Optimal trajectory planning of flexible joint manipulator: Maximum load carrying capacity-minimum vibration

In this paper، optimal trajectory planning of flexible joint manipulator in point-to-point motion is presented in which besides the determining the maximum load carrying capacity، the vibration amplitude is also reduced. The solution method is on the base of the indirect solution of optimal control problem. For this purpose، an appropriate objective function is defined، dynamic equations are derived in state space form، Hamiltonian function is developed and necessary optimality conditions are obtained by using the Pontryagin maximum principle. In order to reduce the vibration of the end effector during the path، an appropriate state variables are defined and the control law is improved to omit the suddenly variation in applied torque. Then، in order to illustrate the power and efficiency of the proposed method، a number of simulation tests are performed for a two-link manipulator. To this end، after deriving the equation in details، two simulations are performed. In the first case، determining the maximum load without considering the vibration is solved، in the second simulation، optimal trajectory with maximum load and minimum vibration is obtained. Finally discussions on the obtained results are presented.