2010 Dynamic Model and Simulation

2010 1st International Conference on Applied Robotics for the Power Industry Delta Centre-Ville Montréal, Canada, October 5-7, 2010
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Dynamic Model and Simulation of an Inspection Robot for Power Transmission Lines: Preliminary Results
Luis G. García-Valdovinos, Arturo Velarde-Sánchez, Luis del Llano-Vizcaya, Tomás SalgadoJiménez, Fernando Hernández-Rosales, Felipe Martínez-Soto
Although the double-arm robot is multi-dof (degrees of freedom), the analysis is reduced to modeling a two dof robot characterizing the turning movement. Rocha and Sequeira [7], propose a two dof vertical robot arm whose motion along the power line resembles the motion of a cabbage worm. The well-known computed torque control scheme is implemented so as to analyze the robot’s behavior when avoiding obstacles; one robot’s extremity grasps the cable while the other one detaches from the cable to negotiate the obstacle. Tang et al. [8] present the kinematics analysis of a 3-arm mobile robot. Both, fore arm and rear arm, are analyzed as a 3 dof robot arm; only the kinematics is presented. Zhu et al. [9], address the problem of maintaining the robot body in a horizontal pose despite the overhead ground wire catenary. A double-arm mobile robot is considered and both, fore arm and rear arm, adjust their vertical position so that the robot can keep the horizontal pose. Lagrange methodology is used to achieve the pose adjustment mechanism dynamics. In [10], de Souza et al. model the robot as a simple pendulum and analyze its performance when wind is acting on the robot. The aforementioned works propose different approaches to study the behavior of inspection robots, however, none of them present a complete non linear robot dynamics. In this paper, the Euler-Lagrange formalism is used to develop the dynamic model of a double-arm inspection robot. Considering an open kinematics chain, with rigid joints and links, fully actuated robot, the dynamic model is verified through numerical simulations under PD+G and PID control schemes. A. Contribution Preliminary results that validate the kinematics and dynamics of the 5 dof robot arm are presented. Full nonlinear dynamics as well as inverse, direct and differential kinematics have been obtained to verify the performance of the robot when it is requested to follow a circumference. Simulation results are present to show that the task is exactly done as requested, in time and space. It has practical implications, since before manufacturing a prototype is possible and necessary to study the robot’s behavior. Dynamics can be as complex (complete) as required, starting from this idea dynamics becomes very useful, for instance, when it is required to know the actuators capacity in order to perform a task exactly as requested, even in the presence of disturbances.
Abstract-- Power line inspection and maintenance are fields of application where robotics has yet to be introduced. This paper presents the dynamic model and control of a 5 dof (degrees of freedom) dual-arm hanging robot manipulator. Prior to the construction of a prototype, it is worthwhile and necessary to model and analyze the robot performance, by means of numerical simulation, under conditions closer to reality, such as wind currents, joint and contact friction, sampling time, train gear and actuator dynamics, control strategies, among others. For the sake of simplicity, and without loss of generality, the inspection robot is considered as an open kinematics chain, wherein one of its extremities is fixed to the line and the other one is free to move. Based on the Euler-Lagrange formalism, the accomplished model is non-linear, fully actuated, and nonredundant, with rigid links and joints. Validity of the dynamic model is verified through numerical simulations by using Matlab-Simulink. Index Terms—Robot dynamics, Inspection robot, Power transmission lines, Robot arm control.
I. INTRODUCTION EVERAL works can be found in the literature addressing the modeling and analysis of power transmission lines inspection robots. In [1], Wang et al. present the kinematics and a simplified dynamic model of a double-arm mobile robot. The control system is decomposed into two subsystems, a slowly-changing subsystem and a fast-changing subsystem based on a singular perturbation model. In [2], ADAMS is used to analyze the kinematics and dynamics of a double-arm mobile robot. Relationship between joint motions, tracking of end arm, among other design parameters is obtained from the simulation. On the other hand, Xiao et al. [3,4], present a dynamic model that takes into account the cable dynamics. Both models are coupled in the grasping point under two typical postures of passing obstacles. Lagrange equations of motion and modal synthesis methodologies are used. Li Cai et al. [6] propose a hierarchical control strategy, wherein a fuzzy control scheme is implemented at the low level (actuators).
This work was supported in part bythe SEP-CONACyT Sectorial Fund under Grant 61449 and the CFE-CONACyT Sectorial Fund under Grant 48325. All authors are with the Applied Research Division, Center for Engineering and Industrial Development (CIDESI), Av. Pie de la Cuesta 702, Col. Desarrollo San Pablo, C.P. 76130, Querétaro, Querétaro, México. Tel. +52 442 211 9800, e1262 (corresponding author e-mail: ggarcia@cidesi.mx, luisgovinda@https://www.wendangku.net/doc/c513048793.html, ).
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978-1-4244-6634-4/10/$26.00 ?2010 IEEE

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B. Organization The paper is organized as follows. Section II pre presents an overview of the kinematics and dynamics, finally, Section III , presents the numerical results of the robot performing a task.
II. KINEMATICS AND DYNAMICS ICS Prior to the manufacturing of a robot prototype is worthwhile and necessary to analyze its behavi by means of behavior valid mathematical models, such as kinematics and dynamics. Although, mathematical modeling can be dull and cumbersome, it represents great benefits such as: , ? Mechanical design of the robot (materials, geometrical form of links, kinematics c configuration, location of center of mass, torque load). Choice of suitable actuators and train gears. Analysis of the robot performance when it is subject to disturbances (wind currents, joint friction and contact friction, impacts) erformance Analysis of the robot performance subject to parametric uncertainty. Synthesis of new control laws or choice of suitable control laws for specific conditions. Optimal planning of trajectories for the obstacles avoidance Active compensation of gravity to reduce control input torques
? ?
Fig 2. Free-body diagram of the 5 dof robot arm.. body
? ? ? ?
From Fig. 2, the inspection robot is analyzed as an open obot a kinematics chain, wherein one of its extremities is fixed to the extremit line and the other one is free to move. Based on the DenavitHartenberg (D-H) convention as well as the Euler-Lagrange we formalism, respectively, the direct kinematics and the th dynamics are attained. The result is a nonlinear, fully actuated, and non-redundant model, with rigid joints and links. ant A. Direct Kinematics
H According to Fig. 2, the D-H parameters are shown in Table
To get started, Fig. 1 depicts the 5 dof inspection robot which is composed of two arms joined by a prismatic joint. Each arm has a gripper in its extremity along with the drive wheels.
I.
TABLE I. DENAVIT-HARTENBERG PARAMETERS OF THE ROBOT.
Drive wheels & Grippers Arm 1
Arm 2
Link 1 2 3 4 5
θ q1 q2 0 q4 q5
d d1 0 q3 0 d5
a 0 0 0 0 0
α
π/2 π/2 ?π/2 π/2 0
After some calculations, the direct kinematics is given by (1). p x = 0.5d 5 s124 ? 0.5d 5 s1? 2 ? 4 + 0.5q3 s12 ? 0.5q3 s1? 2
p y = 0.5d 5 c1? 2 ? 4 ? 0.5d 5 c124 + 0.5q3 c1? 2 ? 0.5q3 c12 (1) p z = ? d5 c24 ? q3c2 + d1
where:
s124 = sin( q1 + q 2 + q 4 )
Electronics Box (counterbalance)
Fig. 1. An isometric view of te 5 dof inspection rob e robot.
s1? 2 ? 4 = sin( q1 ? q 2 ? q 4 ) s12 = sin( q1 + q 2 ) c1? 2 ? 4 = cos(q1 ? q 2 ? q 4 ) and so on.
In Fig. 2 one can see a free-body diagram of the proposed body robot as well as the associated frame to each joint.

3 B. Inverse Kinematics Inverse kinematics is computed by using a geometrical approach [12]; it is possible to decouple the inverse kinematics problem into two simpler problems, known respectively, as inverse position kinematics and inverse orientation kinematics. Firstly, the position of the intersection of the wrist axes has to be found, hereafter called the wrist center, and then finding the orientation of the wrist. The inverse position kinematics is (2) (10) Where is the generalized coordinate, denotes the symmetric positive-definite inertia matrix, represents the vector of Coriolis and centrifugal forces, denotes the gravitational torques, represents the vector of friction torques, is the control input torque, and is the number of degrees of freedom. Each element of (3) is computed by applying the EulerLagrange formalism [11] as follows
3) (4) The inverse orientation kinematics for determined from the expression and can now be
(11)
(12)
(5) as (6) Final two joint angles can be found as a set of Euler angles corresponding to . Notice that that the right hand side of (6) is completely known since is given (proposed by the user) and can be calculated once the three first joint variables are known. C. Differential Kinematics It is necessary to obtain a mathematical expression that relates the speeds between linear and angular end-effector velocities and the joint velocities (7) where is called the Jacobian matrix. Differentiating (7) with respect to time gives rise to the differential kinematics at the level of acceleration (8) Jacobian matrix and its time derivative are omitted here because of the reduced space. D. Dynamics The dynamic model of a robot manipulator is (9)
Friction Model The friction model is the combination of viscous and Coulom components (13) Next, simulation results validating the mathematical models are presented. III. SIMULATION RESULTS Kinematics and dynamics are verified through numerical simulations using Matlab-Simulink, with ODE45 variable step solver, see block diagram in Fig. 3
Fig. 3. Block diagram in Matlab-Simulink environment.
Simulation is carried out considering a PD+G control [18]; each run lasts 15 seconds.

4 A. Control Design For the sake of simplicity and in order to validate the proposed mathematical models, a PD+G control (Proportional Derivative with Gravity Compensation [13]) is proposed.
Parameters of the Robot: Robot parameters are shown in Table IV.
TABLE IV. ROBOT PARAMETERS.
Parameter
Value (15.8,1,2,1,15.8) (0.5,0.5) 9.81
Unit [kg] [m] [m/ ]
Friction Model Coefficients of the and friction model . (13) are set to
Fig. 4. PD+G control system
Then, the control law is (14) where and are an diagonal positive definite feedback gain matrices; and are -dimensional vectors of desired joint position and desired joint velocity, respectively. Feedback Gains: Feedback gains of the PD+G control are shown in Table II.
TABLE II. FEEDBACK GAINS OF THE PD+G CONTROL.
where
denotes de identity matrix.
The 3D space trajectory is shown in Fig. 5, the real and desired trajectories were plotted as well as different views of the control on Figures 5 to 7.
Gain Kp Kv B. Task Definition
Value diag(250, 300, 95, 120,50 ) diag(4, 5.6, 5.5, 4.5, 6)
The robot is requested to follow a circumference with radius , centered at , parameterized in time with , where and . Thus, one circumference is realized every T seconds. Initial conditions: Joint initial conditions are shown in Table III.
TABLE III. JOINT POSITION AND VELOCITY INITIAL CONDITIONS.
Fig. 5. 3D view of real trajectory (dotted) versus desired trajectory (solid)
As can be seen in Fig. 5, the plot shows the behavior of the desired coordinate axis corresponding to . It is clear that the proposed controller guarantees position tracking, and moreover, the validation of kinematics and dynamics. Figures 6 and 7, depict Cartesian position tracking and joint position tracking, respectively.
Joint ( ( ( ( (
Value (0.5,0) (1.803,0) (1.366,0) (2.2231,0) (3.1416,0)
Unit [rad, rad/s] [rad, rad/s] [m, m/s] [rad, rad/s] [rad, rad/s]

5
Fig. 6. End-effector Cartesian tracking (real (solid) versus desired (dotted)).
In next figures 6 and 7, the plots show the performance paths for each of the links of the manipulator.
Fig. 8. Control signals applied to each joint.
IV. CONCLUSIONS AND FUTURE WORK A dynamic model and control of the 5-dof manipulator was proposed. This method was applied to test a virtual prototype robot by using Simulink and Matlab. To validate the kinematics and dynamics a PD+G control was programmed in order to request the robot to follow a trajectory in 3D space. To the best of our knowledge, there is not any previous work regarding a complete nonlinear model in the field of inspection robots. This work opens a new line of research in the direction of synthesizing new control strategies for inspection robots as well as the construction of more complete dynamics considering actuators dynamics, wind currents, friction, backlash, just to name a few.
V. ACKNOWLEDGEMENT
Fig. 7. Joint position tracking
Finally, torques input control are depicted in Fig. 8. As expected the, joints 2 and 3 are the ones that develop more effort since joint 2 has to load the sliding bar plus the arm 2 as well as joint has to load arm 2.
L.G. García-Valdovinos acknowledges CONACyT grant support #61499. A. Velarde-Sánchez thanks support of CONACyT graduate scholarship.
VI. REFERENCES
[1] L. Wang, S. Cheng, Jianwei Zhang and Ying Hu, “Control of a Redundantly Actuated Power Line Inspection Based-on a Singular Perturbation Model”, IEEE International Conference on Robotics and Biomimetics, Bangkok, Thailand, Feb. 21-26, 2009. G. Wu, X. Xiao, E Du, S. Li, “Kinematics and Dynamics Simulation of Inspection Robot for Power Transmission Line,” 5th WSEAS Int. Conf.
[2]

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on Signal Processing, Robotics and Automation, pp. 70 70-76, Madrid, Spain, Feb. 15-17, 2006. Xiao, X., Wu, G. Du E, and Shi Tie-Lin, “Dynamic Simulation and Lin, Experimental Study of Inspection Robot for High-voltage Transmission Line,” Journal of Center South University of Technology Vol. 12, No. 6, Technology, Dec. 2005. E Xiao, X., Wu, G. and Li, S., “Dynamic Coupling Simulation of a Power Transmission Line Inspection Robot with its Flexible Moving Path when Overcoming Obstacles,” 3rd Annual IEEE Conference on Automation Science and Engineering, Scottdale, AZ, Sept. 22 , 22-25, 2007. G. Wu, Xiao X., Hua X., Jinchun D., and Zhenglie Huang, “Motion Planning of Non-Collision Obstacles Overcoming for High Collision High-Voltage Power Transmission Line Inspection Robot”, Lecture Notes on Artificial Intelligence, pp.1195-1205, 2008. Li Cai, Zize Liang, Zeng-guang Hou, and Min Tan, “Fuzzy Control of guang the Inspection Robot for Obstacle-Negotiation,” IEEE International Negotiation,” Conference on Networking, Sensing and Control pp. 117-122, Apr. Control, 2008. The J. Rocha, and J. Sequeira , “The Development of a Robotic System for Maintenance and Inspection of Power Lines,” 35th International Symposium on Robotics, Paris, France, 2004. Tang Li , Fu Shuangfei, Fang Lijin , Wang Hongguang, “Obstaclenavigation Strategy of a Wire-suspend Robot for Power Transmission suspend Lines,” Int’l. Conference on Robotics and Biomimetics Sapporo, Japan, Biomimetics, 2004. X. Zhu, H. Wang, L. Fang, M. Zhao, and Jiping Zhou, “ “Dual Arms Running Control Method of Inspection Robot Based on Obliquitous Sensor,” IEEE/RSJ International Conf. on Intelligent Robots and Systems, pp. 5273-5278, Beijing, China, 2006. Reliable N. Pouliot, P. Latulippe and S. Montambault, “Reliable and Intuitive Teleoperation of LineScout: a Mobile Robot for Live Transmission Line Maintenance,” IEEE/RSJ International Conference on Intelligent Robots and Systems,St. Louis, USA, pp. 1703-1710, 2009. 1710, L-W Tsai, “Robot Analysis: The Mechanics of Serial and Parallel Robot Manipulators,” John Wiley & Sons, New York, N.Y., 1999. Mark W. Spong & M. Vidayasagar, “Robot Dynamics and Control”, ” g ”, John Wiley & Sons, New York, N.Y., 1989. R. Kelly, V. Santibá?ez, J.A. Loria Pérez, “Control of Robot Manipulators in Joint Space” Series Advanced Textboo in Control and Textbooks Signal Processing, Springer, 2005, XXVI, 426 p. T. Salgado Jimenez was born in Guerrero, Mexico, on June 21, 1974. He graduated from the Michiacana University, Mexico, in 1996. He received the Master degree in Mecatrónica by the CINVESTAV-IPN, Mecatrón Mexico in 1999 and the Ph. D. degree in Automation by the LIRMM, France in 2004. His research interest are underwater robotics (ROVs and AUVs), Mobil robotics and system control. At present he works at the Center for Engineering and Industrial a Development (CIDESI).
[3]
[4]
[5]
[6]
[7]
[8]
Luis F. Martínez-Soto (SM’06) was born in Martínez Guanajuato, Mexico, on December 12, 1983. He anajuato, 12 received the B.Eng. (Hons.) degree in 2007 from the Instituto Tecnológico de Querétaro (ITQ), Querétaro, (ITQ) México. He is currently pursuing the MEng degree in pu the Instituto Tecnológico Superior de Irapuato (ITESI), at Irapuato, Guanajuato, México. He is also , a Project Engineer at the Center for Engineering and Industrial Development (CIDESI), at Queretaro, (CIDESI) México. His research interests lie in the dynamic and interest steady-state analysis of power systems. state
[9]
[10]
[11] [12] [13]
Fernando Hernández-Rosales received the B.S. Hernández degree in electronics engineering from the Instituto Tecnológico of Orizaba in 1990. In 1995 and 2004, respectively, he received the M.S. and Ph.D. degrees Ph from the Research Center for Advanced Studies (CINVESTAV), carrying out his studies at the Electronics Division of the Electrical Engineering Department, in Mexico City. Since April 2005, he is Professor at the Division of Applied Research and Academic Degree Programs at the Center for Engineering and Industrial Development (CIDESI) in Querétaro, Mexico. His main interests are intelligent systems, combustion re processes, and energy assessment of industry processes
VII. BIOGRAPHIES
Luis G. García-Valdovinos received the B.S. degree in electronics engineering from the Instituto Tecnológico de Lázaro Cárdenas (ITLAC) in 2000. In 2003 and 2006, respectively, he received the M.S. and Ph.D. y, degrees from the Research Center for Advanced Studies (CINVESTAV), carrying out his studies at the Mechatronics Division of the Electrical Engineering Department, in Mexico City. Since November 2006, he is Professor at the Division of Applied Research and Academic Degree Programs at the Center for Engineering and Industrial Development (CIDESI) in Querétaro City. México. His main interests are robotics, bilateral teleoperación systems, and haptic interfaces
J. Arturo Velarde-Sánchez received his Eng. degree from University of Guadalajara (in Lagos de Moreno Moreno, Jalisco) in Mechatronics in 2007. He is now a M.S. candidate in Science and Technology w specialty in with Mechatronics at the Center of Engineering and Industrial Development, Queretaro México His México. research interests focus on modeling and robotics.

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大学英语网考试题及答案 大学英语B统考模拟试卷及参考答案一 第一部分交际英语 1.— Would you mind helping me to get it upstairs? — _____ A. Yes, it is. B. No, it isn't. C. Sure. D. No, of course not. 正确答案：D 题目解析：译文：你能帮我把它拿到楼上去吗？解析：A是的，它是。B不，它不是。C当然。D不，当然不介意。所以根据题意正确答案为D 2.— Is this beautiful? — _____ A. Yes, rarely have I seen this before. B. Yes, I need a rest. C. No, tomorrow will be fine. D. No, the work should be done by him. 正确答案：A 题目解析：译文：这个好看吗？解析：A是的，我之前很少看到过这么好看的。 B是的，我需要休息。C不，明天就可以。D不，这项工作需要由他来完成。根据题意正确答案为A。 3.― _____ ― An accident has happened. A. Where was the accident? B. What happened? C. When was the accident? D. Why did it happen? 正确答案：B 题目解析：译文：一场事故发生了。解析：答案A这场事故在哪儿？答案B发生什么事情了啊？答案C这个事故什么时候发生的啊。答案D为什么会发生啊？根据回答表示问的是发生什么了，正确答案选B。 4.― Excuse me, how soon does this train leave? ― _____ A. It leaves every half an hour. B. It leaves in ten minutes. C. The next trains leaves at ten. D. There is one at four. 正确答案：B