Robot Manipulators 2011 Part 10 docx

Robot Manipulators 306 Finally, the FPGA utility of the motion control IC for robot manipulator in Fig. 4 is evaluated and the result is listed in Table 3. The overall circuits included a Nios II embedded processor (5.1%, 2,468 ALUTs) and a motion control IP (14.4%, 6,948 ALUTs) in Fig. 4, use 19.5% (9,416 ALUTs) utility of the Stratix II EP2S60. Nevertheless, for the cost consideration, the less expensive device - Stratix II EP2S15 (12,480 ALUTs and 419,329 RAM bits) is a better choice. In Fig. 4, the software/hardware program in parallel processing enhances the controller performance of the motion system for the robot manipulator. (0 degree) (0 degree) (51.25 degree) (116.87 degree) (168.13 degree) (26.56 degree) (26.56 degree) (56.19 degree) (114.31 degree) (-58.13 degree) (a) (b) (45.0 degree) (45 degree) (-34.88 degree) (66.81 degree) (-31.94 degree) (c) Figure 11. Simulation result of Cartesian space (a) (0,0,0) (b) (200,100,300) (c) (300,300,300) to join space Resource usage in FPGA (ALUTs) Module Circuit 71Others circuit 316Five sets of PMW module 206Position controller module 748Speed controller module 5,322Inverse kinematics module 9,416Total 285Five sets of QEP module 2,468Nios II embedded processor IP Resource usage in FPGA (ALUTs) Module Circuit 71Others circuit 316Five sets of PMW module 206Position controller module 748Speed controller module 5,322Inverse kinematics module 9,416Total 285Five sets of QEP module 2,468Nios II embedded processor IP Table 3. Utility evaluation of the motion control IC for robot manipulator in FPGA 5. Experimental system and results Figure 12 presents the overall experimental system which includes an FPGA experimental board, five sets of inverter, five sets rectifier, a power supplier system and a Mitsubishi Movemaster RV-M1 micro articulated robot. The micro articulated robot has five servo axes FPGA-Realization of a Motion Control IC for Robot Manipulator 307 (excluding the hand) and its specification is shown in Fig.13. Each axis is driven by a 24V DC servo motor with a reduction gear. The operation ranges of the articulated robot are wrist roll ±180 degrees (J5-axis), wrist pitch ±90 degrees (J4-axis), elbow rotation 110 degrees (J3-axis), shoulder rotation 130 degrees (J2-axis) and waist rotation 300 degrees (J1-axis). The gear ratios for J1 to J5 axis of the robot are 1:100, 1:170, 1:110, 1:180 and 1:110, respectively. Each DC motor is attached an optical encoder. Through four times frequency circuit, the encoder pulses generate 800pulses/cycle at J1 to J3 axis and 380pulses/cycle at J4 and J5 axis. The maximum path velocity is 1000mm/s and the lifting capacity is 1.2kg including the hand. The total weight of this robot is 19 kg. The inverter has 4 sets of IGBT type power transistors. The collector-emitter voltage of the IGBT is rating 600V, the gate-emitter voltage is rating ±12V, and the collector current in DC is rating 25A and in short time (1ms) is 50A. The photo-IC, Toshiba TLP250, is used for gate driving circuit of IGBT. Input signals of the inverter are PWM signals from FPGA chip. The FPGA-Altera Stratix II EP2S60F672C5ES in Fig. 1(a) is used to develop a full digital motion controller for robot manipulator. A Nios II embedded processor can be download to this FPGA chip. Robot manipulator FPGA board (5) Inverter for DC motor (5) Rectifier Power Figure 12. Experimental system In Fig.12 or Fig.4, the realization in PWM switching frequency, dead-band of inverter, position and speed control sampling frequency are set at 18k Hz, 1.28 μs, 762 Hz and 1525 Hz, respectively. Moreover, in the position loop P controller design, the controller parameters at each axis of robot manipulator are selected with identical values by P-gain with 2.4. However, in the speed loop PI controller design, the controller parameters at each J1~J5 axis are selected with different values by [3.17, 0.05], [3.05, 0.12], [2.68, 0.07], [2.68, 0.12] and [2.44, 0.06], respectively. To confirm the effectiveness of the proposed motion control IC, the square-wave position command with ±3 degrees amplitude and 2 seconds period is firstly adopted to test the dynamic response performance. At the beginning of the step response testing, the robot manipulator is moved to a specified attitude for joints J1-J5 rotating at the [9 o , 40 o , 60 o , 45 o , 10 o ] position. Figure 14 shows the experimental results of the step response under these design Robot Manipulators 308 conditions, where the rise time of the step responses are with 124ms, 81ms, 80ms, 151ms and 127 ms for axis J1-J5, respectively. The results also indicate that these step responses have almost zero steady-state error and no oscillation. Next, to test the performance of a point-to- point motion control for the robot manipulator, a specified path is run where the robot moves from the point 1 position, (94.3, 303.5, 403.9) mm to the point 2 position, (299.8, 0, 199.6) mm, then back to point 1. After through inverse kinematics computation in (17) ~ (23), moving each joint rotation angle of the robot from point 1 to point 2 need rotation of -72.74 o (-16,346 Pulses), 23.5 o (8,916 Pulses), 32.16 o (8,173 Pulses), -56.72 o (-11,145 Pulses) and -71.18 o (-8,173 Pulses), respectively. Additionally, a point-to-point control scheme with constant acceleration/deceleration trapezoid velocity profile adopts to smooth the robot manipulator movement. Applying this motion control scheme, all joins of robot rotate with simultaneous starting and simultaneous stopping time. The acceleration/deceleration time and overall running time are set to 256ms and 1s, and the computation procedure in paragraph 3.3.1 is applied. Figure 15 shows the tracking results of using this design condition at each link. The results indicate that the motion of each robot link produces perfect tracking with the target command in the position or the velocity response. Furthermore, the path trajectory among the position command, actual position trajectory and point-to-point straight line in Cartesian space R 3 (x,y,z) are compared, with the results shown in Fig. 16. Analytical results indicate that the actual position trajectory can precisely track the position command, but that the middle path between two points can not be specified in advanced. Next, the performance of the linear trajectory tracking of the proposed motion control IC is tested, revealing that the robot can be precisely controlled at the specified path trajectory or not. The linear trajectory path is specified where the robot manipulator moves from the starting position, (200, 100, 400) mm to the ending position, (300, 0, 300) mm, then back to starting position. The linear trajectory command is generated 100 equidistant segmented points from the starting to the ending position. Each middle position at Cartesian space R 3 (x,y,z) will be transformed to joint space ( * 5 * 4 * 3 * 2 * 1 ,,,, θθθθθ ), through the inverse kinematics computation, then sent to the servo controller of the robot manipulator. The tracking result of linear trajectory tracking is displayed in Fig. 17. The overall running time is 1 second and the tracking errors are less than 4mm. Similarly, the circular trajectory command generated by 300 equidistant segmented points with center (220,200,300) mm and radius 50 mm is tested again and its tracking result is shown in Fig. 18. The overall running time is 3 second and the trajectory tracking errors at each axis are less than 2.5mm. Figures 17~18 show the good motion tracking results under a prescribed planning trajectory. Therefore, experimental results from Figs. 14~18, demonstrate that the proposed FPGA-based motion control IC for robot manipulator ensures effectiveness and correctness Movemaster RV-M1 micro articulated robot J1-axis J2-axis J3-axis J4-axis J5-axis 1:110380 ±180 0 (±20667 pulse) J5 wrist roll 1:180380 ±90 0 (±17676 pulse) J4 wrist pitch 1:110800110 0 (27958 pulse)J3 elbow 1:170800130 0 (49311 pulse)J2 should 1:100800300 0 (67416 pulse)J1 waist Gear ratio Encoder pulse x 4 (ppr) Max. working range (degree) No.Name of link 1:110380 ±180 0 (±20667 pulse) J5 wrist roll 1:180380 ±90 0 (±17676 pulse) J4 wrist pitch 1:110800110 0 (27958 pulse)J3 elbow 1:170800130 0 (49311 pulse)J2 should 1:100800300 0 (67416 pulse)J1 waist Gear ratio Encoder pulse x 4 (ppr) Max. working range (degree) No.Name of link Figure 13. Mitsubishi Movemaster RV-M1 micro articulated robot FPGA-Realization of a Motion Control IC for Robot Manipulator 309 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4 6 8 10 12 14 Time (s) Position (degree) J1-axisJ1-axis command response 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 34 36 38 40 42 44 46 Time (s) Position (degree) J2-axis 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 34 36 38 40 42 44 46 Time (s) Position (degree) J2-axisJ2-axis 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 54 56 58 60 62 64 66 Time (s) Position (degree) J3-axis 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 54 56 58 60 62 64 66 Time (s) Position (degree) J3-axis (a) (b) (c) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 40 42 44 46 48 50 Time (s) Position (degree) J4-axis 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 40 42 44 46 48 50 Time (s) Position (degree) J4-axis 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4 6 8 10 12 14 16 Time (s) Position (degree) J5-axis 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4 6 8 10 12 14 16 Time (s) Position (degree) J5-axis (d) (e) Figure 14 Position step response of robot manipulator at (a) J1 axis (b) J2 axis (c) J3 axis (d) J4 axis (e) J5 axis 0.5 1.0 1.5 2.0 2.5 0 4000 8000 12000 16000 Time (s) Position (pulse) Position command Position Tracking J1-axis 0.5 1.0 1.5 2.0 2.5 -20,000 -10,000 0 10,000 20,000 Time (s) Velocity (pulse/sec) Velocity Profile Velocity Tracking 0 0 J1-axis 0.5 1.0 1.5 2.0 2.5 -20,000 -10,000 0 10,000 20,000 Time (s) Velocity (pulse/sec) Velocity Profile Velocity Tracking 0.5 1.0 1.5 2.0 2.5 -18,000 -16,000 -14,000 -12,000 -10,000 Time (s) Position (pulse) Position command Position Tracking J2-axis 0 0 J2-axis 0.5 1.0 1.5 2.0 2.5 -20,000 -10,000 0 10,000 20,000 Time (s) Velocity (pulse/sec) Velocity Profile Velocity Tracking 0.5 1.0 1.5 2.0 2.5 15,000 17,000 19,000 21,000 23,000 Time (s) Position (pulse) Position command Position Tracking J3-axis 0 0 J3-axis (a) (b) (c) 0.5 1.0 1.5 2.0 2.5 -20,000 -10,000 0 10,000 20,000 Time (s) Velocity (pulse/sec) Velocity Profile Velocity Tracking 0.5 1.0 1.5 2.0 2.5 -12,000 -8,000 -4,000 0 Time (s) Position (pulse) Position command Position Tracking J4-axis 0 0 J4-axis 0.5 1.0 1.5 2.0 2.5 -20,000 -10,000 0 10,000 20,000 Time (s) Velocity (pulse/sec) Velocity Profile Velocity Tracking 0.5 1.0 1.5 2.0 2.5 0 2,000 4,000 6,000 8,000 Time (s) Position (pulse) Position command Position Tracking J5-axis 0 0 J5-axis (d) (e) Figure 15 Position and its velocity profile tracking response of robot manipulator at (a) J1 axis (b) J2 axis (c) J3 axis (d) J4 axis (e) J5 axis Robot Manipulators 310 0 100 200 300 400 0 100 200 300 400 150 200 250 300 350 400 450 X - a x i s ( m m ) Y - a x i s ( m m ) Z-axis (mm) Position command & actual Position trajectory (94.3 , 303.5 , 403.9 ) (299.8 , 0 , 199.6 ) Point-to-point straight line 0 100 200 300 400 0 100 200 300 400 150 200 250 300 350 400 450 X - a x i s ( m m ) Y - a x i s ( m m ) Z-axis (mm) Position command & actual Position trajectory (94.3 , 303.5 , 403.9 ) (299.8 , 0 , 199.6 ) Point-to-point straight line 0.5 1.0 1.5 2.0 2.5 -20 -10 0 10 20 Time (s) Error (mm) X-error Y-error Z-error 0.5 1.0 1.5 2.0 2.5 -20 -10 0 10 20 Time (s) Error (mm) X-error Y-error Z-error (a) (b) Figure 16 (a) Point-to-point path tracking result of robot manipulator (b) tracking error 200 220 240 260 280 300 0 50 100 300 320 340 360 380 400 (200,100,400) (300,0,300) Position command Position tracking X - a x i s ( m m ) Y - a x i s ( m m ) Z-axis (mm) (a) 0.2 0.4 0.6 0.8 1.0 -4 -2 0 2 4 X- error Y- error Z- error Time (s) Position error (mm) 01.2 (b) Fig. 17 (a) Linear trajectory tracking result of robot manipulator (b) tracking error 160 180 200 220 240 260 150 200 250 290 295 300 305 310 X - a x i s ( m m ) Y - a x i s ( m m) Z-axis (mm) (a) Position command Position tracking 0.5 1.0 1.5 2.0 2.5 3.0 -4 -2 0 2 4 X- error Y- error Z- error Time (s) Position error (mm) 0 (b) Figure 18 (a) Circular trajectory tracking result of robot manipulator (b) tracking error FPGA-Realization of a Motion Control IC for Robot Manipulator 311 6. Conclusion This study presents a motion control IC for robot manipulator based on novel FPGA technology. The main contributions herein are summarized as follows. 1. The functionalities required to build a fully digital motion controller of a five-axis robot manipulator, such as the function of a motion trajectory planning, an inverse kinematics, five axes position and speed controller, five sets of PWM and five sets of QEP circuits have been integrated and realized in one FPGA chip. 2. The function of inverse kinematics is successfully implemented by hardware in FPGA; as the result, it diminishes the computation time from 5.6ms using Nios II processor to 840ns using FPGA hardware, and increases the system performance. 3. The software/hardware co-design technology under SoPC environment has been successfully applied to the motion controller of robot manipulator. Finally, the experimental results by the step response, the point-to-point motion trajectory response and the linear and circular motion trajectory response, have been revealed that based on the novel FPGA technology, the software/hardware co-design method with parallel operation ensures a good performance in the motion control system of robot manipulator. Compared with DSP, using FPGA in the proposed control architecture has the following benefits. 1. Inverse kinematics and servo position controllers are implemented by hardware and the trajectory planning is implemented by software, which can all be programmable design. Therefore, the flexibility of designing a specified function of robot motion controller is greatly increased. 2. Parallel processing in each block function of the motion controller makes the dynamic performance of the robot’s servo drive increasable. 3. In the commercial DSP product, it is difficult to integrate all the functions of implementing a five-axis motion controller for robot manipulator into only one chip. 7. References Altera Corporation, (2004). SOPC World. Altera (2008): www.altera.com Hall, T.S. & Hamblen, J.O. (2004). System-on-a-programmable-chip development platforms in the classroom, IEEE Trans. on Education, Vol. 47, No. 4, pp.502-507. Monmasson, E. & Cirstea, M.N. (2007) FPGA design methodology for industrial control systems – a review, IEEE Trans. Industrial Electronics, Vol. 54, No. 4, pp.1824-1842. Kabuka, M.; Glaskowsky, P. & Miranda, J. (1988). Microcontroller-based Architecture for Control of a Six Joints Robot Arm, IEEE Trans. on Industrial Electronics, Vol. 35, No. 2, pp. 217-221. Kung, Y.S. & Shu, G.S. (2005). Design and Implementation of a Control IC for Vertical Articulated Robot Arm using SOPC Technology, Proceeding of IEEE International Conference on Mechatronics, 2005, pp. 532~536. Kung, Y.S.; Tseng, K.H. & Tai, F.Y. (2006) FPGA-based servo control IC for X-Y table, Proceedings of the IEEE International Conference on Industrial Technology, pp. 2913- 2918. Robot Manipulators 312 Kung, Y.S. & Tsai, M.H. (2007). FPGA-based speed control IC for PMSM drive with adaptive fuzzy control, IEEE Trans. on Power Electronics, Vol. 22, No. 6, pp. 2476-2486. Lewis, F.L.; Abdallah C.T. & Dawson, D.M. (1993). Control of Robot Manipulators, Macmillan Publishing Company. Li, T.S.; Chang S.J. & Chen, Y.X. (2003) Implementation of Human-like Driving Skills by Autonomous Fuzzy Behavior Control on an FPGA-based Car-like Mobile Robot, IEEE Trans. on Industrial Electronics, Vol. 50, No.5, pp. 867-880. Oh, S.N.; Kim, K.I. & Lim, S. (2003). Motion Control of Biped Robots using a Single-Chip Drive, Proceeding of IEEE International Conference on Robotics & Automation, pp. 2461~2469. Schilling, R. (1998). Fundamentals of Robotics – Analysis and control, Prentice-Hall International. Shao, X. & Sun, D. (2005). A FPGA-based Motion Control IC Design, Proceeding of IEEE International Conference on Industrial Technology, pp. 131-136. Wei, R.; Gao, X.H.; Jin, M.H.; Liu, Y.W.; Liu, H.; Seitz, N.; Gruber, R. & Hirzinger, G. (2005). FPGA based Hardware Architecture for HIT/DLR Hand, Proceeding of IEEE/RSJ International Conference on intelligent Robots and System, pp. 523~528. Xu, N.; Liu, H.; Chen, X. & Zhou, Z. (2003). Implementation of DVB Demultiplexer System with System-on-a-programmable-chip FPGA, Proceeding of 5 th International Conference on ASIC, Vol. 2, pp. 954-957. Yang, G.; Liu, Y.; Cui, N. & Zhao, P. (2006). Design and Implementation of a FPGA-based AC Servo System, Proceedings of the Sixth World Congress on the Intelligent Control and Automation, Vol. 2, pp. 8145-8149. Yasuda, G. (2000). Microcontroller Implementation for Distributed Motion Control of Mobile Robots, Proceeding of International workshop on Advanced Motion Control, pp. 114-119. Zhou, Z.; Li, T.; Takahahi, T. & Ho, E. (2004). FPGA realization of a high-performance servo controller for PMSM, Proceeding of the 9 th IEEE Application Power Electronics conference and Exposition, Vol.3, pp. 1604-1609. 17 Experimental Identification of the Inverse Dynamic Model: Minimal Encoder Resolution Needed Application to an Industrial Robot Arm and a Haptic Interface Marcassus Nicolas 1 , Alexandre Janot 2 , Pierre-Olivier Vandanjon 3 and Maxime Gautier 1 1 IRCCyN & Nantes University, 2 Haption S.A. & CEA, LIST, Service de Robotique Interactive, 3 Laboratoire Central des Ponts et Chaussées France 1. Introduction To develop appropriate control laws and use fully the capacities of robots, a precise modelization is needed. Classic models such as ARX or ARMAX can be used but in the robotic field the Inverse Dynamic Model (IDM) gives far better results. In this model, the motor torques depend on the acceleration, speed and position of each joint, and of the physical parameters of the link of the robots (inertia, mass gravity, stiffness and friction). The parametric identification estimates the values of these last parameters. These estimations can also help to improve the mechanical conception during retro-engineering steps… It comes that the identification process must be as accurate and reliable as possible. The most popular identification methods are based on the least-squares (LS) regression “because of its simplicity” (Atkeson et al., 1986), (Swevers et al., 1997), (Ha et al., 1989), (Kawasaki & Nishimura 1988), (Khosla & Kanade 1985), (Kozlowski 1998), (Prüfer et al., 1994) and (Raucent et al., 1992). In the last two decades, the IRCCyN robotic team has designed an identification process using IDM of robots and LS regressions which will be developed in the second part of this chapter. This technique was applied and improved on several robots and prototypes (see Gautier et al., 1995 – Gautier & Poignet 2002 for example). More recently, this method was also successfully applied on haptic devices (Janot et al., 2007). However, it is very difficult to know how much these methods are dependent on the measurement accuracy, especially when the identification process takes place when the system is controlled by feedback. So, we ignore the necessary resolution they require to produce good quality and reliable results. Some identification techniques seem robust with respect to measurement noises. They are called “robust identification methods”. But even if they give reliable results, they are only applied on linear systems and, overall, they are very time consuming as can be seen in (Hampel, 1971) and (Hubert, 1981). Finally, it seems difficult to apply them on robots and we do not know how much they are robust with respect to these noises. Robot Manipulators 314 Another simple and adequate way consists in derivating the CESTAC method (Contrôle et Estimation Stochastique des Arrondis de Calculs developed in Vignes & La Porte, 1974) which is based on a probabilistic approach of round-off errors using a random rounding mode. The third part of this chapter introduces the design and the application of a derivate of the CESTAC method enabling us to estimate the minimal resolution needed for an accurate parametric identification. This theoretical technique was successfully applied on a 6 degrees of freedom (DOF) industrial arm (Marcassus et al., 2007) and a 3 DOF haptic device (Janot et al., 2007), the major results obtained will be used to illustrate the use of this new tool of reliability. 2. Inverse dynamic model and Least Squares estimation 2.1 General Inverse Dynamic Model The IDM calculates the joint torques as a function of joint positions, velocities and accelerations. It is usually represented by the following equation:     vs Γ=A(q)q+H(q,q)+F q+F si g n(q) (1) where Γ is the torques vector of the actuators, q, and are respectively the joint positions, velocities and accelerations vector of each links, () Aq is the inertia matrix of the robot, () Hq, is the vector regrouping Coriolis, centrifugal and gravity torques applied on the links, v F and s F are respectively the viscous and Coulomb friction matrices. The parameters used in this model are jj jj j j XX , XY , XZ ,YY , YZ , ZZ the components of the inertia tensor of link j, noted j j J , the mass of the link j called j M , the inertia of the actuator noted Ia j , the first moments vector of link j around the origin of frame j noted ⎡⎤ = ⎣⎦ T j jj j MX MY MZ j MS , j FV and j FS respectively the viscous and Coulomb friction coefficients and an offset of current measurement noted OFFSET j . The kinetic and potential energies being linear with respect to the inertial parameters, so is the dynamic model (Gautier & Khalil, 1990). Equation (1) can thus be rewritten as:  s Γ=D (q,q,q)χ (2) where  s D (q,q,q) is a linear regressor and χ is a vector composed of the inertial parameters, it is written: ⎡ ⎤ ⎣ ⎦ T 1T 2T nT χ= χχ χ (3) with j χ the dynamic parameters of link j and its actuator written: j χ = [ XX j , XY j , XZ j , YY j , YZ j , ZZ j , MX j , MY j , MZ j , M j , Ia j , FV j , FS j , OFFSET j ] T (4) To calculate the dynamic model we do not need all these parameters but only a set of base parameters which are the ones necessary for this computation. They can be deduced from Experimental Identification of the Inverse Dynamic Model: Minimal Encoder Resolution Needed Application to an Industrial Robot Arm and a Haptic Interface 315 the classical parameters by eliminating those which have no effect on the dynamic model and by regrouping some others. Actually, they represent the only identifiable parameters. Two main methods have been designed for calculating them: a direct and recursive method based on calculation of the energy (Gautier & Khalil, 1990) and a method based on QR numerical decomposition (Gautier, 1991). The numerical method is particularly useful for robots consisting of closed loops. By considering only the b base parameters, equation (2) has to be rewritten as follows: ()  b Γ=D q,q,q χ (5) where ()  D q,q,q is the linear regressor and b χ is the vector composed of the base parameters. 2.1 Least Squares Method 2.1.1 General theory Generally, ordinary LS technique is used to estimate the base parameters by solving an over- determined linear system obtained from the sampling of the dynamic model, along a specifically dedicated trajectory (q, q  , q  ), (Gautier et al., 1995) or (Khalil et al. 2007). X being the b minimum parameters vector to be identified, Y the torques measurements vector, W the observation matrix and ρ the vector of errors, the system is described as follows:  Y(Γ)=W(q,q,q)X+ρ (6) ˆ X being the solution of the LS regression, it minimizes the 2-norm of the errors vector ρ. W is a r ×b full rank and well conditioned matrix, obtained by tracking exciting trajectories and by considering the base parameters, r being the number of samplings along a given trajectory, r>>b. Hence, there is only one solution ˆ X , (Gautier, 1997) : () -1 TT+ ˆ X= W W W Y=W Y (7) with W + the pseudo-invert matrix of W. Standard deviations of the identified parameters, σ i ˆ X , are estimated using classical and simple results from statistics considering that the matrix W is deterministic and ρ is a zero- mean additive independent noise with a standard deviation such as: T2 ρρr C=E(ρρ )=σ I (8) where E is the expectation operator and I r the r×r identity matrix. An unbiased estimation of ρ σ is: [...]... makes a robot reprogrammable and multi-functional is the robot controller The robot controller, also known as the robot brain”, represents the component which gives functionality and autonomy to a certain robotic system Basically, the robot controller is formed of two main parts: controller hardware and controller software The complexity and the configuration of a controller differ from robot to robot. .. [degrees], [mm] 1800 310 [mm] 350 [mm] 3600 Table 2 The robot joints mechanical properties Max Speed [0/s],[mm/s] ~18 [0/s] 20 [mm/s] 20 [mm/s] 180 [0/s] Towards Simulation of Custom Industrial Robots 337 Fig 3 presents the 3D model of the robot arm and the real robot arm (first three joints) Figure 3 The virtual and the real robot arm 3 The Robot Controller By definition, an industrial robot must be a re-programmable... dynamics AIBO robots and also simulates the interaction of these robots with objects in the working space; Rohrmeier’s industrial robot simulator (Rohrmeier, 2000) simulates serial robots using VRML in a web graphical interface Our primary objective was to design and build a simulation system containing a custom industrial robot and an open architecture robot controller in the first part and a simulation... 1992, pp 101 1 -101 6 Swevers J., Ganseman C., Tückel D.B., de Schutter J.D & Van Brussel H (1997) Optimal Robot excitation and Identification, IEEE Trans On Robotics and Automation, vol 13(5), 1997, pp 730-740 Vignes, J & La Porte, M (1974) Error Analysis in Computing, Information Processing’74, north-Holland, Amsterdam, 1974 18 Towards Simulation of Custom Industrial Robots Cosmin Marcu and Radu Robotin... Bidard, C & Brisset, J (2005) Design of a high fidelity haptic device for telesurgery, IEEE Int Conf on Robotics and Automation, pp 206-211, Barcelone 2005 330 Robot Manipulators Ha I.J., Ko M.S & Kwon S.K (1989) An Efficient Estimation Algorithm for the Model Parameters of Robotic Manipulators, IEEE Trans On Robotics and Automation, vol 5(6), 1989, pp 386-394 Hampel, F.R (1971) A general qualitative definition... For simple tasks and robot structures the controllers may have simple configurations Nowadays, the production of industrial robot controllers is taken over by the robots manufacturers mostly because the industrial robots are used in mass production applications where high-level controllers are needed For simple robotic systems, where simple mechanical structures are used, the robot controller can be... Services C) application for PIC microcontroller • 338 Robot Manipulators 3.1 The controller architecture The robot controller was designed taking into consideration our previous researches made within the open architecture robot design area, especially the results that we obtained in the “ZeeRO” mobile robot project (Rusu et al., 2006) Therefore, the robot controller should be: open and modular in order... controller in the first part and a simulation software package using well known and open source programming languages in the last part The custom industrial robot is a RPPR robot having cylindrical coordinates In the first part of the project we designed and modeled the robotic structure and we obtained the forward kinematics, inverse kinematics and dynamic equations From the mechanical point of view,... 2 The Robot Modelling 2.1 Forward kinematics In order to build the simulation system we considered a 4 degrees-of-freedom robot structure having two rotation joints and two translation joints The kinematic scheme of the robot is presented in Fig 1 Figure 1 The kinematic scheme of the robot To obtain the equations which determine the position and the orientation of the gripper relative to the robot. .. y ⋅ sq 1 + a x ⋅ cq 1 + q 1 2 + 2 ⋅ q 1 ⋅ q 3 l4 + l6 − q3 ) (23) 2.3 Robot mechanics In order to build the mechanical structure of the robot we initially designed and 3D modelled the robot components The mechanical structure chosen for this project is a 4 degrees-of-freedom (DOF) industrial robot having a rotation joint in the robot base represented by a gear unit, two translation joints using ball . profile tracking response of robot manipulator at (a) J1 axis (b) J2 axis (c) J3 axis (d) J4 axis (e) J5 axis Robot Manipulators 310 0 100 200 300 400 0 100 200 300 400 150 200 250 300 350 400 450 X - a x i s . (degree) No.Name of link 1: 1103 80 ±180 0 (±20667 pulse) J5 wrist roll 1:180380 ±90 0 (±17676 pulse) J4 wrist pitch 1: 1108 00 110 0 (27958 pulse)J3 elbow 1:170800130 0 (49311 pulse)J2 should 1 :100 800300 0 (67416. 1.0 1.5 2.0 2.5 -20,000 -10, 000 0 10, 000 20,000 Time (s) Velocity (pulse/sec) Velocity Profile Velocity Tracking 0 0 J1-axis 0.5 1.0 1.5 2.0 2.5 -20,000 -10, 000 0 10, 000 20,000 Time (s) Velocity