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The main objective of this paper is to propose a novel minimum-energy trajectory planning for an LCD glass-handing robot, which is driven by a permanent magnet synchronous motor (PMSM). The system is described by a mathematical model of the electromechanical system. To generate the minimum-energy trajectory, we employ a high-degree polynomial with suitable conditions of angular displacement, speed, acceleration and jerk at the start and end points. The real-coded genetic algorithm (RGA) is used to search for the minimum-energy point-to-point (PTP) trajectory for the motion profile. The coefficients of the polynomial are determined by the RGA with the fitness function of minimum-energy input. The results are compared for various degrees of polynomials and to obtain the minimum energy input. It is concluded that the proposed methodology with minimum-energy input can also be applied to any electromechanical system driven by a PMSM.