# Cartesian Aerial Manipulator with Compliant Arm
## 2 System Description  
### Motivation  
The Cartesian manipulator aims to avoid three inconveniences of the human-like robotic arms developed in our previous work [7; 19]. First of all, several manipulation tasks like grasping or peg-in-hole are defined in the Cartesian space rather than in the joint space, so it is more convenient that the mapping between both spaces is straightforward in order to improve the positioning accuracy. According to the forward kinematic model, the XYZ position of the end effector depends simultaneously on the rotation angle of the three [19] or four [7] joints of the manipulator (shoulder and elbow). Therefore, the joint position errors, as well as errors associated with the manufacturing and assembly of the arm (clearance, misalignment), will be propagated to the three Cartesian coordinates of the end effector. Additionally, the mechanical deflection of the joints in a compliant arm [7] may cause deviations of several centimeters in the position of the end effector with respect to an equivalent stiff-joint arm. In a Cartesian manipulator, instead, the position of the end effector on each axis is controlled with its own actuator independently from the other joints, so the position errors are decoupled and the trajectory control in the task space is simplified.  
Secondly, the effective reach of a human-like manipulator (-50 cm reach) is in practice relatively small, around 30 cm, taking into account that the nominal operation position of the arm is typically an L-shaped configuration (forearm lifted 90\({}^{\circ}\)) and due to the limit in the rotation angle of the elbow joint. Note that humans extend the reach of the hands with the torso and legs, whereas in an aerial manipulator the motion of the arms is usually constrained by the landing gear and the perimeter of the propellers. In this sense, the Cartesian base avoids dead-zones in its workspace due to joint limits, allowing access to points close to the multirotor base, which can be useful, for example, in object retrieval and  
Figure 1: Cartesian manipulator (**left**) integrated in S550 hexarotor platform (**right**).  
storage. Finally, a two link manipulator in the upper arm-forearm morphology typically requires a significant amount of torque and energy to lift its own weight, whereas in the developed prototype the Cartesian manipulator only has to compensate for the inertia and friction of the carriage, reducing in this way the required torque of the actuators, and thus, their weight. Not only that, but the linear guide also isolates the actuators from impacts and loads, avoiding the design of bearing-based protection mechanisms, as in [7].  
The Cartesian manipulator shown in Figure 1 implements a Prismatic-Prismatic-Revolute (PPR) configuration, introducing a revolute joint attached at the Cartesian base, since the landing gear and central body of the hexa-rotor platform do not allow the placement of a linear actuator in the vertical axis, and because this configuration extends the reach of the end effector in the X-axis (forward direction). No additional degrees of freedom are considered for end effector positioning due to the convenience of reducing the weight, complexity and size of the manipulator, and because the capabilities of the robot can be extended with the additional degrees of freedom provided by the aerial platform [13; 32].