First Analysis and Experiments in Aerial Manipulation Using Fully Actuated Redundant Robot Arm

Transcription

1 203 IEEE/RSJ International Conference on Intelligent Robot and Sytem (IROS) November 3-7, 203. Tokyo, Japan irt Analyi and Experiment in Aerial Manipulation Uing ully Actuated Redundant Robot Arm elix Huber, Kontantin Kondak, Kai Krieger, Dominik Sommer, Marc Schwarzbach, Maximilian Laiacker, Ingo Koyk, Sven Paruel, Sami Haddadin and Alin Albu-Schäffer Abtract In thi paper we decribe a ytem for aerial manipulation compoed of a helicopter platform and a fully actuated even Degree of reedom (Do) redundant indutrial robotic arm. We preent the firt analyi of uch kind of ytem and how that the dynamic coupling between helicopter and arm can generate diverging ocillation with very low frequency which we called phae circle. Baed on the preented analyi, we propoe a control approach for the whole ytem. The partial decoupling between helicopter and arm - which eliminate the phae circle - i achieved by mean of pecial movement of robotic arm utilizing it redundant Do. or the underlying arm control a pecially deigned impedance controller wa propoed. In different flight experiment we howcae that the propoed kind of ytem type might be ued in the future for practically relevant tak. In an integrated experiment we demontrate a baic manipulation tak - impedance baed graping of an object from the environment underlaying a viual object tracking control loop. Camera Tank Turbine IMU GPS Object Gripper Manipulator ig.. irt experimental platform for aerial manipulation with a 7-Do indutrial robot arm. A. Application, Motivation I. INTRODUCTION Unmanned Aerial Sytem (UAS) have meanwhile become an important tatu in indutrial and cientific field. Normally mentioned in the coure of tandard application like inpecting, filming, exploring, oberving or in military apect. The integration of further robotic technologie into UAS extend the range of poible application. An UAS with an integrated robotic arm can be ued for manipulation tak involving direct phyical interaction with the environment like: All author are with the Intitute of Robotic and Mechatronic, DLR - German Aeropace Center, Weling, Germany,f.huber at dlr.de inpection and maintenance of indutry ite (chimney, pipeline, tank etc.). or thi operation a contact with the environment can be neceary or even unavoidable. contruction in uneven terrain. taking ample of material from area difficult to acce for cientific (geological, biological) purpoe. taking ample of material (oil, leave) for foretry (pet infetation of tree) and agriculture (control and optimization of fertilizer ue) purpoe. catatrophic cenario, e.g. building up baic infratructure in diater area. Equipment like antenna for communication or not drop-able firt aid upply could be intalled by UAS. a tet platform for imulating on-orbit ervicing operation. Progre in that field of reearch wa already hown by a few author [] - [8]. In mot of thee intereting concept a imple manipulation device with a low-complexity gripper wa ued. In thi work, we addre the tak of manipulation by an UAS with a even Do redundant robot arm (ig.). According to our experience in robotic manipulation, even for imple tak a fully actuated manipulator i needed. A we how in thi paper, an additional degree of freedom can be ued for minimizing the influence of the arm motion to the helicopter platform. The paper i organized a follow. After completing the firt ection with a general decription of the ytem and the expected problem in manipulation from a hovering helicopter, we pa in Section II to the mathematical decription of the interaction between helicopter and arm and of the occurrence of the phae cycle phenomena. In Section III we go into ome detail of the arm control epecially the uage of the additional Do for minimizing the manipulator influence to the helicopter. The etup of the experimental platform i decribed in Section IV. inally we ummarize reult and experience in Section V. B. General Decription of the Sytem ig. depict the principle tructure of the ytem. It i compoed of three main component: a flying platform, a manipulator rigidly mounted on the fuelage and a enor ytem, e.g. a viion ytem, for tracking the manipulation object. In thi paper we conider the following general implified miion: navigation to the pecified target area uing GPS, activation of the camera ytem for object tracking, approaching the item to perform a manipulation uing data /3/$ IEEE 3452

2 from the camera ytem, hovering very cloely to the object and manipulating with the robot arm. C. Apect of the Tak To fulfill the aforementioned repreentative miion following apect hould be invetigated: a precie helicopter control, the interaction between hovering helicopter and moving manipulator, a proper control for the robot arm, and the interaction between complete ytem and fixed environmental object. A high performance poition control for hovering i neceary for the ucce of the manipulation tak. The control of the helicopter and manipulator in the lat phae can be realized by different approache. The ytem can be controlled by: completely decoupled controller, the arm motion i a diturbance for the helicopter controller and vice vera. eparate controller for the ubytem, but taking into account the their kinematic coupling. one controller taking into account the dynamic of the complete ytem. We uppoe that the third approach could provide the bet performance. But in thi cae an exact model of the whole ytem, probably with online adaptation, i required. In imulation experiment we figured out that in the firt approach the interaction between arm and helicopter could generate diverging ocillation with low frequency which we called phae circle (helicopter tart to move lowly in circle with increaing radiu). Therefore, we develop the ytem according to the econd approach taking into account the kinematic coupling between arm and helicopter platform. Thi coupling and the arm control are decribed in the following ection in detail. The high preciion helicopter control i preented in [9]. I I z ig. 2. II. ORCE INTERACTION BETWEEN HOVERING HELICOPTER AND MOVING ROBOT ARM I x r τ MR f MRz f R u Interaction between hovering helicopter and moving robot arm. Thi ection introduce the implified model of a helicopter to undertand the effect when a moving robot arm i mounted under the helicopter fuelage. The flying platform i compoed of two rigid bodie, the fuelage and the main u 3 τ R x rotor. The econd i modeled a a olid dik rotating around it vertical axi, with ame ma ditribution and diameter a the real rotor. The frame i fixed to the fuelage a depicted in ig.2. We introduce ix generalized velocitie: u,2,3 for the tranlation of frame and u 4,5,6 for the roll, pitch and yaw rate alo defined in. The toque τ MR,2 and the lifting force f MR3 generated by the main rotor are conidered a the ytem input. The equation of the tranlational and rotational dynamic of the helicopter can be found in more detail in [0]. With the decribed aumption in [0] the rotational dynamic have the following reduced form: τ MR τ R + K 2 u 5 + K u 4 = 0, () τ MR2 τ R2 + K 2 u 4 + K 22 u 5 = 0. (2) The coefficient K xx depend on contant parameter and on the contant rotor peed ω MR. The motion around the z axi (in () and (2) not conidered) i controlled mainly by the tail rotor and thu the equation for u 6 i aumed to be decoupled. One can clearly ee that () and (2) are coupled through u 4,5. A moving robot arm beneath the aircraft create additional torque τ R interacting with the ytem. Alo like in [], conidering the torque τ MR and τ R a contant and due to the linearity of () and (2) a cloed form olution can be calculated : u 4 = (τ MR2 τ R2 ) + in(...), 2β (3) u 5 = (τ MR τ R ) + co(...). 2β (4) Here β depend on the fuelage and rotor propertie and it rotation peed. In (3) and (4) the ret term on the right hand ide do not contribute to the undertanding of the decribed interaction between arm and helicopter and are neglected for ake of clarity. One can clearly ee from the firt part of the equation that torque applied to the roll axi generate a rotation around the perpendicular pitch axi. Thi o-called gyro-effect ha a eriou influence on an aerial manipulation tak. Aume the helicopter i hovering at the target area with the Tool Center Point (TCP) at the deired poition. A diplacement of the fuelage x force the robot arm to move in an extended configuration to keep it TCP poition contant ( x TCP = 0), ee ig.3. Thi adjutment motion generate a movement x CoG of the Center of Gravity (CoG) of the ytem. The CoG movement x CoG induce a torque τ R2 to the fuelage around the y axi. According to (3) the helicopter i rolling around it x axi and the thrut f MR3 caue a motion in u 2 direction. Continuing thi principle yield the chain x x CoG τ R2 u 4 u 2 y y CoG... (5) Thi ytem behavior can be decribed with the cheme in ig.4 for more detail refer to [0]. Without block P and P 2 the decoupled feedback ytem correpond to a helicopter with the two independently controlled direction (x,y) and the output y = x, y 2 = y. The input r,2 are the deired poition value x d and y d. The block C t,2 and Cr,2 repreent 3453

3 ,0 0,3 0,25 0,5 0,2 x CoG x,y [m] 0 0,5 x,y [m] 0,5 0, 0,05 0 x,0 0,05 0, x TCP = 0 ig. 3. Movement of the ytem CoG a reult of diplacement compenation by the manipulator. the controller for the tranlation and rotation repectively. P and P 2 imply the reaction of the helicopter due to the movement of the arm, with the output torque τ R and τ R2 acting on the fuelage. In ig.4 the inverion and decoupling block of the controller are combined with correponding block in the helicopter model o the tranlational and rotational dynamic of the helicopter are implified repreented by integrator. In cae of a ymmetric ytem with C t,r = Ct,r 2 the tranfer function G = y /r can be written a C r C t 3 +(C r ) 2 C t 2 +(C r C t ) 2 P G = P C r 5 +(C r ) 4 + 2(C r C t ) (C r ) 2 C t 2 +(C r C t ) 2 P P 2 The term P P 2 in the denominator ha influence on the ytem pole. It can be hown that for practically relevant ytem parameter the ytem pole could have non-negative real part and yield low frequency ocillation of the ytem tate. Thee will induce the ytem to move in cycle with increaing radiu (phae cycle), ee left picture of ig.5. One elegant olution to avoid thi effect, i to et one of the block P or P 2 to zero, a imulation reult i hown in the right graph of ig.5. Thi can be realized with a retricted motion of the arm which keep it CoG in the lateral plane of the helicopter. or thi we preent a capable arm controller in the next ection. (6), time [] 0, time [] ig. 5. Simulation reult: Sytem tate x and y tart to ocillate due to the coupling (left). Ocillation do not occur when one of the block P P 2 i eliminated (right). retain all ix end-effector Do. Therefore, we ue a 7 Do Light Weight Robot (LWR) for manipulation. Beide the good payload to weight ratio of more than 0.5, it i alo beneficial for the application that we have the poibility of meauring all even joint torque (τ J,i, i =...7) with built in enor. Thi allow u to implement complex control trategie like impedance control, e.g. decribed in [2]. We think impedance control i an ideal control concept becaue it give the arm an active elaticity and hence a further poibility to reduce the interaction force on the fuelage in cae of a contact. Epecially by an undeired colliion, the arm can react with a preet tiffne and aborb a part of the impact. or the manipulation tak the motion i defined by a deired Carteian poition x d. With the impedance control and an adequate trajectory interpolation, the TCP of the arm i pulled to the deired poition by a virtual pring damper ytem, like illutrated in ig.6. x x y fuelage I x d I z I x I y r - C t C r + y EE x D x D z D y K y K z r 2 Robot P P 2 - C2 t - C2 r + ig. 4. Simplified cheme of helicopter with manipulator in x and y direction. III. ROBOT ARM CONTROL A reaonable realization of the aforementioned feature i only feaible with a redundant robot arm to be able to y 2 EE y EE ig. 6. Illutration of impedance control for the LWR robot arm. x i the actual end effector poition. D x,y,z and K x,y,z are the tunable component of the virtual pring damper ytem. Due to the redundancy we do not have a completely defined configuration of the robot joint and thoe which do not move the end-effector poition have to be conidered. Thu a nullpace trategy mut be deigned. Thi open up the poibility for additional condition e.g. the aforementioned CoG control. In the following thi control trategy will be outlined. The robot arm can be decribed by the following ytem EE z K x 3454

4 of differential equation: M(q) q+c(q, q) q+g(q)=τ J + τ ext (7) B θ + τ J = τ m τ f (8) τ J = K(θ q)+ D ( θ q ). (9) Where θ and q are the motor the link ide poition, repectively. M(q),G(q, q) q and g(q) are the link ide inertia matrix, the centrifugal and Corioli vector, and the gravity vector repectively. The input on the right hand ide of (7) are the joint torque τ J and the external torque τ ext acting on the robot arm. The joint torque τ J, which i primary characterized by the harmonic-drive gearboxe and the torque enor, i modeled in (9) a a linear pring damper ytem with the joint tiffne matrix K=diag(k i ) for the intrinic elaticity and a damping matrix D=diag(d i ). B in (8) i the motor inertia matrix and τ f contain the friction torque. The Carteian impedance control conit of an underlying joint torque controller with the deired torque vector τ d a input (τ m = τ m (τ d )). The deired torque i compoed a τ d = τ d,cart + τ d,nsp + g(q) (0) with τ d,cart a the Carteian impedance controller torque only affecting the end-effector and τ d,nsp for the manipulator nullpace motion. or the reaching tak τ d,cart i deigned a τ d,cart = J T q (K x(x(q) x d )+D x (ẋ(q) ẋ d )) () with the manipulator Jacobian J(q) with the current Carteian end-effector poition x(q) and velocity ẋ(q). K x and D x are poitive definite matrice for the deired tiffne and damping. The deired Carteian poition x d and velocity ẋ d are provided by the viual tracking. urthermore equation (0) include a gravity compenation term g(q). We get the actual gravitation from the on-board attitude enor. The deired nullpace behavior can be decribed a a force f CoG acting on the forth joint (ellbow joint) trying to pull the arm in a configuration that ha the CoG of the manipulator a cloe to the lateral plane P of the helicopter a poible (ee ig.7). The relationhip between the force f CoG and the torque τ CoG can be written a τ CoG = J T 4(q)f CoG (2) with the manipulator Jacobian J 4 (q) at the forth link. The vector τ CoG ha to be projected into the nullpace in order to prevent interference with the end-effector control. A ufficient mapping i given by ( τ d,nsp = I ( J(q) + J(q) ) ) T τ CoG (3) where I i the identity matrix and J(q) + the peudoinvere (Moore-Penroe) of the manipulator Jacobian J(q) (ee [3]). The force in (2) can be characterized by e.g. a pringdamper ytem, therefore it i proportional to the ditance d P,CoG between the CoG r CoG and the vertical plane P and ha the direction of d P,CoG f CoG = f CoG (d P,CoG, d P,CoG ). (4) τ R d P,CoG y plane P helicopter CoG manipulator CoG τ R d P,CoG ig. 7. Influence of different LWR configuration on helicopter fuelage. Keeping the CoG near by the plane P reduce the interaction torque τ. The TCP poition i fixed. The ditance vector d P,CoG i d P,CoG = nt de r CoG n T de p n de (5) n with the normal n de and an arbitrary point p in the plane P. f CoG trie to keep the CoG a cloe to the plane P a poible. P n de d P,CoG y x P r CoG f CoG ig. 8. Ilutration for equation (4) and (5). To avoid colliion of the gripper with the kid element and to prevent the robot arm TCP to be beyond the kid plane, the arm wa caged in virtual wall to keep it in a good working poition (ee ig.9). A virtual force f VW, with repelling character, i created when the robot arm attempt to move beyond thee wall. Thi force acting at the TCP i mapped into the joint pace imilar to (2): τ VW = J T (q)f VW. (6) Equation (6) ha to be added to (0) to get the final control law. In the ret of the paper we give a hort overview of the firt experiment. IV. EXPERIMENTAL PLATORM The helicopter we ue for our firt tet i an experimental platform provided by the company SWISS UAV with a claical etup compoed of a main and a tail rotor. Both rotor of thi platform are driven by a turbine with a rated power of 25 kw. The mounting point of the arm allow the trim of the entire ytem a can be een in ig

5 ,,,, ig. 9. / Manipulator ytem with illutrated virtual wall, to avoid elf-colliion. Operating the end-effector beneath the kid plane i avoided due to afety reaon. Due to that, the working pace wa retricted to a cubic area of about 300 mm length, 300 mm width and 200 mm height. The maximal allowed Carteian velocity of the end effector i ẋ max = m/ and it maximum acceleration ẍ max = 0 m/ 2. The robot arm i equipped with a pneumatic gripper. It air preure tank are fixed at the fuelage. or the robot arm control the author ue the Robot Control Unit (RCU) framework [4] which wa uccefully teted in many experiment at German Aeropace Center (DLR). The control cheme ued in the firt experiment i hown in ig.0. Tran. / Rot. influence could be compenated by helicopter controller a a diturbance without taking the arm into account. or that following flight tet were conducted: the helicopter wa hovering in poition control mode, the TCP of the arm wa moved between extreme poition in the workpace with different peed. The reult were a expected. The influence of dynamic during the arm movement within pecified range, ee Sec.IV, i negligible. An indirect confirmation for exitence of phae circle we got from the following experiment: the helicopter wa hovering in manual control mode and the arm wa commanded to move the TCP from one extreme poition in the workpace to the other one. After the arm tarted to move, the afety pilot did not change the poition of control tick for couple of econd in order to allow the helicopter to generate natural repone to the arm motion. An example of thi natural repone i hown in ig. where the angular peed for roll u 4 and pitch u 5 are hown. The rectangle ignal in ig. i the poition of ixth arm joint q 6 and denote the tart and end of arm movement. In ig. the reaction of the fuelage in roll and pitch axe to the arm movement can be een (marked with red circle in the ig.). Thi correpond to the behavior decribed by (4) and (3) and to the caual chain given by (5) which can generate phae circle decribed in Sec.II. To verify the poibility to perform a imple manipulation tak a general implified miion decribed in Sec.I-B wa executed. Interpolator Impedance 0.4 u4 u5 q6 Viion CoG Virtual Wall ig Torque, Scheme of control tructure Robot Arm rot. velocity [rad/] / poition [rad] V. EXPERIMENTS The experimental work wa devoted to the following two ubject: invetigation of a principal poibility to operate the propoed ytem and invetigation of poibility to perform imple manipulation tak. are generally difficult to operate due to ocillation effect caued by the main rotor, e.g. mechanical reonance in the air and ground reonance. A erial manipulator connected to the helicopter fuelage make the ytem extremely enitive to all vibration and reonance effect. In the very firt tep we had to verify mechanical tability of the ytem, poibility to avoid reonance during the eed-up of the rotor and during the flight. After that, the reitance of the arm electronic wa uccefully verified. In the third tep we verified the calculated influence of the arm movement on the helicopter in hovering. Due to our calculation, the tatic (very low) diplacement of the CoG caued by arm movement in the defined workpace, hould have only a mall influence on the helicopter. Thi time [] ig.. Roll u 4 and pitch u 5 rate meaured during arm movement (only q 6 i plotted). After a take-off, the helicopter approached the target area by GPS way-point. During thi flight the arm wa parked in a afe configuration. After arrival at manipulation area, the viion ytem wa activated for exact localization of the object. After it activation, the arm tarted the manipulation while compenating the movement of the helicopter. After fulfilling the manipulation uccefully, the arm wa folded in it afe park configuration and the platform returned to home bae. Snaphot of thi experiment are hown in ig.2 and 3 from different point of view. The propoed aerial manipulation ytem wa able to grap the pole and to pull it out of the fixing. The video of the experiment can be een in the upplementary multimedia material of thi paper. 3456

6 The defined limit for the dynamic of the arm in Sec.IV allowed the compenation of the helicopter movement caued by the wind gut and ground effect. The experiment were conducted by good weather condition, wind peed under 4 m/. ig. 2. Snaphot of manipulation tak. i arriving at the target area, hovering with activated viion ytem and graping the pole. ig. 3. Thi equence how the robot arm compenating the helicopter movement during the graping tak. VI. CONCLUSIONS In thi paper we preented a firt ytem for aerial manipulation compoed of a helicopter and a fully actuated redundant robot arm. The coupling between helicopter and moving arm generate intereting hidden effect. One of them - the low frequency diverging ocillation (phae circle) - we decribed in the paper. We have hown that the phae circle are eliminated by retricting the movement of arm CoG in the lateral plane of the helicopter. Utilizing thi reult we propoed the control approach for the whole ytem. The propoed controller i compoed of the helicopter poition controller and arm controller with mentioned motion retriction for the arm CoG. Thi retriction contitute the coupling between two controller on kinematical level. Uing a 7-Do arm, we are able to move TCP with 6-Do - without drawback for manipulation tak. In flight experiment we have hown that a ytem with a erial manipulator mounted on the helicopter fuelage could be operated. Pleae note that a theoretical proof of thi fact or a reliable computer imulation i hardly poible. We have alo hown in flight experiment that uing the propoed controller a imple manipulation i poible. We think that for many practical application the uage of a fully actuated arm with a payload of about 0 kg i required. So the etup we preented in thi paper i a tarting point for practical invetigation of thee application and for developing of correponding technologie. The next tep in our reearch work will be devoted to increaing the TCP poitioning preciion and to invetigation of force interaction between TCP and object. The mechanical mounting of the arm will be alo modified in order to increae the workpace of TCP. ACKNOWLEDGMENT Thi work ha been partially founded by the European Commiion Seventh ramework Programme a part of the project ARCAS (ICT-28767) and the DLR Helman Project. REERENCES [] K. Kondak, A. Ollero, I. Maza, K. Krieger, A. Albu-Schäffer, M. Schwarzbach, and M. Laiacker, Handbook of Unmanned Aerial Vehicle. Berlin, Germany: Springer-Verlag, 203, ch. Unmanned Aerial Sytem Phyically Interacting with the Environment. Load Tranportation, Deployment and Aerial Manipulation. [2] A. Alber, S. Trautmann, T. Howard, T. A. Nguyen, M. rietch, and C. Sauter, Semiautonomou flying robot for phyical interaction with environment, in Robotic, Automation and Mechatronic, 200. [3] P. Pound and A. Dollar, Hovering tability of helicopter with elatic contraint, in Proceeding of the ASME Dynamic Sytem and Control Conference, 200. [4] P. E. I. Pound, D. R. Berak, and A. M. Dollar, Graping from the air: Hovering capture and load tability, in ICRA. IEEE, 20, pp [5] D. Mellinger, M. Shomin, N. Michael, and V. Kumar, Cooperative graping and tranport uing multiple quadrotor, in Proceeding of the International Sympoium on Ditributed Autonomou Robotic Sytem, November 200. [6] D. Mellinger, Q. Lindey, M. Shomin, and V. Kumar, Deign, modeling, etimation and control for aerial graping and manipulation, in IROS. IEEE, 20, pp [7] C. M. Korpela, T. W. Danko, and P. Y. Oh, MM-UAV: Mobile manipulating unmanned aerial vehicle, Journal of Intelligent and Robotic Sytem, vol. 65, no. -4, pp. 93 0, 202. [8] S. Abiko, R. Lampariello, and G. Hirzinger, Impedance control for a free-floating robot in the graping of a tumbling target with parameter uncertainty, in Intelligent Robot and Sytem, 2006 IEEE/RSJ International Conference on, oct. 2006, pp [9] K. Kondak, M. Bernard, N. Loe, and G. Hommel, Elaborated modeling and control for autonomou mall ize helicopter, in International ISR/Robotik Joint Conference. VDI, 2006, pp [0] K. Kondak, M. Bernard, N. Meyer, and G. Hommel., Autonomouly flying vtol-robot: Modeling and control. IEEE International Conference on Robotic and Automation, ICRA, [] K. Kondak, K. Krieger, A. Albu-Schäffer, M. Schwarzbach, M. Laiacker, I. Maza, A. Rodriguez-Catano, and A. Ollero, Cloed-loop behavior of an autonomou helicopter equipped with a robotic arm for aerial manipulation tak. IJARS, 203. [2] A. Albu-Schäffer, C. Ott, and G. Hirzinger, A unified paivitybaed control framework for poition, torque and impedance control of flexible joint robot, The International Journal of Robotic Reearch, vol. 26, no., pp , [3] C. Ott, Carteian Impedance Control of Redundant and lexible-joint Robot. Berlin, Germany: Springer-Verlag, [4] S. Paruel, S. Haddadin, and A. Albu-Schäffer, Modular tate-baed behavior control for afe human-robot interaction: A lightweight control architecture for a lightweight robot, in IEEE International Conference on Robotic and Automation, ICRA 20,, 20, pp