Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation

Received December 27, 2017, accepted March 23, 2018, date of publication May 4, 2018, date of current version June 20, 2018. Digital Object Identifier 10.1109/ACCESS.2018.2833160 Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation ALEJANDRO SUAREZ , GUILLERMO HEREDIA , AND ANIBAL OLLERO Robotics, Vision and Control Group, University of Seville, 41092 Seville, Spain Corresponding author: Guillermo Heredia ([email protected]) This work was supported in part by the European Commission H2020 project AEROARMS under Grant H2020-ICT-2014- 644271, and in part by the Spanish MINECO Retos projects AEROCROS under Grant DPI2015-71524-R and ARM-EXTEND under Grant DPI2017-89790-R. The work of A. Suarez was supported by the Spanish Ministerio de Educación, Cultura y Deporte through its FPU program. ABSTRACT This paper presents an anthropomorphic, compliant and lightweight dual arm manipulator designed and developed for aerial manipulation applications with multi-rotor platforms. Each arm provides four degrees of freedom in a human-like kinematic configuration for end effector positioning: shoulder pitch, roll and yaw, and elbow pitch. The dual arm, weighting 1.3 kg in total, employs smart servo actuators and a customized and carefully designed aluminum frame structure manufactured by laser cut. The proposed design reduces the manufacturing cost as no computer numerical control machined part is used. Mechanical joint compliance is provided in all the joints, introducing a compact spring-lever transmission mechanism between the servo shaft and the links, integrating a potentiometer for measuring the deflection of the joints. The servo actuators are partially or fully isolated against impacts and overloads thanks to the flange bearings attached to the frame structure that support the rotation of the links and the deflection of the joints. This simple mechanism increases the robustness of the arms and safety in the physical interactions between the aerial robot and the environment. The developed manipulator has been validated through different experiments in fixed base test-bench and in outdoor flight tests. INDEX TERMS Aerial manipulation, aerial robots, design of floating-base manipulators, compliance. I. INTRODUCTION Aerial manipulation proposes the development of flying robots equipped with one or more [1] robotic arms capable to perform certain operations in workspaces out of the reach for humans. This technology is intended to simplify and reduce the costs associated to inspection and maintenance tasks that are typical in a wide variety of scenarios in the industry. Some examples include the detection and repair of leaks in high altitude pipes in chemical plants, the insulation of cracks in the blades in wind turbines, the installation and retrieval of sensor devices in buildings and other structures, or the measurement of the deflection in the metal beams in bridges. The platforms employed in aerial manipulation are vertical take-off and landing (VTOL) unmanned aerial vehicles (UAV) due to the necessity of staying in hover during the execution of the operation carried out by the robotic arms. Autonomous helicopters [2], [3] and quadrotors [4] have been employed in grasping and transportation tasks in outdoors. Grasping moving objects [5] and cooperative grasping with multiple UAVs [6] have been also demonstrated previously. Two approaches can be identified in the development of aerial manipulation robots: 1) integrating a conventional robotic arm designed for ground applications, or 2), designing a specific manipulator intended to aerial platform. The first approach is followed in [2] and [7], where a 7 degrees of freedom (DOF’s) industrial manipulator is integrated in a helicopter with high payload capacity, or in [4], where a quadrotor is equipped with a 7-DOF robotic arm commercially available. Several research prototypes have been designed for multirotors and tested on flight, with different number of degrees of freedom, from two up to seven [8]–[12]. Aerial manipulators have been applied in a wide variety of applications, including valve turning with quadrotors [13], visual servoing [14], contact based inspection [15], or grasping [16], [17]. Mechanical compliance is a highly desirable feature for an aerial manipulation robot as it increases safety in operations involving physical interactions with the environment [18]–[20]. The ability of springs and other elastic elements for absorbing the energy of impacts and overloads at VOLUME 6, 2018 This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ 29173 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation higher rates than the actuators can provide in a passive way prevents that contact forces are rigidly propagated through the manipulator to the aerial platform, destabilizing it. Series elastic actuators [21] introduce an elastic transmission element between the actuator and the output link, allowing the estimation of the forces based on deflection measurement. This principle can be exploited in low weight robotic arms built with low cost servos that do not provide any torque control or feedback capabilities. That is, the joint torque and the contact forces can be estimated just measuring the deflection of the elastic element [22]–[24]. Mechanical joint compliance also protects the gearbox of the servos against peak forces caused by impacts, the transition from contactless to contact situations, or overloads caused by motion constraints, for example in closed kinematic chain configurations. In our previous work, two research prototypes of human-size, compliant and very low weight robotic arms where developed, demonstrating their application to soft collision detection and reaction, payload estimation [25], force torque estimation and control, and obstacle localization [26]. TABLE 1. Main features of different aerial manipulators. Bimanual manipulation has been considered in some recent works, as the valve turning task described in [13], the grasping and transportation application shown in [27], or the human-size dual arm aerial manipulator presented in [28]. The main motivation for a dual arm manipulator is to extend the range of tasks that a flying robot is able perform w.r.t. a single arm, allowing for example grasping large objects, manipulating two devices at the same time, or increasing the maximum lift load. This is done however at expenses of increasing the payload of the UAV, so the effort now is in the design of very low weight manipulators [29]. The main features of several lightweight and compliant manipulators are compared in TABLE 1. The main contribution of the paper is the development and experimental validation of an anthropomorphic, compliant and lightweight (1.3 kg) dual arm manipulator designed for aerial manipulation applications. Each arm provides 4 DOF’s for positioning the end effector in a human-like kinematic configuration. A simple and compact compliant transmission mechanism is integrated in all the joints with a deflection potentiometer, allowing the estimation and control of the joint torque and the contact forces. A customized and carefully designed aluminum frame structure manufactured by laser cut isolates the servo actuators against impacts and radial-axial overloads, supporting the rotation of the output links and the spring-lever transmission. The paper details the design and construction of the arms, covering the kinematics, dynamics, and the force-torque relationships. Identification experiments have been conducted for evaluating the impact response and the frequency behavior. Deflection control experiments show how compliance can be exploited for reducing the interaction forces between the aerial manipulator and the environment on flight. The developed dual arm manipulator was integrated in a hexarotor platform, demonstrating bimanual aerial grasping. The rest of the paper is organized as follows. Section II introduces some general design considerations related to aerial manipulation. Section III presents the design of the dual arm manipulator with its mechanical specifications, the kinematics and the control architecture. Section IV details the spring-lever transmission mechanism integrated in the joints, deriving the force-torque relationships. Section V describes the structure of the arms, providing the mass and inertia values. Experimental results validating the design are shown in Section VI, whereas Section VII summarizes the conclusions of this work. II. DESIGN CONSIDERATIONS A. REQUIREMENTS IN AERIAL MANIPULATION 1) LOW WEIGHT AND INERTIA FEATURES The first two parameters that should be determined in the design of a robotic arm to be integrated in an aerial platform are its weight and maximum lift load. Let us call PLUAV to the maximum payload that the UAV is able to lift, and marm and PLarm to the weight and expected payload that the arm should lift, respectively. Then, the following equation can be defined: marm +PLarm ≤η·PLUAV (1) Here η∼ =0.7 is the dynamic margin constant that indicates how far away the brushless motors of the UAV are from the saturation in normal operation. If the aerial platform is overloaded (η > 0.8), the propellers may suffer overheating and they might not respond properly to motion commands. In order to reduce the inertia of the arms, and thus the influence of arms motion over the aerial platform, it results convenient to place the servos as close as possible to the base of the aerial platform. Different transmission mechanisms can be employed for this purpose, including timing belts [10], pulley-wire [20] or rigid bars [28]. However, these solutions typically increase the weight of the manipulator, reduce the range of rotation of the joints, and complicate the design and assembly of the manipulator. The mass distribution of the different components employed in the construction of the arms is represented in Fig. 1, whereas TABLE 2 indicates the mass density of the materials. 2) ACTUATORS The design and development of robotic arms intended to aerial manipulation is still a hard task due to the multiple 29174 VOLUME 6, 2018 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation FIGURE 1. Mass distribution (grams and %) of the developed dual arm. TABLE 2. Materials employed in the lightweight dual arm. design requirements imposed by the aerial platform in terms of very low weight, low inertia, mechanical robustness and dexterity. What is more, there exist important technological limitations as only a few brands of actuators are suitable for this purpose. In this sense, the so called smart servos, such as Herkulex or Dynamixel, are nowadays the best option for building low weight manipulators [4], [8], [11]. These devices include the motor, gearbox, electronics, control and communications in a compact device that can be easily assembled in a frame structure, providing high torque to weight ratios. However, the performance of these actuators from the control point of view is quite limited, as they do not provide any torque feedback or control, the control rates are usually low (<100 Hz), and the embedded controller has to be interfaced. Although the lift load of the arms should be determined by the application, its value is given in practice by the combination of servo actuators employed, taking into account that the stall torque parameter provided by the manufacturer is usually 2–3 times higher than the maximum dynamic torque that the servo is able to provide. 3) KINEMATICS The choice of the kinematic configuration of the arms is determined in the first place by the task that the aerial robot is expected to perform. Almost all aerial manipulators that can be found on literature consider at least two joints, shoulder pitch and elbow pitch [8], [9], with the forearm and upper arm links. Some prototypes exploit the rotation of the UAV around the yaw angle instead of employing a servo for this purpose [8]. Other works implement the typical configuration with three joints for positioning and two [10] or three [11] DOF’s for wrist orientation. Motivated by the convenience to provide a human-like manipulation capability, this work follows a bio-inspired design approach, so the kinematics and size of the human arm are replicated. The idea is that the application of the arms results more comfortable and intuitive for a human operator, without requiring special training. The mechanical construction of this configuration also results in a compact and robust design, as it will be seen later. B. COMPONENTS AND MATERIALS 1) FRAME STRUCTURE Aluminum and carbon fiber are widely used for building low weight robotic arms intended to aerial manipulation due to their mechanical robustness and low weight. ABS or PLA plastics should be avoided as they are not impact resistant and may suffer deformations for temperatures around 40 ◦ C. Note that in case of impact, the manipulator will support the kinetic energy of the whole aerial platform (0.625 J for a 5 kg weight platform moving at 0.5 m/s). Most aerial robots employ carbon fiber in the frame structure of the arms. However, the manufacturing cost and the material itself is quite expensive with respect to aluminum. Besides its low cost, aluminum is highly malleable, so L-shaped or U-shaped frames can be easily manufactured bending a flat frame. The possibility of introducing these geometries is important in the design of the frame structure and its parts. 2) COMPLIANT TRANSMISSION As mentioned before, one of the main contributions of this work is the development of a simple, compact and low weigh spring-lever transmission mechanism integrated in all the joints of the arms to provide compliance. Conventional steel springs are preferred rather than other elastic materials like elastomers due to their high linearity and low hysteresis. The mechanism makes use of igus flange bearings screwed to the aluminum frame structure for supporting the rotation of the output links w.r.t. the servo shafts. These components provide low friction and vibration dampening, being also robust against impacts and radial/axial loads. FIGURE 2. 3-D model of the anthropomorphic dual arm integrated in a hexarotor. Take-off/landing (left) and operation (right) configurations. C. INTEGRATION IN AERIAL PLATFORM In order to maintain the symmetry of the aerial platform in terms of geometry and mass distribution, the manipulator is typically installed under the central hub of the UAV, trying to reduce the displacement of the center of mass (CoM) with respect to the vertical axis. This implies that the arms should be placed between the legs of the landing gear, what may reduce the workspace of the arms due to motion constraints. The solution adopted in this work is the one shown in Fig. 2. Thanks to the anthropomorphic kinematic VOLUME 6, 2018 29175 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation configuration, the arms can be lifted rotating the shoulder roll joints, so the upper arm and forearm links are above the landing gear for UAV take-off and landing. An adaptation frame consisting of two transversal hollow aluminum profiles is attached to the base of the landing gear. The configuration of the arms during the take-off and manipulation phases can be seen in Section VI-D. FIGURE 3. Phases involved in the design, development and experimental validation of an aerial manipulation prototype. D. DEVELOPMENT METHODOLOGY The development of an aerial manipulation robot involves a number of phases, graphically represented in Fig. 3. The first one is the concept design, which consist of defining the main specifications of the manipulator (payload, size, number of joints, capabilities), and drawing different designs on paper to have an idea of its structure. Once a preliminary design is proposed, the different frame parts are modelled using 3D computer aided design software such as CATIA or Solid Edge. It is convenient to specify the mass density of all the components in the model in order to obtain an estimation of the mass and inertia of the prototype during its design. It is also necessary to take into account the limitations and constraints associated to the manufacturing and assembly processes, as stated in Section II-B. Several iterations may be necessary in the design until this can be implemented in the desired way. Once the prototype is assembled, the next step consists of integrating the sensors, electronics, and wiring in the frame structure. The hardware/software architecture, described in more detail in Section III-C, is the basis for the development of the different functionalities of the aerial manipulator, such as position, trajectory, and force control, collision detection and reaction, teleoperation, or visual servoing for grasping. All these capabilities must be extensively validated in testbench before integrating the manipulator in the aerial vehicle in order to prevent accidents due to unexpected behaviors, evaluating the reliability and accuracy through experimental results. The installation of the arms in the multirotor requires an additional frame structure which should be attached at the landing gear or well at the base of the platform. This structure can also support the batteries, the computer board, and other sensors, as the camera. The validation of the aerial robot in outdoor flight tests requires the participation of at least two persons: the pilot of the UAV and the operator of the arms. Security nets and ropes should be used in the first tests for preventing potential crashes, especially if the evaluated task involves contact forces. The position and orientation of the multirotor, the applied control signals, the angular position of the actuators and their references should be logged in data files so the experimental results can be analyzed offline. FIGURE 4. Anthropomorphic, compliant and lightweight dual arm. FIGURE 5. Detailed view of the joints in the right arm. Hands-up pose. III. ANTHROPOMORPHIC DUAL ARM DESIGN A. DESCRIPTION A picture of the developed anthropomorphic, compliant and lightweight dual arm manipulator can be seen in Fig. 4, with a detailed view of the right arm construction in Fig. 5. The dual arm system was designed and developed completely from scratch, although several design concepts are taken from our previous work [25], [26], [28]. The actuators used are the Herkulex DRS-0101 and DRS-0201 smart servos from Dongbu Robot, introducing the igus EFOM-08 and EFSM- 06 flange bearings in the frame structure for isolating the servos from impacts and overloads and for building the compliant transmission mechanism. The frame structure of the arms consists of a set of 34 customized aluminum parts manufactured by laser cut, two 8 mm Ø shafts for the shoulder 29176 VOLUME 6, 2018 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation pitch joint, and four 6 mm Ø hollow profiles for the upper arm and forearm links. The laser cut frames include 2 mm, 8 mm and 10 mm thickness parts. The U-shaped aluminum frames in the shoulder pitch-yaw and in the elbow pitch structures (see Section V) are built bending 90 deg the 2 mm thickness flat profile sections. The frame structure has been designed in such a way that the cost and complexity of the manufacturing processes is reduced as much as possible. TABLE 3. Specifications of the compliant dual arm. TABLE 4. Specifications of the joints of the arms. The main specifications of the dual arm manipulator are summarized in TABLE 3, providing additional information relative to each joint of the arms in TABLE 4. The maximum lift load was obtained placing a payload mass at the grippers with the arm fully stretched, rotating it from the vertical to the horizontal position so the torque due to gravity is maximum. The kinematic configuration, described in more detail in the following subsection, as well as the dimensions are similar to the human arm motivated by the convenience of having human-like manipulation capabilities in an aerial platform. The shoulder roll joints are used for lifting the arms above the landing gear before the landing maneuver. Finally, two Futaba S3003 servos have been employed for building a simple gripper, integrating a micro switch in the palm for detecting the contact with the object to grasp. The developed manipulator satisfies the following design requirements imposed in the first stage of the design process: 1) Low weight and inertia. 2) Mechanical robustness, with high servo protection. 3) Intersection of the four joint axes in a common point, which simplifies the inverse kinematics. 4) Integration of compliant transmission mechanism. 5) Integration of deflection potentiometers in the joints. 6) Low clearance for increasing the accuracy in the positioning of the end effector. All these features contribute to increase the probability of success in the application of an aerial manipulation robot to inspection and maintenance tasks in outdoor environments. FIGURE 6. Kinematic configuration of the anthropomorphic dual arm and reference frames of both arms attached to the shoulder joint. B. KINEMATICS 1) KINEMATIC CONFIGURATION The anthropomorphic dual arm provides 4 DOF’s for end effector positioning in a human-like kinematic configuration with the shoulder pitch joint at the base, followed by the shoulder roll, shoulder yaw and the elbow pitch joint. The corresponding joint variables of the output links are denoted by qi 1,qi 2,qi 3, and qi 4, respectively, with i=1,2 for the left and right arms. The wrist orientation joints have not been implemented in this version. A rendered view of the arms with the parameters of the kinematic model is represented in Fig. 6, including the forearm and upper arm lengths, the separation between the arms, and the joint angles with the positive direction of rotation given by the right-hand criteria. A reference frame Xi 0Yi 0Zi 0attached to the intersection point of the joints of the shoulder of each arm is defined, so the tool center point (TCP) or any point in the workspace will be referenced to this frame. Each arm provides one redundant DOF that can be exploited for collision avoidance, null space control, or for orienting the end effector. In this work the shoulder roll angle is considered as a parameter, qi 2=ϕi, which can VOLUME 6, 2018 29177 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation be tuned according to the task. For example, in the takeoff or landing operations, the arms should be in a position such that the elbow and wrist points are above the landing gear, so ϕi= ±90 degrees, whereas in a visual servoing task, this angle will take values around ϕi= ±10 degrees. 2) FORWARD KINEMATICS Let FKi:<4→ <3represents the forward kinematics of the i-th arm. The position of the TCP of each arm is obtained multiplying the transformation matrices associated to each joint, defined as follows: 0 1Tiqi 1=    ci 10si 10 01 0 0 −si 1 0 0 0 ci 1 0 0 1     1 2Tiqi 2=    1 0 0 0 0ci 2−si 20 0 0 si 2 0 ci 20 0 1     2 3Tiqi 3=    ci 3−si 30 0 si 3ci 30 0 0 0 si 2 0 1 0 0 1     3 4Tiqi 4=    ci 40si 40 0 1 −si 20 −si 4 0 0 0 ci 4−L1 0 1     (2) Here ci j=cos(qi j) and si j=sin(qi j). The upper arm link length (from shoulder to elbow) and the forearm length (from elbow to TCP) are denoted by L1and L2, respectively. The last transformation matrix is referred to the elbow joint, so it is displaced the upper arm link length L1. The position of the TCP referred to each frame is computed as follows: ri TCP qi=  xi yi zi =FKiqi =  4 Y j=1 j−1 jTqi j ·    0 0 −L2 1     (3) where qi=[qi 1,qi 2,qi 3,qi 4]Tis the angular position vector of the output link, denoting as θi=[θi 1, θi 2, θi 3, θi 4]Tthe servo position vector. 3) INVERSE KINEMATICS In order to provide an analytical solution to the inverse kinematics, it was imposed by design that the rotation axis of all the joints intersect in a common point. The joint angles of the output links can be determined from the desired Cartesian position applying the inverse kinematics IKi:R3→R4: IKiri TCP=FK−1 iri TCP=    qi 1 qi 2 qi 3 qi 4     (4) As mentioned before, it is imposed for simplicity that qi 2=ϕi, considering the angle ϕias a parameter. The elbow pitch angle only depends on the position of the TCP and on the forearm and upper arm links lengths: qi 4= −cos−1 sx2 i+y2 i+z2 i−L2 1−L2 2 2·L1·L2 (5) It can be demonstrated that the shoulder pitch joint satisfies the following trigonometric equation whose analytical solution is omitted for space reasons: xi·sin qi 1+zi·cos qi 1wi(6) wi=L2 2−L2 1+x2 i+z2 i+2·L1·yi·sin qi 2 2·L1·cos qi 2(7) Note however that the resulting quadratic equation may have two solutions, corresponding to the elbow-up/down poses. The shoulder yaw angle is finally obtained: qi 3=atan2ai,bi(8) ai=xi·si 1·si 2+yi·ci 2+zi·ci 1·si 2(9) bi=xi·ci 1−zi·si 1(10) FIGURE 7. Cartesian position/velocity controller based on inverse kinematics. C. ARMS CONTROL BASED IN INVERSE KINEMATICS A position/velocity controller based on inverse kinematics has been implemented. The block diagram can be seen in Fig. 7. In this example, the arms are operated using a 6-DOF mouse that generates the velocity references, although this scheme has been also applied to visual servoing. The inverse kinematics module generates then the joint references taken as input by the low level arms controller, giving as output the reference position and play time (PT) sent to the servos. 29178 VOLUME 6, 2018 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation The proposed scheme exploits the controller embedded in all the Herkulex smart servos, which generates a trapezoidal velocity profile for reaching the goal position in the desired play time. Smooth trajectories can be achieved imposing that the position references are sent at the midpoint of the velocity profile. FIGURE 8. Components and architecture of the compliant dual arm. D. HARDWARE/SOFTWARE ARCHITECTURE The architecture of the compliant dual arm manipulator is depicted in Fig. 8. The components of each arm are the four Herkulex servos indicated in TABLE 4, the Murata SV 01A deflection potentiometers attached to the joints, and a Futaba S3003 servo used in the gripper. The servos on each arm are connected in daisy chain to the Intel NUC board through an USB-to-USART device. As all the servos share the same TTL bus, the command/read rate is set to 50 Hz in order to prevent high packet loss. The analog signals provided by the deflection potentiometers are converted by the Analog to Digital Converter (ADC) in the STM32VL Discovery microcontroller board, which also generates the PWM signals that control the servos of the grippers. The microcontroller board, programmed in C using the Atollic True Studio IDE, is also connected to the Intel NUC computer through the USART interface. The control program executed in this board over Ubuntu 14.04 was developed in C/C++, making use of the cmake tool in order to facilitate the portability of the software project between different computer boards. The higher level class of the program is the Task Manager, which implements several tasks or routines that can be selected by the operator from the Ground Control Station (GCS). The task manager gathers information from the state of the arms from the corresponding threads, providing the reference trajectories to the left/right arm controllers. These modules make use of the inverse kinematic model described previously for obtaining the joint references sent to the embedded servo controller through the USART interface. IV. COMPLIANT JOINT WITH DEFLECTION FEEDBACK A. BENEFITS OF MECHANICAL JOINT COMPLIANCE In most industrial manipulators, the torque is estimated from the current injected to the motor, or measuring the micro deflections of an aluminum structure attached between the motor shaft and the output link employing strain gauges. However, current-based torque estimation and control lacks of accuracy due to the friction of the gearbox, and torque sensors based on strain gauges require special electronics and a calibration process which increases the cost of the devices. What is more, although joint compliance and even variable stiffness/impedance can be achieved at software level controlling the torque at high rate (∼1 KHz), the joint is intrinsically stiff and therefore less safe than a mechanically compliant joint in an environment shared with humans. FIGURE 9. Deflection potentiometer integrated in the shoulder roll (left) and in the elbow pitch joints (right). Introducing flexible elements like springs or elastomers for transmitting the motion of the motor to the output link is a simple and low cost method for providing compliance at hardware level. These components act as low pass filters, absorbing the energy of impacts and overloads in a passive way thanks to their natural dampening. This feature results of special interest for protecting the servo actuators against peak torques in those situations in which the manipulator enters in contact with the environment. A potentiometer or encoder can be introduced in the compliant joint for building a simple torque sensor based on the deflection of the springs. This idea was previously introduced in the 3-DOF compliant arm prototype, demonstrating experimentally its application to force control in [26]. Fig. 9 shows two compact Murata SV01A potentiometers integrated in the frame structure of two joints of the developed dual arm system. A D-shaped shaft attached to the servo horn is inserted in the hollow shaft of the potentiometer for measuring the relative rotation of the output link with respect to the servo shaft. B. SPRING-LEVER TRANSMISSION MECHANISM 1) MECHANICS Two of the main requirement imposed in the arms design, mechanical joint compliance and servo protection, have been implemented employing the igubal EFOM-08 and EFSM-06 flange bearings manufactured by igus. These components provide excellent features that can be exploited in the design of low weight robotic arms: low mass density w.r.t. steel bearings (1.4 g/cm3vs 8.5 g/cm3), low friction, maintenance free, high axial and radial load support, and high impact and thermal resistance. Also the pivot angle of the ball is useful for compensating the misalignment errors associated VOLUME 6, 2018 29179 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation FIGURE 10. Shoulder pitch spring-lever mechanism. Full servo protection. to the bending of the aluminum frames. Fig. 10 shows the EFOM-08 flange bearings installed in the shoulder pitch and elbow pitch structures. The double flange bearing in side-by- side configuration provides full isolation of the servo against axial/radial loads introduced by the crossing shaft. The low friction and damping of the iglidur W300 plastic allows the smooth rotation of the shaft. The spring-lever transmission mechanism consists of a pair of compression springs that transmit the motion of the servo shaft to the output link. The L-shaped lever frame is screwed to the servo horn, pushing the springs that push the T-shaped transmission frame of the output link. The design parameters of this mechanism are the lever length and the stiffness of the springs. The torque-deflection characteristic is described in more detail in [26]. The torsional stiffness of the compliant joint is obtained in the following way: τi j∼ =Ki j·li j2·1θi j=ki j·1θi j(11) where Ki jis the stiffness of the compression spring, li jis the lever length, ki jis the equivalent torsional stiffness, and 1θi j is the deflection of the j-th joint of the i-th arm, defined as: 1θi j=θi j−qi j(12) This angle is measured by the potentiometer attached at the frame structure, as depicted in Fig. 9, allowing the estimation and control of the torque. 2) COMPLIANT JOINT DYNAMICS The dynamic model of a compliant joint actuator consists of two parts, the servo-side and the output link-side dynamics, related through the torque transmitted by the spring-lever transmission mechanism. Let us consider an arbitrary joint, omitting the indices for clarity in the notation. If τm,τf, and τrepresent the torque generated by the motor, the friction of the gearbox, and the torque transmitted to the output link, then the following balance equation can be stablished: τm=b¨ θ+τf+τ(13) where bis the inertia of the rotor. That is, the torque of the servo motor is spent in accelerating the rotor, compensating the friction, and pushing the output link. On the other hand, the output link will be affected by external forces/torques due to contacts, impacts or motion constraints, the gravity, and by the torque introduced from the compliant transmission mechanism: J¨q+mgLsin (q)=τ+τext (14) Here m,J, and Lare the mass, inertia, and length of the link respectively, whereas gis the gravity constant. Note that the common term in equations (14) – (15) is the transmitted torque τ. Taking into account equations (12) – (13), and the damping due to the friction of the output link shaft with the flange bearing, the joint torque can be computed as follows: τ=k(θ−q)+d˙ θ− ˙q=k·1θ +d·˙ 1θ (15) where dis the joint damping. This equation shows that the torque can be estimated from the joint position and velocity signals provided by the servo and the deflection sensor. It is necessary to remark that most low cost servos only accept as input position references, but torque estimation and control can be achieved thanks to the deflection of the springs. The Herkulex servos were experimentally characterized in the time and frequency domains, concluding that a first-order dynamics with delay models properly the actuator: G(s)=θ θref =eTdelay·s 1+Tservo ·s(16) where Tdelay =0.02[s] is the time delay associated to the serial interface, and Tservo =0.035[s] is the time constant. 3) DUAL ARM MANIPULATOR DYNAMICS The dynamic model of a compliant joint manipulator can be expressed in the usual matrix form, obtaining the equations of motion from the Euler-Lagrange method based on the Lagrangian and the generalized equation of the forces and torques. References [30] and [31] can be followed for a more in detail description of the modeling and control of compliant joint manipulators. As in the single joint case, the equations of the dynamic model of a compliant joint arm can be divided into two parts. Firstly, the servo-side dynamics includes the torque of the motor, the friction of the gearbox, the torque transmitted by the spring-lever mechanism, and the inertia of the rotor: τi m=Biθi¨ θi+τi f+τi(17) Here Bi∈R4×4is the servo inertia matrix, and τi m,τi f, and τi∈R4are the motor, friction and transmitted torques of the i-th arm. Now, the output link dynamics includes the inertia, Coriolis and centrifugal terms, and the gravity component: Miqi¨ qi+Ciqi,˙ qi+Giqi=τi+τi ext (18) where MiR4×4is the output link inertia matrix, Ciand Gi∈R4are the Coriolis and gravity terms, respectively, and τi ext ∈R4is the torque due to external forces exerted over the 29180 VOLUME 6, 2018 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation i-th arm. The common term in (17) and (18) is the torque τi which can be estimated from the joint deflection: τi=Kiθi−qi+Di˙ θi−˙ qi=Ki1θi+Di1˙ θi (19) where Ki=diag(ki j) and Di=diag(di j)∈R4×4are the joint stiffness and damping matrices, respectively. C. AERIAL MANIPULATOR DYNAMICS The derivation of the complete dynamic model of a dual arm aerial manipulator is out of the scope of this work, although previous research in dual arm space manipulators [32] and underwater manipulators [33] are suggested. In our previous work [28] we developed the equations of the Euler-Lagrange formulation for a stiff-joint dual arm aerial robot, expressed in the usual matrix form with the inertia, Coriolis and gravity terms. In the case of the compliant manipulator described in this paper, the vector of generalized coordinates ξ∈R22 includes both the servo and the output link angular position vectors, as well as the UAV position and attitude vectors, r and η∈R3, respectively: ξ=hrTηTθ1,Tq1,Tθ2,Tq2,TiT(20) The vector of generalized forces 0∈R22 includes the forces and torques acting over the aerial platform, FUAV and τUAV ∈R3, the torque τitransmitted by the motors, and the external torque τi ext acting over the output links: 0=hFT UAV τUAV Tτ1,Tτ1,T ext τ2,Tτ2,T ext iT(21) The equations of the dynamic model are obtained from the Lagrangian Land the generalized equation of the forces and torques. d dt ∂L ∂˙ ξ−∂L ∂ξ=0;L=K−V(22) where Kand Vare the kinetic and potential energy of the system, respectively. Note that the potential energy includes two terms, the gravitational potential and the elastic potential energy associated to the flexible joints, which depends on the joint stiffness and the deflection angle. After some work, it is possible to express the model in the following matrix form: M(ξ)¨ ξ+Cξ,˙ ξ+G(ξ)+K(ξ)+Dξ,˙ ξ=0(23) where M∈R22×22 is the generalized inertia matrix, C∈ R22 represents the centrifugal and Coriolis terms, G∈R22 is the gravity component of the wrenches, whereas Kand D∈R22 are the components associated to the deflection and the friction of the compliant joints. According to the notation, all these terms depend on the generalized coordinate vector, or well on a specific group of coordinates. The position of the manipulator relative to the base of the aerial platform and the angular position of the links modifies the value of the inertia matrix and the thrust that the propellers should deliver to compensate the torque due to gravity when the center of mass is displaced. In general, it is convenient that the manipulator is as close as possible to the geometric center of the UAV, maintaining the symmetry in the mass distribution, although from the theoretical point of view, the particular location of the arms does not affect the model. FIGURE 11. Geometric model considered for deriving the force-torque relationships. D. FORCE-TORQUE RELATIONS 1) GEOMETRIC INTERPRETATION In many manipulation operations it is necessary to estimate and control the contact forces at the end effector. This can be done measuring the deflection of the joints and applying the force-torque relations. These can be obtained in two steps: 1) compute the torque vector τi j=Fi j×ri jfor all the joints, that is, the cross product between the force acting over the link of the joint and its position, and 2) project the torque on the corresponding joint axis. The matrix representation is then obtained. Let consider the diagram shown in Fig. 11, where S,Eand Ware the shoulder, elbow and wrist points referred to frame 0iattached to the shoulder joint. These points, whose position vectors are rs=0,reand rw, define the SEW plane and the normal vector nsew. The elbow and wrist points are obtained from the forward kinematic model. From now on, superscript iis omitted for clarity in the notation. The normalized position vectors shoulder-elbow and elbow-wrist are denoted by use and uew, and are defined as follows: use =re krek(24) uew =rw−re krw−rek(25) The normal vector to the SEW plane can be computed as: nsew =use ×uew kuse ×uewk(26) It will be assumed that the contact force Fis applied at the wrist point. The torque supported by the elbow pitch and the shoulder yaw joints is firstly obtained from the vector: τew =F×(rw−re)(27) VOLUME 6, 2018 29181 A. Suarez et al.: Design of an Anthropomorphic, Compliant, and Lightweight Dual Arm for Aerial Manipulation multi-rotor platform. Both left and right arms provide 4-DOF for end effector positioning in a human-like kinematic configuration. The robust aluminum frame structure and the use of a simple and compact spring-lever transmission mechanism introduced in all the joints provide a high level of protection to the servo actuators against impacts and joint overloads. This features is highly convenient for reducing the cost and time associated to repairs, as the servo actuators represent around the 70% of the cost in materials of the manipulator. One of the main conclusions derived from the experiments is that the capacity of the compliant joints to support impacts and joint overloads associated to motion constraints increases the probability of success in a grasping task with respect to a stiff joint manipulator. The mechanical tolerance of the joints also results extremely useful for the realization of several tasks involving the cooperation of both arms, as bimanual grasping, without requiring a highly accurate coordination of the arms. As future work, it would be necessary to evaluate the accuracy and reliability of the force-torque estimation method. ACKNOWLEDGMENT The authors wish to acknowledge the support provided by V. Vega in the realization of the outdoor flight tests. REFERENCES [1] AEROARMS Project Home Page. Accessed: May 5, 2018. 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ALEJANDRO SUAREZ received the degree in telecommunication engineering and the M.Sc. degree in automation and robotics from the University of Seville, Spain, in 2012 and 2013, respectively. Since 2012, he has been with the Robotics, Vision and Control Group, University of Seville, involved in the FP7 EC-SAFEMOBIL project, and in the PERIGEO and CLEAR Spanish projects. In 2014, he received a FPU Grant from the Spanish Ministry of Education, Culture and Sport for supporting his research activity as Ph.D. student in the frame of the AEROARMS H2020 project. He stayed three months at the Robotics and Mechatronics Institute, DLR, Oberpfaffenhofen. His research interests are humanoid robotics and the design and development of anthropomorphic, and compliant and lightweight robotic arms intended to aerial manipulation. GUILLERMO HEREDIA was Visiting Researcher with the Field Robotics Centre, Carnegie Mellon University, Pittsburgh, PA, USA, and worked for an International Automobile Manufacturer (General Motors). He participated as a senior researcher in 50 Research and Development projects (EU, NASA, and national projects) leading 10 of them, including the Spanish team of the FP7-EC project ECSAFEMOBIL and the AEROCROS national project. He is currently a Professor with the University of Seville, Spain. He is author or co-author of over 70 publications on aerial manipulation, autonomous vehicles, and fault detection and reconfiguration. He is currently member of the Board of Directors of the Spanish Robotics Research and Development Society SEIDROB. ANIBAL OLLERO has been a Full Professor with the Universities of Santiago and Malaga (Spain), Researcher with the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA, and LAAS-CNRS, Toulouse, France. He is currently a Full Professor and a Head of GRVC, University of Seville, and a Scientific Advisor of the Center for Advanced Aerospace Technologies, Seville, Spain. He authored over 650 publications, including 10 books and 130 journal papers and led about 150 projects, transferring results to many companies. He has participated in 25 European Projects being coordinator of six, including the current ERC Advanced Grant GRIFFIN and the H2020 AEROARMS. He was a recipient of 15 awards, has supervised 36 Ph.D. Thesis, and is currently a co-chair of the IEEE Technical Committee on Aerial Robotics and Unmanned Aerial Vehicles and a member of the Board of Directors and coordinator of the Aerial Robotics Topic Group of euRobotics. VOLUME 6, 2018 29189