Two adaptive control strategies are proposed to drive robot manipulators to follow desired trajectories. The first strategy uses the idea of the combination of feedforward plus feedback control. A complete on-line control scheme is designed in the second strategy. All the calculations, both on-line and off-line, are performed by step-by-step optimization so that a quadratic function is minimized for each step. The control delay associated with time taken for on-line computation is eliminated by a state-and-control prediction strategy. Based on the proposed strategies a general FORTRAN program has been developed for simulations. An example is taken to investigate the tracking ability of robot manipulators in trajectories with different velocity amplitudes and various frequencies by simulations. The tracking ability is also examined by using a random trajectory generator.

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