چكيده به لاتين
Abstract
In this thesis, the trajectory planning problem is studied in both point to point and open-loop and point to point and closed-loop cases. In the first case, the problem of designing an optimal path and determining the load carrying capacity (DLCC) of the manipulator is considered, while the second one investigated these two problems regarding point to point and closed-loop case. In the point to point and open-loop case, the load carrying capacity of the manipulator is evaluated for a two-link manipulator with fixed and mobile bases respecting several constraints such as non-holonomic constraints of base (related to the two-link robot with mobile base), the maximum torque of motor, the stability consideration, and etc.
To determine the load carrying capacity of the manipulator and the design of an optimal path in point to point and open-loop case, the direct method is used which attempts to optimize an objective function regarding all the dynamic and kinematic constraints. In this thesis in order to design the optimum path, a meta-heuristic algorithm, called vibration damping optimization (VDO) algorithm is used.
For designing the controller in the closed-loop case, the game theory approach as an extension of non-linear optimal control, is employed in which the dynamism of the starter system is considered beside the dynamism of the manipulator. Furthermore, the game theory approaches make evaluating the defined disturbances of starter system possible. In the proposed method, the voltage of motive motors and disturbances of the system are considered as two players of the game. The optimal strategies of players are calculated based on Nash equilibrium and then the optimal values of controlling inputs are determined using a repetitive algorithm which is based on solving of Riccati equations.
The problem of designing the controller is formulated as a sum-zero differential game in which the payoffs of the players are completely conflicted so that the profit earned by one of the players equals the other player’s loss.
Keywords: Trajectory planning, Vibration damping optimization, Load carrying capacity, Robot control, Game theory, Sum-zero game
