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Trajectory planning of redundant manipulators for minimum energy consumption without matrix inversion

In this paper a method to solve the trajectory generation problem in redundant degree of freedom manipulator has been proposed, and the variational approach within the B-spline function are introduced for minimization of the consumed electrical energy of a robot manipulator system. In the proposed method, the inverse matrix of Jacobian calculation is not required, and the minimal trajectory error is guaranteed while minimizing the consumed electrical energy. The theory, simulation, and experiments are presented in the paper.