Snake Aerial Manipulators: A Review <s> D. AERIAL MANIPULATION DESIGN CONSIDERATIONS 1) RESTRICTIONS ON THE ROTATION OF PROPELLERS <s> In this paper a novel aerial manipulation system is proposed. The mechanical structure of the system, the number of thrusters and their geometry will be derived from technical optimization problems. The aforementioned problems are defined by taking into consideration the desired actuation forces and torques applied to the end-effector of the system. The framework of the proposed system is designed in a CAD Package in order to evaluate the system parameter values. Following this, the kinematic and dynamic models are developed and an adaptive backstepping controller is designed aiming to control the exact position and orientation of the end-effector in the Cartesian space. Finally, the performance of the system is demonstrated through a simulation study, where a manipulation task scenario is investigated. <s> BIB001 </s> Snake Aerial Manipulators: A Review <s> D. AERIAL MANIPULATION DESIGN CONSIDERATIONS 1) RESTRICTIONS ON THE ROTATION OF PROPELLERS <s> We propose a novel multi-rotor flying platform, ODAR (omni-directional aerial robot), which is fully-actuated (i.e., can assume arbitrary motion in SE(3) or generate arbitrary control wrench in se(3)) by six opportunistically distributed rotors, each driven by reversible ESC (electronic speed controller) for bi-directional thrust generation. Due to this omni-directional wrench generation, the ODAR system can realize such powerful behaviors impossible with conventional multi-rotor flying platforms as: 360° photo/video shooting while holding its position for VR scene generation; or resisting sideway gust while keeping its attitude and exerting downward pushing force larger than its own weight for aerial manipulation applications. This paper presents optimal mechanical design, modeling and control, hardware and software implementation, and experimental verification of the ability of the ODAR system to attain those behaviors impossible with the conventional drones as stated above. <s> BIB002 </s> Snake Aerial Manipulators: A Review <s> D. AERIAL MANIPULATION DESIGN CONSIDERATIONS 1) RESTRICTIONS ON THE ROTATION OF PROPELLERS <s> This paper presents a theoretical study on omni-directional aerial vehicles with body-frame fixed unidirectional thrusters. Omniplus multi-rotor designs are defined as the ones that allow to exert a total wrench in any direction using positive-only lift force and drag moment (i.e., positive rotational speed) for each rotor blade. Algebraic conditions for a design to be omniplus are derived, a simple necessary condition being the fact that at least seven propellers have to be used. An energy optimal design strategy is then defined as the one minimizing the maximum norm of the input set needed to span a certain wrench ellipsoid for the adopted input allocation strategy. Two corresponding major design criteria are then introduced: firstly, a minimum allocation-matrix condition number aims at an equal sharing of the effort needed to generate wrenches in any direction; secondly, imposing a balanced design guarantees an equal sharing of the extra effort needed to keep the input in the non-negative orthant. We propose a numerical algorithm to solve such optimal design problem and a control algorithm to control any omnidirectional platform. The work is concluded with informative simulation results in non-ideal conditions. <s> BIB003
Once in the phase of aerial manipulation, three important computational implications arise, the first one is concerned to the rotation of the motors, this means that while the control can reach positive and negative bounds, some aircraft like multirotors require that their propellers do not change their preset direction of rotation in order to avoid effects of selfrotation, this is seen as an optimization problem and is described in  , BIB002 , BIB003 : However, when it is possible to change the sense of rotation of the propellers, it can not be performed arbitrarily and follows negative resultant compensation procedures, one way is to add an additional motor that will counteract vectorially all the negative moments and forces generated by the rest of the thrusters BIB001 .