# Mechanical Design of a 6-DOF Aerial Manipulator for assembling bar structures using UAVs

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3 has 4-DOF, so theoretically some of the six manipulator DOF could even be replaced by some of the four platform DOF. Since the aerial platform dynamic is slower than the manipulator one, some manipulation tasks would be difficult to perform. Finally, although the inverse kinematics model of a manipulator can be calculated for any simple 6-DOF chain integrated by rotation joints, it is not always possible to obtain it analytically. Numerical methods are a common alternative, but they are usually slower and often lead to problems of convergence, so they are not recommended for real-time applications with high sampling time. Since the solution of the problem may not be unique, the analytical expression has the additional advantage of being able to include simple programming strategies to choose the most suitable solution among all possible. Therefore, in order to obtain an analytic expression of the inverse kinematics, a mathematical method developed by Pieper (1968) is used for its calculation. This method requires as a condition that the axes of three consecutive joints intersect at a point or are parallel. To overcome this condition, it was decided that the manipulator joints 4, 5 and 6 are respectively roll-pitch-roll. possible to move the end effector very fast in any direction and far enough from the workspace boundary, it will be considered as a base position to perform precise maneuvers, such as the insertion of the bar. By contrast, a singular configuration with the manipulator fully extended would not be advisable, since any disturbance of the aerial platform may require a not reachable end effector position. 2.2 Manipulability study The above performance analysis gives rise to one main arquitecture with regards to the choice and order of the DOF. However, it provides two major solutions in terms of the DOF location. For the first solution, the DOF distribution from the base of the manipulator to the end effector is yawpitch/pitch-roll-pitch-roll. An elongated structure (designed by / ) would be located between the first and the second pitch-type joints to gain some extra length. For the second solution, the DOF distribution is yaw-pitch-pitch/roll-pitchroll and the elongated structure would be between the second pitch-type joint and the following roll-type one. In this section, the degree of manipulability of both sequences is examined to choose the most favorable. Specifically, it is analyzed the dexterity of the manipulator to move the end effector in arbitrary directions with equal ease, since this ability is crucial to reduce the uncertainty in the positioning of the aerial platform when it hovers. One of the most representative manipulability index of a manipulator with a given configuration is the volume of the manipulability ellipsoid (Yoshikawa (1990)). The measures of, corresponding to a manipulator configurations sweeping in the range of the expected position during the insertion of the bar, are shown in Fig. 2. In particular, pitch-type joints are analyzed at the intervals, while the rest of joints are fixed to. Reference lengths of 5 cm for each link and 20 cm for the elongated structure are considered. The higher manipulability volume is reached by the sequence yaw-pitch/pitch-roll-pitch-roll, so this one will be chosen for the manipulator design. It is obtained for the configuration shown in Fig. 3. Since around this optimal configuration is Fig. 2. Manipulability ellipsoid volume for considered sequences. The maximum volume obtained for yaw-pitch/pitch-roll-pitch-roll sequence (in blue) is m 3, while for yaw-pitch-pitch/rollpitch-roll (in red) is m 3. Fig. 3. Manipulator configuration for the maximum volume of the manipulability ellipsoid. Joint coordinates pitch-type (in red) are, and. The intersection between the ellipsoid and the plane is an ellipse shown on scale 1:4.

4 2.3 Motorization pre-evaluation The motorization for driving the manipulator joints is selected by ensuring that the expected maximum torques, provided by the manipulator dynamic model, are always reachable. Although this model is initially unknown, a previous simplified evaluation can be made in order to have a useful first approach to face the design process. The manipulator dynamic model can be written in the general form: where is the external torque vector, is the mass matrix, is the gravity terms vector, considers centrifugal and Coriolis effects, includes friction terms and represents the torques generated by contact forces during bar installation, being the manipulator joint coordinates vector. Friction effects are usually quite difficult to model, but in some cases are negligible compared to the other terms. Coriolis and centrifugal effects are relatively small since the speeds involved are small, while the inertia term is relevant in cases in which high mass needed to accelerate at a great distance from axis of articulation. (1) 4. DESIGN The manipulator consists of three components, shown in Fig. 4: a fixed base, a multi-joint arm and an end effector specifically developed for grasping bars. Structural materials used are commercial Carbon Fiber Reinforced Plastic (CFRP) and aluminum. Fasteners such as screws, nuts and washers are mostly aluminium made ones in order to save weight. The base reaches an approximate mass of 650 g, while moving components, the arm and the end effector, represent a combined mass of 750 g. Then, the total mass of the manipulator is 1.4 kg, below the limit imposed as a requirement due to the payload limitation of aerial platforms. The manipulator total length, when it is completely extended, is 450 mm from the first joint of the arm to the end effector. The position of the arm clamping point on the base is displaced about 100 mm from the center of the latter, so that planned initial length of 500 mm has been reduced. The proposed pre-evaluation of the motorization considers motors able to provide maximum torques that satisfy (2) where is the most unfavorable configuration of the manipulator with regard to gravitational effects; is a vector of approximated mass inertia moments; and is a vector of angular accelerations of each joint that is calculated to compensate the aerial platform oscillations caused by the turbulences in the air stream entering the platform rotors. The mass inertia moments vector is estimated assuming a manipulator structural mass of 150 g uniformly distributed, as well as an end effector mass of 200 g and a bar mass of 100 g. The concentrated mass of each motor is also considered. The maximum torques required at each joint for the horizontally extended configuration of the manipulator is shown in Table 1. Robotis-Dynamixel DC servo motors are selected for being small and lightweight, and having a geometry that facilitates the installation. Fig. 4. Manipulator components: base, arm and end effector. 3.1 Base The base is an auxiliary fixed component that supports the mobile parts of the manipulator, as shown in Fig. 5. The main element of the base is a plate made of CFRP, where the rest of elements are installed on. It is attached to the UAV landing gear by four CFRP fittings and has both longitudinal and transverse stiffeners that provide a great rigidity. The arm is screwed at the front of the plate and some reinforcements are also placed close to the clamping point. Table 1. Previous assessment of manipulator motorization. Art. Type (Kg cm) (Kg cm) (Kg cm) (Kg cm) (Kg cm) Motor 6 ROLL - - 6,25 6,25 8 AX18A 5 PITCH 0,29 3,20-3,48 8 AX18A 4 ROLL - - 6,25 6,25 8 AX18A 3 PITCH 0,67 7,67-8,34 10 MX28T 2 PITCH 2,09 23,36-25,45 30 MX106T 1 YAW ,25 11,25 17 MX64T Fig. 5. Top view (left) and bottom view (right) of the manipulator base.

5 3.2 Arm The arm is an articulated component that contains all the manipulator DOF. It includes a first section with two motorized joints, yaw-pitch, followed by an elongated structure in the shape of a "U", made in CFRP. There is a second section composed of a chain of four motors driving the remaining joints, pitch-roll-pitch-roll, as shown in Fig. 6. driven by a single motor. Lower fingers, also connected, are moved simultaneously by this same motor through a gear transmission. The contact between the bar and each claw takes place in three points placed at 120 using rubber wheels. This envelope configuration, very resistant to disturbances, also helps during the bar gripping to its selfcentering. Moreover, since the length of the bar is quite large, about 500 mm, in comparison with the end effector, the claws are designed spaced 80 mm to increase stability. Fig. 6. Manipulator arm and DOF order. The "U" structure is formed by four rods embedded at their ends. A central stiffener curves the rods, originally straight. Rods prestressed in this manner make a highly stiff and lightweight structure. The design of the "U" structure allows the manipulator to adopt a compact configuration in situations that it is not used or while bar is being transported. The deployment process from the compact configuration to the base position is shown in Fig. 7. When the arm is retracted, the "U" structure can accommodate within the motors chain. Fig. 8. Manipulator end effector with the gripper in a closed position. 5. KINEMATIC MODEL The manipulator Direct Kinematic Model is obtained by using the well-known Denavit-Hartenberg (D-H) method. Coordinate frames associated to each DOF and the corresponding links are represented in Fig. 9, while D-H parameters are shown in Table 2. Craig convention (Ollero (2001)) is followed for mathematical developments. Fig. 7. Arm deployment sequence: the manipulator goes from the compact configuration (1) to the base position (3) passing through (2). 3.3 End efector The manipulator end effector is gripper-style and has two claws designed for a robust hold by mechanical pressure. This architecture, particularly adapted to the bar used in experiments, cylindrical and 20 mm outer diameter, is shown in Fig. 8. Each claw is formed by two CFRP fingers, one upper and one lower. Upper fingers of both claws are connected for greater structural rigidity and they are directly Fig. 9. Coordinates frames for DH method. Y-axis is not represented for simplicity. Vectors and describe the end-effector position and orientation respectively. Vector defines end effector rotation around Z 6 axis. Table 2. D-H parameters. The origins of Frame 4 and Frame 5 are coincident for simplicity. Link Denavit-Hartenberg parameters L L L L6

6 The model is given by the following equations (typical simplified notation is used for trigonometric functions, where, y ): (3) (4) (5) (6) (7) (8) (9) (10) (11) 5. CONCLUSIONS (21) (22) (23) (24) This paper presents a methodology to perform the mechanical design of a 6-DOF lightweight manipulator for assembling bar structures using a rotary-wing UAV. For a suitable choice of the number, type and order of the DOF, it has become clear the importance of conducting a thorough analysis of the expected manipulator performance. A manipulability study is also useful to maximize the manipulator dexterity, while a preliminary motor evaluation allows a first estimation of the weight and volume distribution to face the design process. A manipulator of this type developed for the ARCAS project is shown in Fig. 10. This robotic manipulator has been tested by teleoperation. In next months, an automatic control system will be developed to be integrated into the quadrotor controller to perform flight tests before the construction of bar structures. The manipulator Inverse Kinematic Model has been calculated following a specific development (Barrientos et al. (2007)) that uses Pieper method to achieve an analytical solution. This development allows a kinematic decoupling of the three first joint variables of the arm, obtained by purely geometrical methods, from the three later, calculated in a more systematic way from the homogeneous transform. The model is given by the following equations: (12) Fig DOF Aerial manipulator developed for ARCAS project. where (13) (14) (15) (16) (17) (18) (19) (20) ACKNOWLEDGEMENTS This work was partially funded by the FP7 European Commission project ARCAS (FP ) and the Spanish Science Ministry project CLEAR (DPI C02-01). REFERENCES Barrientos, A. L.F. Peñín, C. Balaguer and R. Aracil (2007). Fundamentos de Robótica, McGraw-Hill. Danko, T. W. and P. Y. Oh (2013). A Hyper-Redundant Manipulator for Mobile Manipulating Unmanned Aerial Vehicles, 2013 International Conference on Unmanned Aircraft Systems (ICUAS). Doyle, C. E., J. J. Bird, T. A. Isom, C. J. Johnson, J. C. Kallman, J. A. Simpson, R. J. King, J. J. Abbott, and M. A. Minor (2011). Avian-Inspired Passive Perching Mechanism for Robotic Rotorcraft, 2011 IEEE/RSJ.

7 Jimenez-Cano, J. A. E., J. Martin, G. Heredia, R. Cano and A. Ollero (2013). Control of an aerial robot with multilink arm for assembly tasks, Proceedings of the 2013 IEEE International Conference on Robotics and Automation. Kondak, K., K. Krieger, A. Albu-Schaeffer, M. Schwarzbach, M. Laiacker, I. Maza, A. Rodriguez-Castaño and A. Ollero (2013). Closed loop behavior of an autonomous helicopter equipped with a robotic arm for aerial manipulation tasks, International Journal of Advanced Robotic Systems, Vol 10, pp 1-9. Lindsey, Q., D. Mellinger and V. Kumar (2011). Construction of Cubic Structures with Quadrotor, Proceedings of Robotics: Science and Systems VII. Mellinger, D., Q. Lindsey, M. Shomin and V. Kumar (2011).Design, Modeling, Estimation and Control for Aerial Grasping and Manipulation, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. Ollero, A. (2001). Robótica. Manipuladores y robots móviles, Marcombo. Pieper, D. L. (1968), The kinematics of manipulators under computer control, Stanford Artificial Intelligence Lab., MEMO AIM-72. Pounds, P. E. I., D. R. Bersak, and A. M. Dollar (2011). Grasping From the Air: Hovering Capture and Load Stability, 2011 IEEE International Conference on Robotics and Automation. Yoshikawa, T. (1990). Foundations of Robotics. Analysis and Control, Massachussets Institute of Technology, MIT Press.

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