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Robotics and Computer-Integrated Manufac b , f Science, Science In manufacturing industry of wooden furniture, CAD/ machines cannot be applied to the sanding task of the workpiece with free-formed surface. Accordingly, we must depend on skilled workers who can not only perform workers usually use handy air-driven tools such as a double Industrial robots have been progressed remarkably and applied to several tasks such as painting, welding, handling and so on. In these cases, it is important to precisely ARTICLE IN PRESS control the position of the end-effector attached to the tip of the robot arm. On the contrary, when the robots are applied to polishing, deburring or grinding task, it is 0736-5845/$-see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2006.04.004 C3 Corresponding author. Tel.: +81836884547; fax: +81836883400. E-mail address: nagataed.yama.tus.ac.jp (F. Nagata). CAM systems and NC machine tools have been introduced widely and generally, so that the design and machining processes are rationalized drastically. However, the sand- ing process after machining is hardly automated yet, because it requires delicate and dexterous skills so as not to spoil the beauty and quality of the surface. Up to now, several sanding machines have been developed for wooden materials. For example, the wide belt sander as shown in Fig. 1 is used for flat workpieces constructing furniture. The profile sander as shown in Fig. 2 is suitable for the sanding around the edge. However, these conventional action sanding tool and an orbital sanding tool as shown in Fig. 4. In order to produce a better surface quality, the double action sander simultaneously performs rotational and eccentric motions. As can be guessed, such tools spread out unhealthy noise, vibration and dust. The most serious problem in the sanding process is that the sanding task in such a bad working environment is extremely hard for skilled workers. From this reason, an advanced sanding machine which can even partially replace the skilled workers is being required in the furniture manufacturing industry. wooden materials constructing furniture. Handy air-driven tools can be easily attached to the tip of the robot arm via a compact force sensor. The robotic sanding system is called the 3D robot sander. The robot sander has two novel features. One is that the polishing force acting between the tool and wooden workpiece is delicately controlled to track a desired value, e.g., 2kgf. The polishing force is defined as the resultant force of the contact force and kinetic friction force. The other is that no complicated teaching operation is required to obtain a desired trajectory of the tool. Cutter location (CL) data, which are tool paths generated by a CAD/CAM system, are directly used for the basic trajectory of the handy tool attached to the robot arm. The robot sander can be applied to the sanding task of free- formed curved surface with which conventional sanding machines have not been able to cope. The effectiveness and promise are shown and discussed through a few experiments. r 2006 Elsevier Ltd. All rights reserved. Keywords: Robotic sanding; CAD/CAM; Cutter location data; Non-taught operation; Surface following control; Polishing force 1. Introduction appropriate force control of sanding tools but also deal with complex curved surface as shown in Fig. 3. Skilled In this paper, a sanding system based on an industrial robot with a surface following controller is proposed for the sanding process of Robotic sanding system for with free-formed Fusaomi Nagata a,C3 , Yukihiro Kusumoto a Department of Electronics and Computer Science, Tokyo University o b Interior received in revised Abstract turing 23 (2007) 371379 new designed furniture surface Yoshihiro Fujimoto b , Keigo Watanabe c Yamaguchi, Daigaku-Dori 1-1-1, Sanyo-Onoda 756-0884, Japan Center, Agemaki 405-3, Ohkawa, Fukuoka 831-0031, Japan and Engineering, Saga University, Honjomachi 1, Saga 840-8502, Japan form 10 March 2006; accepted 7 April 2006 ARTICLE IN PRESS Fig. 2. Conventional profile sander. Fig. 3. Sanding scene by a skilled worker. Fig. 1. Conventional wide belt sander. F. Nagata et al. / Robotics and Computer-Integrated372 indispensable to use some force control strategy without damaging the object. For example, polishing robots and finishing robots were presented in 15. Automated robotic deburring and grinding were also introduced in 610. Two representative force control methods have been ever proposed. They are impedance control 11 and hybrid position/force control 12. The impedance control is one of the most effective strategies for a manipulator to desirably reduce or absorb the impact force with an object. It is characterized by an ability that controls the mechanical impedance such as inertia, damping and stiffness acting between the end-effector and its environment. The impedance control does not have a force control mode or a position control mode but it is a combination of the force and velocity of the end-effector. On the other hand, the Fig. 4. Handy air-driven sanding tools usually used by skilled workers. Manufacturing 23 (2007) 371379 hybrid position/force control method simultaneously con- trols the position and force of a robot manipulator. However, the six constraints which consist of 3-DOF positions and 3-DOF forces in a constrained frame cannot be simultaneously satisfied. In order to avoid the inter- ference between the force control system and position control system, either force control mode or position control mode is selected in each direction. Surface following control is a basic sanding strategy for industrial robots. It is known that two control schemes are needed to realize the surface following control system. One is the position/orientation control of the sanding tool attached to the tip of the robot arm. The other is the force control to stably keep in contact along the curved surface of the workpiece. It should be noted that if the geometric information on the workpiece is unknown, then it is so difficult to satisfactorily control the contact force moving with a higher speed 13. To suppress overshoots and oscillations, for example, the feed rate must be given a small value. Furthermore, it is also difficult to control the orientation of the sanding tool, keeping in contact with the workpiece from normal direction. The authors have conducted relevant fundamental studies. As for force control, impedance model following force control method was proposed for an industrial robot with open architecture concept 14. The force controller adjusts the contact force acting between a sanding tool and workpiece through a desired impedance model. In 15, fuzzy environment model was presented for environments with unknown physical property. The fuzzy environment model is learned with genetic algorithm and can estimate the stiffness of unknown environment. The effectiveness was evaluated through simulations using a dynamic model of PUMA560 manipulator. In 16, a gravity compensator was considered to remove the influence of tool weight from measured force. In 17, concerning tool position and so that we can try to program new functions such as force control, compliance control and so on. The 6-DOF industrial robot shown in Fig. 5 is a FS20N with a PC- based controller provided by Kawasaki Heavy Industries. The proposed robotic sanding system is developed based on the industrial robot whose tip has a compact force sensor. A handy sanding tool can be easily attached to the tip of the robot arm via the force sensor. A PC is connected to the PC-based controller via an optical fiber cable. The PC-based controller provides several Windows API (ap- plication programming interface) functions, such as servo control with joint angles, forward/inverse kinematics and so on. By using such API functions, for instance, the position and orientation at the tip of the robot arm can be ARTICLE IN PRESS F. Nagata et al. / Robotics and Computer-Integrated Manufacturing 23 (2007) 371379 373 orientation control, it was further considered how to realize non-taught operation for industrial robots. Further- more, hyper CL data were also presented to deal with new statements about the regulation of sanding parameters in 18. In this paper, a robotic sanding system is integrated for new designed furniture with free-formed curved surface. The robotic sanding system provides a practical surface following control that allows industrial robots not only to adjust the polishing force through a desired impedance model in Cartesian space but also to follow a curved surface keeping contact with from normal direction. The polishing force is assumed to be the resultant force of contact force and kinetic friction force. We also describe how to apply the sanding system to a sanding task of wooden workpiece without complicated teaching process. A few sanding experiments are shown to demonstrate the effectiveness and promise of the proposed robotic sanding system using the surface following controller. 2. Robotic sanding system Recently, open architectural industrial robots have been proposed to comply with users various requests with regard to application developments. The industrial robot has an open programming interface for Windows or Linux, Fig. 5. Robotic sanding system developed based on controlled easily and safely. In the following section, the surface following controller is implemented for robotic sanding by using the Windows API functions. 3. Surface following control for robotic sanding system The robotic sanding system has two main features: one is that neither conventional complicated teaching tasks nor post-processor (CL data ! NC data) is required; the other is that the polishing force acting on the sanding tool and tool position/orientation are simultaneously controlled along free-formed curved surface. In this section, a surface following control method indispensable for realizing the features are described in detail. 3.1. Desired trajectory Robotic sanding task needs a desired trajectory so that the sanding tool attached to the tip of the robot arm can follow the objects surface, keeping contact with the surface from the normal direction. In executing a motion using an industrial robot, the trajectory is generally obtained in advance, e.g., through conventional robot teaching pro- cess. When the conventional teaching for an object with complex curved surface is conducted, the operator has to input a large number of teaching points along the surface. an open architectural industrial robot FS20N. The desired tool angles y r1 k, y r2 k of inclination and rotation at the discrete time k can be calculated as y rj ky j ify j i 1C0y j ig kx d kC0pik ktik , (11) where j 1;2. If (11) is substituted into (8), (9), (10), we finally obtain o da ksiny r1 kcosy r2 k, (12) o db ksiny r1 ksiny r2 k, (13) o dg kcosy r1 k. (14) x d k and o d k mentioned above are directly obtained from the CL data without any conventional complicated teaching, and used for the desired position and orientation of a sanding tool attached to a robot arm. 3.2. Polishing force In this section, a sanding strategy dealing with polishing force is described in detail. The polishing force vector FkF x k F y k F z kC138 T is assumed to be the resultant force of contact force vector fkf x k f y k f z kC138 T ARTICLE IN PRESS Y 2 afii9826 (i ) Fig. 7. Normalized tool vector ni represented by y 1 i and y 2 i in robot base coordinate system. tegrated Such a teaching task is complicated and time-consuming. However, if the object is fortunately designed and manufactured by a CAD/CAM system and an NC machine tool, then the CL data can be referred as the desired trajectory. In order to realize non-taught operation, we have already proposed a generalized trajectory generator 19,20 using the CL data, which yields the desired trajectory rk at the discrete time k given by rkx T d k o T d kC138 T , (1) where x d kx dx k x dy k x dz kC138 T and o d k o da k o db k o dg kC138 T are the position and orientation components, respectively. o d k is the normal vector at the position x d k. In the following, we detail how to make rk using the CL data. A target workpiece with curved surface is generally designed by a 3D CAD/CAM, so that the CL data can be calculated by the main-processor of the CAM. The CL data are sequential points along the model surface given by a zigzag path or a whirl path. In this approach, the desired trajectory rk is generated along the CL data. The CL data are usually calculated with a linear approximation along the model surface. The ith step is written by CLip x i p y i p z i n x i n y i n z iC138 T , (2) fn x ig 2 fn y ig 2 fn z ig 2 1, (3) where pip x i p y i p z iC138 T and nin x i n y i n z iC138 T are position and orientation vectors, respectively. rk is obtained by using linear equations and a tangential velocity v t k represented by v t kv tx k v ty k v tz kC138 T . (4) A relation between CLi and rk is shown in Fig. 6. In this case, assuming rk2CLi; CLi 1C138 we obtain rk through the following procedure. First, a direction vector ti is given by tipi 1C0pi (5) so that each component of v t k is obtained by v tj kkv t kk t j i ktik j x;y;z. (6) Using a sampling width Dt, each component of the desired position x d k is given by x dj kx dj k C0 1v tj kDt j x;y;z. (7) Next, the desired orientation o d k is considered. We define two angles y 1 i;y 2 i as shown in Fig. 7. y 1 i and y 2 i are the tool angles of inclination and rotation, respectively. Using y 1 i and y 2 i, each component of ni is represented by aisiny 1 icosy 2 i, (8) bisiny 1 isiny 2 i, (9) F. Nagata et al. / Robotics and Computer-In374 gicosy 1 i. (10) Workpiece CL(i-1) r (k) r (k + 1) r (k + 2) CL(i+1) CL(i) Fig. 6. Relation between CL data CLi and desired trajectory rk. X Z O afii9835 (i) afii9835 1 (i) afii9828 (i) afii9825 (i ) Manufacturing 23 (2007) 371379 and kinetic friction force vector F r kF rx k F ry k F rz kC138 T that are given to the workpiece as shown finishing, it is fundamental and effective to stably control the polishing force. When the robotic sanding system runs, the polishing force is controlled by the impedance model following force control with integral action given by v normal kv normal k C01e C0B d =M d Dt e C0B d =M d Dt C0 1 K f B d E f k K fi X k n1 E f n, 19 ARTICLE IN PRESS tegrated Manufacturing 23 (2007) 371379 375 in Fig 8, where the sanding tool is moving along on the surface from (A) to (B). F r k is written by F r kdiagm x ;m y ;m z kfkk v t k kv t kk diagZ x ;Z y ;Z z v t k, 15 where diagm x ;m y ;m z kfkkv t k=kv t kk is the Coulomb friction, and diagZ x ;Z y ;Z z v t k is the viscous friction. m i and Z i i x;y;z are the i-directional coefficients of Coulomb friction per unit contact force and of viscous friction, respectively. Each friction force is generated by fk and v t k, respectively. Fk is represented by FkfkF r k. (16) The polishing force magnitude can be easily measured by using a 3-DOF force sensor attached between the tip of the arm and the sanding tool, which is given by Tip of robot arm Force sensor Sanding tool Workpiece vt F f F r (A) (B) Fig. 8. Polishing force Fk composed of contact force fk and kinetic friction force F r k. F. Nagata et al. / Robotics and Computer-In kFkk f S F x kg 2 f S F y kg 2 f S F z kg 2 q , (17) where S F x k, S F y k and S F z k are the each directional component of force sensor measurements in sensor coordinate system. In the following section, the error E f k of polishing force magnitude is calculated by E f kF d C0kFkk, (18) where F d is a desired polishing force. 3.3. Feedback control of polishing force In the manufacturing industry of wooden furniture, skilled workers usually use handy air-driven tools to finish the surface after machining or painting. These types of tools cause high frequency and large magnitude vibrations, so that it is so difficult for the skilled workers to sand the workpiece keeping the polishing force a desired value. Consequently, undesirable unevenness tends to appear on the sanded surface. In order to achieve a good surface where v normal k is the velocity scalar; K f is the force feedback gain; K fi is the integral control gain; M d and B d are the desired mass and desired damping coefficients, respectively. Dt is the sampling width. Using v normal k, the normal velocity vector v n kv nx k v ny k v nz kC138 at the center of the contact point is represented by v n kv normal k o d k ko d kk . (20) 3.4. Feedforward and feedback control of position Currently, wooden furniture are designed and machined with 3D CAD/CAM systems and NC machine tools, respectively. Accordingly the CL data generated from the main-processor of the CAM can be used for the desired trajectory of the sanding tool. The tool path (CL data) as shown in Fig. 9, which are calculated in advance based on a zigzag path, is considered to be a desired trajectory of the sanding tool. Fig. 10 shows the block diagram of the surface following controller implemented in the robot sander. The position and orientation of the tool attached to the tip of the robot arm are feedforwardly controlled by the tangential velocity v t k and rotational velocity v r k, respectively, referring x d k and o d k. v t k is given through an open-loop action so as not to interfere with the force feedback loop. The polishing force is regulated by v n k which is perpendicular to v t k. v n k is given to the normal direction referring the orientation vector o d k. It should be noted, however, that using only v t k is not enough to precisely carry out desired trajectory control along the CL data: actual trajectory tends to deviate from Fig. 9. Zigzag path generated from main-processor of CAM. ARTICLE IN PRESS Cartesian-Based Sander Control Law tegrated the desired one, so that the constant pick feed (e.g., 20mm) cannot be performed. This undesirable phenomenon leads to the lack of uniformity on the surface. To overcome this problem, a simple position feedback loop with small gains is added as shown in Fig. 10 so that the tool does not deviate from the desired pick feed. The position feedback control law generates another velocity v p k given by v p kS p K p E p kK i X k n1 E p n () , (21) where S p diagS x ;S y ;S z is a switch matrix to realize a weak coupling control in each direction. If S p diag1;1;1, then the coupling control is active in all directions; whereas if S p diag0;0;0, then the position feedback loop does not contribute to the force feedback loop in all directions. E p kx d kC0 xk is the position error vector. xk is the current position of the sanding tool attached to the tip of the arm and is obtained from the forward kinematics of the robot. K p diagK px ;K py ;K pz and K i diagK ix ;K iy ;K iz are the position feedback gain and its integral gain matrices, respectively. Each compo- nent of K p and K i must be set to small values so as not to obviously disturb the force control loop. Finally, recomposed velocities v n kv T n k 000C138 T , v t k T T T T T Position Feedback Control Law Servo Controller + + x d (k) x (k) x d (k) : desired position o d (k) : desired position Based on CL Data S p v p (k) Fig. 10. Block diagram of the surface following controller implemented in the robot sander. Force Feedback Control Law Robot + F d o d (k) F (k) F d : desired polishing force Position/Orientation Feedforward S p : switch matrix v t (k) v n (k) F. Nagata et al. / Robotics and Computer-In376 v t k v r kC138 and v p kv p k 000C138 are summed up, and those of which are given to the reference of the Cartesian-based servo controller of the industrial robot. It is known that the six constraints, which consist of 3- DOF positions and 3-DOF forces in a constraint frame, cannot be simultaneously satisfied 21. However, the delicate cooperation between the position feedback loop and force feedback loop is an
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