Trajectory Optimization of Flexible Mobile Manipulators Using Open-Loop Optimal Control Method

In this paper Open-loop optimal control method is proposed as an approach for trajectory optimization of flexible mobile manipulator for a given two-end-point task in point-to-point motion Dynamic equations are derived using combined Euler–Lagrange formulation and assumed modes method. To solve the optimal control problem an indirect method via establishing the Hamiltonian function and deriving the optimality condition from Pontryagin's minimum principle is employed. The obtained equations provide a two point boundary value problem which is solved by numerical techniques. The main advantage of this method is obtaining various optimal trajectories with different characteristics by changing the penalty matrices values which able the designer to choose the best trajectory. Finally, a two-link flexible manipulator with mobile base is simulated to illustrate the performance of the method.