Optimal Control of a Two-Link Flexible Manipulator Along Specified Path

In this paper a technique is proposed to find near time-optimal control solution of a two-link manipulator with torque and path constraints. Both links and joints are assumed to be flexible. The proposed approach is based on transforming the optimal control problem into an equivalent unconstrained optimum design problem using penalty function methods. Since in flexible manipulators the point for which the prescribed motion is specified and the application points of control torques are connected by elastic bodies, their inverse dynamics is non-causal. The proposed algorithm takes into account the non-causality of such systems via considering pre-actuation and post-actuation in the solution procedure.