Optimal trajectories for minimizing the dissipative energy of a manipulator in PTP motion under gravity

Taking the global problem of the diminution of energy resources into consideration, optimal trajectories for a two-link manipulator system in PTP motion mider gravity is developed with a, view of saving the dissipated energy. The Generalized Newton-Raphson method is used to solve the nonlinear differential equations of the problem. Though conventionally the starting function was Considered only in different starting functions are presented and their respective energy Consumption are Compared. Tile domains of the optimal starting functions and the corresponding optimal trajectories are also presented.