Maximum payload for flexible joint manipulators in point-to-point task using optimal control approach

In this paper, finding the maximum dynamic load carrying capacity of flexible joint manipulators in point-to-point motion is formulated as an optimal control problem. The computational methods are classified as indirect and direct methods. This work is based on the indirect solution method of optimal control problem. The application of Pontryagin's minimum principle to this problem results in a two-point boundary value problem (TPBVP) solved numerically. Two algorithms are developed on the basis of the solution of the TPBVP. The first one is used to plan the optimal path for a given payload, and the other one is exploited to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories are obtained with different characteristics and different maximum payload. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to illustrate the power and efficiency of the proposed method in the presence of flexibility in joints, a number of simulation tests are performed for a two-link manipulator. Then, the effect of flexibility on the maximum payload value is investigated and compared with rigid one. Finally, for the sake of comparison with previous results in the literature, simulation is performed for a rigid-joint three-link manipulator, and a reasonable agreement is observed between the results.