This paper proposes a decentralized passive impedance control scheme for collaborative grasping using under-actuated aerial manipulators (AMs). The AM system is formulated, using a proper coordinate transformation, as an inertially decoupled dynamics with which a passivity-based control design is conducted. Since the interaction for grasping can be interpreted as a feedback interconnection of passive systems, an arbitrary number of AMs can be modularly combined, leading to a decentralized control scheme. Another interesting consequence of the passivity property is that the AMs automatically converge to a certain configuration to accomplish the grasping. Collaborative grasping using 10 AMs is presented in simulation.

This paper proposes a parameterization method to represent SO (3) over multiple turns. This method is called a memory-based parameterization, because the idea is to integrate the past trajectory of exponential coordinates. The parameterization is consistent in the sense that the true rotation matrix can be reconstructed by using the exponential map. As an application of the proposed method, a 6D impedance controller is designed with a radially unbounded potential function. Consequently, in contrast to the conventional methods, an arbitrarily large angular deflection can be accommodated, resulting in a more realistic impedance behavior. The proposed schemes are validated through simulations and experiments.