## 1 Introduction  
In recent years, a notable interest in the adoption of autonomous systems, such as aerial manipulators, has grown. They can be used for the execution of safety-critical and resource-intensive tasks within various industrial domains. These applications encompass a wide range of activities, including the inspection, assembly, and maintenance of mechanical structures, as well as general inspection and maintenance duties where the enhanced maneuverability of aerial manipulators can be exploited [1, 2]. An Unmanned Aerial Manipulator (UAM) consists of a robotic manipulator attached to an Unmanned Aerial Vehicle (UAV). Multicopters with multiple rotors, which are capable of stable hovering, are the most common choice for the base configuration, ensuring stability while the manipulator executes its tasks [3]. Various designs have been considered for the robotic manipulator, from task-specific grippers to hyper-redundant arms [1, 3], lightweight manipulators [4], and additional arms to stabilize the UAV [5]. The coupling of kinematics and dynamics between UAV and manipulator presents a particular challenge in achieving the precise positioning and control of the end-effector, especially for complex tasks like grasping, due to the motion of the UAV during the maneuver. Two main strategies exist for the control of a UAM: in the coupled strategy, the dynamics of the whole system is considered [6], while in the decoupled strategy, the manipulator and the UAV have distinct control systems [1]. Certain approaches aim to reduce the base motion at the mechanical design level, employing counter-balancing mechanisms or mass distribution strategies [7], while other methods exploit the kinematic redundancy of the manipulator to minimize the dynamic disturbance transferred from the manipulator to the UAV [8; 9]. On the other hand, in space robotics, the control of floating-base manipulators has been addressed assuming the conservation of momentum [10] to compensate for base motions. In this field, inverse kinematic control algorithms based on the Generalized Jacobian enable the precise positioning of the end-effector. An adaptation of the Generalized Jacobian for aerial manipulation is detailed in [9], where gravity and UAV control forces are also considered. CLIK (Closed-Loop Inverse Kinematics) [11] strategies have already been applied to aerial manipulation. In [12], a first-order CLIK algorithm fed by an impedance control module generates reference values for joint angles, UAV position, and its attitude. In [13], a second-order CLIK algorithm working on joint angles, UAV position, and attitude is used. A first-order CLIK algorithm with integral action is introduced in [14]. In [15], the CLIK algorithm with the adjoint of an integral action is used to control the robotic arm, and the UAV is controlled by a distinct non-linear controller; the UAV controller also generates a reference for the torque between the UAV and the robotic arm, and then this torque demand is fulfilled as a secondary task in the CLIK algorithm. In this paper, we propose two novel methods for the solution of the inverse kinematics of serial aerial manipulators to perform trajectory tracking tasks. Both methods are derived from CLIK schemes for fixed-base manipulators and are adapted to take into account UAV motion. These algorithms are used to compute the joint trajectories corresponding to the desired end-effector trajectory; these then constitute the reference input for some feedback kinematic control scheme at the level of joint velocities or accelerations that ensures the desired precision even in the presence of modeling uncertainties and/or unknown disturbances. The proposed methods for the solution of the inverse kinematics consider and compensate for UAV motions caused by the reaction forces/torques due to the robotic arm motion and by known forces/torques (gravity, control forces and torques). At the same time, the feedback of CLIK algorithms is used to compensate for modeling errors and other disturbances.