# Cartesian Aerial Manipulator with Compliant Arm
## 2 System Description
### Mechanical Design
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structure** & **Mass [kg]** & \(\mathbf{I_{xx}}\) [kg\(\cdot\)m\({}^{2}\)] & \(\mathbf{I_{yy}}\) [kg\(\cdot\)m\({}^{2}\)] & \(\mathbf{I_{zz}}\) [kg\(\cdot\)m\({}^{2}\)] \\ \hline Hexa-rotor & 1.27 & \(1.9\times 10^{-2}\) & \(1.8\times 10^{-2}\) & \(3.0\times 10^{-2}\) \\ X–axis & 0.2 & \(7.9\times 10^{-5}\) & \(6.8\times 10^{-3}\) & \(6.8\times 10^{-3}\) \\ Y–axis & 0.14 & \(1.0\times 10^{-3}\) & \(2.1\times 10^{-5}\) & \(1.0\times 10^{-3}\) \\ Servo & 0.08 & \(3.4\times 10^{-5}\) & \(3.0\times 10^{-5}\) & \(1.0\times 10^{-5}\) \\ Link & 0.09 & \(6.0\times 10^{-4}\) & \(6.0\times 10^{-4}\) & \(1.1\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mass and inertia parameters of the hexa-rotor platform and the different structures of the Cartesian manipulator relative to the center of mass. The cross inertial terms (I\({}_{xy}\), I\({}_{xz}\), I\({}_{yz}\)) are omitted since their value is negligible. The compliant arm depicted in Figure 5 employs a Herkulex DRS-0101 servo and a spring-lever transmission mechanism (1.4 Nm/rad stiffness) that allows the estimation and control of the torque from the deflection measurement [19], integrating an AS5048 magnetic encoder to obtain the deflection angle at 500 Hz with 0.2\({}^{\circ}\) accuracy. The estimator described in Section 4.2 employs this signal for collision detection and controls the torque/force/impedance [26] exerted at the end effector. The link of the arm consists of a NS-01-17-200 linear guide and a NW-02-17 carriage that supports the displacement of the end effector (\(\pm\)30 mm range), using a pair of extension springs (3.2 N/mm stiffness) and a linear potentiometer to estimate the pushing/pulling forces in the XZ-axes in grabbing conditions, as will be explained in Section 4.2. Figure 4: Side (**left**) and front (**right**) views of the Cartesian aerial manipulator, indicating the components. Figure 3: Pololu micro metal gear motors employed in the XY axes’ timing pulley-belt transmission. The end effector of the arm can be reconfigured according to the intended task and type of object to be manipulated. This can be a simple hook to retrieve a device with handles, a magnetic gripper for catching ferromagnetic objects as hand tools, or a servo-gripper for grabbing objects of different shapes. As indicated in the previous subsection, one of the main benefits of the Cartesian morphology with respect to the human-like dual arm systems developed in our previous work [7; 26] is that the manipulator wastes lesser energy in lifting its own weight or reaching any point in its workspace, as the displacement of the end effector along the XY-axes is supported by the linear guide system. Note that in a forearm-upper arm configuration, the shoulder actuators must lift a 50 cm length frame structure, including the servo actuators placed in the links. Thus, the proposed solution is more energy efficient in this sense. Finally, it is necessary to remark that the purpose of the Cartesian manipulator and the compliant arm is to provide a certain level of dexterity (3-DOFs) and sense capability (\(F_{x}\), \(F_{z}\), \(\tau_{\theta}\)) to the aerial platform, sufficient to implement a number of functionalities and tasks without unnecessarily increasing the weight with additional sensors or actuators.