This paper presents an adaptive model predictive control scheme to control the underactuated and redundant robot, the robot has highly nonlinear coupling because of the existence of a passive axis. Adaptive model predictive control provides a framework to solve optimal discrete control problem for a nonlinear system under input saturation and state constraints. The optimal reference trajectory is computed by using Quasilinearization (QL) approach to minimize the energy consumption for

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... ted motion between two points. The challenge is to meet the performance requirements e.g. position accuracy, repeatability, and precision, combined with high speed capability. Numerical simulations are conducted to validate the control scheme. Simulation results show very good comparison and prove the adequateness of this control technique for underactuated industrial robots.