ADAMS/MATLAB CO-SIMULATION: Dynamic Systems Analysis and Control Tool

L. Ángel, M. P. Pérez, C. Díaz-Quintero, C. Mendoza Universidad Pontificia Bolivariana, Bucaramanga, Colombia

e-mail: (luis.angel, mary.perez, carlos.diazq)@upb.edu.co, cmendoza_poveda@hotmail.com Keywords: Co-simulation, MATLAB, MSC Adams, robotics, modeling, control strategy. Abstract.In this paper a dynamic simulation methodology of systems is presented by using ADAMS/MATLAB co-simulation. This methodology allows simulation, development and validation of different control strategiesfor robotic manipulator models in a fast way. It provides a first stage into the design of robotic prototypes for researchers and professionals. Finally, the methodology was validated by constructing a simulation model of a double pendulum and by implementing a PD type control strategy. Introduction Simulation is an alternative to prototype design. It provides those processes with a great effectiveness due to a significant reduction in costs and effective manufacture time management; raising the productivity level, among other advantages.As a methodology tool, simulation provides a wide view of a system behavior, enabling error detection, parameters optimization or analysis for testing results.The systems reliability is measured through iterative trials.

It is possible to develop the mathematical model by analytic methods, but in certain cases albeit there is a certain degree of complexity despite of the approximation process, thus simulation is recommended as an easy way to test the system. Simulation models allow to verify or to establish diverse features of the model such as: parameters, weight, dimensions, paths, acceleration, velocity, angles, workspace, range and limits measurement. The use of models simulation is a key asset inside this methodology. There is software available specialized on themodeling ofrobotic manipulators as ANSYS, FREECAD, CATIA, ADAMS and others.

In this paper a co-simulation methodology is presented for a planar robot with two degrees of freedom using ADAMS/MATLAB.Co-simulation is the cooperation of informatics applications in respect to the shortcomings from one of those applications in a specific circumstance. ADAMS allows creating parts to model mechanical systems, to modify systems parameters and to write the codes necessary to the proper functioning and analysis of the system. Once the simulation model of the system is built, different control strategies can be implemented by using MATLAB. Some of co-simulation applications used within the industry can be found in [1-7].

This paper aims to highlight co-simulation importance in robotic prototype research, design and manufacture, which offers automation alternatives for national industry. Furthermore, this paper offers students and professionals a design alternative within the evolution of the up-coming projects. This way, showing that co-simulation is a basic and friendly tool for future researchers, which will be able to expand their knowledge in control, robotics and mechanical design areas amongst others. In the next pages an example of a pendulum system with two degrees of freedom will be show, in which the following steps will be observed: design, simulation, co-simulation and the different PD control strategies that were implemented. Pendulum System The example is based in a manipulator with two degrees of freedom. The kinematic models of the robot, the implemented control strategy and the results obtained for different spatial points will be presented. The goal of this example is to show how to perform a dynamic system co-simulation and

Applied Mechanics and Materials Vol. 232 (2012) pp 527-531© (2012) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.232.527

control response but it will not emphasize design and systems behavior. For detailed information on technical aspects on design and controllers validation, refer to [8]. Mechanical Structure The robot is a planar manipulator with two degrees of freedom. Links are assembled through a rotational shaft and driven by motors, generating motion as described by angles   and   , as shown in Fig. 1a. Simulation model of it mechanical structure is shown in Fig. 1b and the mechanical features are specified in Table 1.

a) b)

Fig. 1.Double pendulum: a) Mechanical structure; b) ADAMS simulation model.

Table 1 Robot Mechanical Features

Link Weight (Kg) Length(cm) Width(cm) Deep (cm) Material 1 1.054 45 4 2 Aluminum 2 1.054 45 4 2 Aluminum

Kinematic Model One of the main goals in positioning control is to program the robot to perform a motion from an initial position to a final position within its workspace. In order to guarantee that motion of robot is smooth and continuous during motor acceleration and deceleration stages, it is necessary to implement a trajectory planner, which takes into account the kinematic model of the robot. Trajectory plannersestablish the path to be followed by final effector in order to reach the desired spatial position. To generate final effector displacement it is necessary to take into account it’s velocity and acceleration. The function representing spatial position of robot in any time is composed by three sections represented by a 6-1-6 polynomial [10]. Kinematic models link spatial position (x,y,z) and joint position of the robot (  ,  ), without take into account the forces which produce motion.The direct kinematic model for the robot is given by the following expressions:

 =   cos    +   cos    −                                                                                                                 (1)  =   sin    +   sin    −     (2)  = 0                                                                                                                                                                 (3)

where,l and   are lengths of links and  ,    are joint positions. The inversekinematic model is given by:

   =     2  ,  −     2    −     (4)    =     2   ,    (5)

where,    =       !"  !  

 !" !  and    = ± $ 1 −     (6)

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Dynamic Model The dynamic model for a manipulator with n degrees of freedom is given by [9]:

&= '     (+ )   , *  *  +        *  (7) where,&is torque performed by each joint actuator, qis joint vector, '    is inertia matrix, )   , * is Coriolis and centrifugal matrix, +   is gravity vector, and   * is residual dynamics. For this example, the manipulator has the following dynamic model [8]:

'      ./                            2        cos      /                          /         cos                       3                          (8)

)   , *   4 2      sen     *        sen     2 *     *  

      sen     *  0 6 (9)

+     4/            +           +                +               6                                                                                 (10)

Control Strategy Fig. 2 shows the control strategies implemented,a) is a PD control and b) is a PD control with gravity compensation [9]. The ROBOT block corresponds to the dynamic simulation model built in ADAMS. The controller input signals are: current joint position and desired joint position as well as current and desired joint velocity. The desired position and velocity input signals are given by the trajectory planner, feedback signals of current position and velocity are given by the simulation model.The control action corresponds to the torque that is required to develop the motion of the mechanical structure of robot.The motors located in each joint generate torque in the system.Kp and Kv are 2x2 design matrix, called proportional and derivative gains, these are symmetric and positive matrices.In the control strategy that uses PD controller with gravity compensation, +    block is the gravity vector from the dynamic model of robot (Eq.10).

a) b)

Fig. 2. Control strategies: a) PD controller; b) PD controller with gravity compensation. The Co-simulation model developed for position control of the simulation model is shown in Fig. 3. In this diagram, the main blocks are: Finalposition,desired final position for the effector. As initial

position it is assumed the equilibrium point of the system.Planner develops the function of the trajectory planner. PDControl implements control strategy.Motor_1 and Motor_2, correspond to each joint motor’s dynamic models. Adams_sub: ADAMS exported simulation model.Gravity vector, vector given by Eq. 10.

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Fig. 3. Simulink control scheme. Test The results of the test that are shown next, correspond to positioning task of the final effector for a given spatial position, assuming that the initial spatial position is given by  0,           . The Kp and Kv matrices are defined by:

7 8   9 50 00 150< and  7 ?   91  0

0  <

The desired spatial position is (636.4,-636.4) mm, which corresponds to a desired joint position for       5°and      0°. Fig. 4 shows generated torque for each joint. Fig. 4a shows torque when PD controller is used, and Fig. 4b shows torque when PD controller with gravity compensation is used. The highest value of torque is generated by joint 1 motor; this is a result that was expected, since this motor moves the combined weight of links 1 and 2. The torque through link 2 has a small value, but is enough to keep the link 2 in the desired position. The perturbation generated when the motion begins, is due to the torque generated by the motors when they break the inertia of each link.In Fig. 4b is possible to observe the positive effect when gravity compensation is added to the controller.

a) b)

Fig. 4.Torque generated by motors during the motion in test: a) PD controller, b) PD controller with gravity compensation.

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Conclusions This paper provides a general vision of ADAMS software as a proper tool for dynamic prototype design, as well as to be implemented in co-simulation with MATLAB software in order to develop control strategies. Co-simulation is used in resent studies of great relevance. It opens doors to new projects and improvements in research and in academic stances. It can be used in virtual learning environments or as a complement in areas such as: electronics, mechanics, robotics and mechatronics among others. References [1] L. Shengqin, H. Le. Co-simulation Study of Vehicle ESP System Based on ADAMS and

MATLAB. Journal of Software, vol. 6, no. 5, may 2011. [2] J. Zhao, C. Zhu, Y. Liu. Research on co-simulation of rigid- flexible coupling system of parallel

robot Industrial Technology, 2009.ICIT 2009.IEEE International Conference on.Gippsland-Australia. 10-13 Feb. 2009. P.1-6. E-ISBN : 978-1-4244-3507-4.

[3] V. D. Makarand. Uncertainty Quantification In Ground Vehicle Dynamics Trough High Fidelity Co-Simulation. University of Wisconsin - Madison. 2008. P-125.

[4] M. Zhang, H. Nie, X. Wei, X. Qian, E. Zhou. Modeling and simulation of aircraft anti-skid braking and steering using co-simulation method.The International Journal for Computation and Mathematics in Electrical and Electronic Engineering. Emerald Group Publishing Limited. 2009. Vol. 28 No. 6. P. 1471-1488.

[5] S. J. Rao, B.S.M.E. Vehicle Modeling and ADAMS-SIMULINK Co-Simulation With Integrated Continuously Controlled Electronic Suspension (CES) and Electronic Stability Control (ESC) Models. The Ohio State University. 2009. P. 91.

[6] Montazeri-G, M.; Soleymani, M.; Mehrabi, N; Dept. of Mech. Eng., Iran Univ. of Sci. &Technol, Tehran. Application of Virtual Prototyping for Optimization of Fuzzy-Based Active Suspension System.Mechatronics and Its Applications.ISMA 2008.5th International Symposium on, Amman-Jordan. P.1-6. E-ISBN: 978-1-4244-2034-6.

[7] Faragalli, M.; Sharf, I.; Trentini, M; Center for Intell. Machines, McGill Univ, Montreal, QC Velocity Control of a Hybrid Quadruped Bounding Robot .Intelligent Robots and Systems, 2008.IROS 2008.IEEE/RSJ International Conference on.California. P.1501-1506 E-ISBN : 978-1-4244-2058-2.

[8] C. Mendoza, Modelado, simulación y control de un manipulador robótico de 2 grados de libertad empleando Adams/MATLAB. Universidad Pontificia Bolivariana. Bucaramanga-Colombia. 2012. P. 75.

[9] R. Kelly, V. Santibáñez, J.A. Loria, Control ofRobot Manipulators in Joint Space. Springer, 1stEdition, 2005. ISBN:13-978-1852339944.

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