In this article, designing an optimal path in two forms of point-to-point is investigated. In the first case, the optimal path planning and determination of the load-carrying capacity of a manipulator in a point-to-point and open-loop case is studied. In the second case, the path-planning problem and maximum load-carrying capacity of manipulators are investigated in a closed-loop point-to-point case. Designing an optimal path in a point-to-point and open-loop case is studied using a vibration damping optimization algorithm. In order to design the controller in the closed-loop case, the game theory approach, which is a generalized form of nonlinear optimum control, is used. In this method, in addition to considering the dynamics of the manipulator, the dynamics of the driving system are also considered. Moreover, the method is able to investigate the effects of the disturbances introduced by the driving system. In the proposed method, the voltage of engines and system disturbances are considered as the players. The optimum strategy of players is calculated based on the Nash equilibrium strategy, and the optimum value of control inputs is determined using an iterative algorithm based on solving Riccati equations. The problem of designing a controller is proposed in the form of a differential game problem with zero sum. The results indicate that for a fixed-base two-link manipulator, the design of the controller based on a differential game made it possible to control the effect of system disturbances so that the load-carrying capacity experienced small changes compared to the desired case and without system disturbances resulting from the data obtained from point-to-point and open-loop cases.
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