Underactuated Flexible Aerial Manipulators: a New Framework for Optimal Trajectory Planning Under Constraints Induced by Complex Dynamics

The aerial manipulators (AMs) are a new class of unmanned aerial systems (UASs) that are created in response to the ever-increasing demand for autonomous object transportation and manipulation. Because of power supply restrictions, the load carrying capacity is limited and therefore it is necessary to reduce the overall weight of these UASs. The past works in the field of AMs consider the multi-rotor unmanned aerial vehicles (UAVs) as the base and manipulators with rigid links as the interactive elements with the environment which are bulky and heavy. To overcome the issue, this paper introduces the AMs endowed with flexible manipulators, their dynamic modeling, a new method for trajectory planning and control algorithm such that the unfavorable effects of using flexible elements like vibrations are minimized. Due to lack of kinematic constraints and the presence of flexibility conditions, conventional methods of trajectory planning for ground wheeled-mobile manipulators (GWMMs) such as extended and augmented Jacobian matrix cannot be applied to AMs. The addition of flexibility to the manipulator increases underactuation degrees (UADs), the complexity of trajectory planning and control synthesis. Considering large deformation assumption for flexible links, the dynamic equations and their induced nonholonomic constraints are derived applying Lagrangian formulation. Then, these constraints with that part of equations of motion corresponding to the links flexibility are solved simultaneously in the context of an optimization algorithm resulting in optimized trajectories. Through simulation results, the proposed method of trajectory planning and vibration control of underactuated flexible AMs has been shown to be effective.