Time-Optimal Handover Trajectory Planning for Aerial Manipulators Based on Discrete Mechanics and Complementarity Constraints

Planning a time-optimal trajectory for aerial robots is critical in many drone applications, such as rescue missions and package delivery, which have been widely researched in recent years. However, it still involves several challenges, particularly when it comes to incorporating special task requirements as well as the aerial robot's dynamics into the planning. In this work, we study a case where an aerial manipulator shall pick up a parcel from a moving mobile robot in a time-optimal manner. Rather than setting up the approach trajectory manually, which makes it difficult to determine the optimal total travel time to accomplish the desired task within dynamic limits, we propose an optimization framework, which utilizes the framework of discrete mechanics and complementarity constraints. In the proposed approach, the system dynamics is considered via discrete variational Lagrangian mechanics that provides reliable estimation results according to our experiments. The handover opportunities are automatically determined and arranged based on the desired complementarity constraints. Finally, the performance of the proposed framework is verified with numerical simulations and hardware experiments with our self-designed aerial manipulator.