Optimal balancing of PUMA-Like robot in predefined path

The balancing of the manipulators is an important subject in the different industries, because with the balancing of manipulators, their consumed energy is reduced and it leads to actuators' size reduction. But the relation between of balancing and energy consumption was unclear until the optimal balancing method became introduced. On the other hand, Different tasks for instance, welding and gluing are devoted to manipulators that in them, path coordinate is predefined and it can have certain tolerance. Previous works on the optimal balancing subject, was further on the static balancing that path was not considered. In this paper, optimal balancing approach is applied on open-chain manipulator for predefined path. It is an optimal control problem for given desired trajectory where states, controls and all the unknown parameters must be determined simultaneously to minimize the given performance index for a predefined path task. Necessary conditions based on Pontryagin’s minimum principle and an additional condition associated with the constant parameters is solved for predefined path. Finally the efficiency of the suggested approach is illustrated by simulation for a PUMA like robot.