Optimal Control in Path Planning of Redundant Manipulators with the Last Flexible Arm based on Rigid Motion in Trajectory Tracking

This paper develops open-loop optimal control approach for path planning of redundant manipulators with the last flexible arm and fixed base in trajectory tracking. In this method, regardless of flexibility, the space of joints answer is obtained for the rigid motion of manipulator. By proper selection of state vector, the cost function and system constraints are turned to classic form of optimization problem. By using Pontryagin’s minimum principle, the obtained equations are changed into two point boundary value problem. To verify the proposed method, simulation for three-link flexible manipulator is conducted. The results and surveys show the effectiveness of the proposed methods.