AC 011-714: DEVELOPMENT OF A ROBOTIC PLATFORM FOR TEACH- ING MODEL-BASED DESIGN TECHNIQUES IN DYNAMICS AND CON- TROL PROGRAM Bingen Yang, University o Southern Caliornia Dr. Bingen Yang is Proessor o Aerospace and Mechanical Engineering, who has taught courses (including AME 301, 40 and 451) and conducted research in the area o dynamics and control at USC or 1 years. He has expertise in modeling, analysis, and simulation o dynamic systems and structures. He has developed more than 300,000 lines o MATLAB codes or simulation o dynamic and control systems, which have been used in some courses taught by him. Dr. Yang is the author o the book Stress, Strain, and Structural Dynamics: An Interactive Handbook o Formulas, Solutions, and MATLAB Toolboxes. Cheng-Yuan Jerry Chen, USC Dr. ChengYuan Jerry Chen is ulltime Lecturer o Aerospace and Mechanical Engineering, who has involved with AME laboratory teaching or more than 8 years in AME341, 441, and 443 classes. His expertise is not only in analytical and computational o dynamic and control systems, but also in experimental and laboratory hardware implementations. He has more than 0 years o advanced machining experience and has accomplished enormous projects in mechanical and electrical designs. He is currently the head leader o the instructional laboratory in the Aerospace and Mechanical Engineering Department. c American Society or Engineering Education, 011
Development o a Robotic Platorm or Teaching Model-Based Design Techniques in Dynamics and Control Program Abstract This paper describes an on-going project o undergraduate curriculum innovation in our department, which is sponsored by Mathworks Inc. and our engineering school. The main purpose o the project is to develop a FANUC robotic platorm, by which we shall signiicantly modiy two existing undergraduate laboratory courses in dynamics and control: Senior Projects Laboratory (100-110 students per year), and Control Systems Laboratory (60-70 students per year). The platorm will be integrated with Mathworks sotware, which will allow our undergraduate students to learn state-o-the art Model-Based Design (MBD) techniques. 1. Introduction Design o complex dynamic systems requires the development o mathematical models with varying complexities, extensive simulation studies or validation o the proposed models, synthesis and analysis o control algorithms, veriication o the perormance the closed-loop systems via numerical simulation, and hardware in the loop simulations. As a modern industry standard, Model-Based Design (MBD) techniques allow or relatively inexpensive design iterations by manipulating parameters o the simulation model instead o costly and time consuming direct experimentation on hardware set-ups. Thus, MBD provides the designer with the ultimate playground or rapid testing o ideas and or investigating what i scenarios on their desktop or in the laboratory, so as thoroughly exploring the entire design space. It is thereore imperative to make MBD the central philosophy or teaching courses in the area o dynamics and control in mechanical engineering education. This paper introduces an on-going project o undergraduate curriculum innovation in our department, which is sponsored by Mathworks Inc. and our engineering school. The objective o the project is to develop a FANUC robotic platorm, by which we shall signiicantly modiy two existing undergraduate laboratory courses in dynamics and control: AME 441Senior Projects Laboratory (100-110 students per year), and AME 443 Control Systems Laboratory (60-70 students per year). The FANUC robotic platorm in development consists o a FANUC robot, an interace between the robot and MATLAB and its toolboxes, and the necessary hardware and sotware or modeling and eedback control o the robot system (Fig. 1). In this paper, we present the initial results obtained in this project, including those on the ollowing issues: development o an accurate model o the robotic by importing 3-D data rom Solidworks to SimMechanics; real-time simulation and control system implementation via conversion o the SimMechanics models into C code or Hardware-in-the-Loop tests using Real- Time Workshop; controller design and system-level analysis via MATLAB and SIMULINK; and experimental veriication. Two sets o control experiments are to be perormed to demonstrate control system development or robotic manipulators: open-loop inverse kinematic
control design, and basic joint space control design, which is a combination o open-loop torques computed using inverse kinematic and closed-loop PD and PID controllers. Figure 1. A FANUC robotic platorm These modiied lab courses and related precursor courses, expose students to dierent aspects o modeling and simulation at an early stage o their studies. We plan to continue exposing students to the various aspects o Model-Based Design (MBD) techniques until the conclusion o their undergraduate education.. The Setting o Fanuc Robotic Platorm The Fanuc LR Mate 00iC robotic arm and R-30iA Mate controller box (see in Figs. and 3) were successully set up in the USC BHE301 lab (or undergraduate teaching in our department). The robotic arm has six degrees o reedom and six axis brakes. The six joints in total mimic the capabilities and reach o a human arm. Counting rom the base the joints are named J1, J, J3, J4, J5, and J6, respectively. The joints' maximum motion speed are J1=350, J=350, J3=400, J4=450, J5=450, and J6=70 in units o degrees per second [1]. Maximum payload is 5 kg, and maximum reach is 0.704 meters with repeatability o ±0.0 mm at ull payload and ull speed with the entire robot work envelope. Figure. The LR Mate 00iC robotic arm
Figure 3. The R-30iA Mate controller box For saety reasons, the arm is presently contained within a rectangular plastic casing measuring 110.5 ± 0.5 cm by 5.5 ± 0.5 cm by 86.3 ± 0.5 cm. Fanuc actory sotware is included in the current setup to limit the operating range o the arm such that limits are reached beore the end eector comes into contact with the sides o the encasing. Dimensions and reach o the arm are detailed in Fig. 4.. Figure 4. Dimensions and reach o the LR Mate 00iC robotic arm The controller box, as it is currently set up, is designed to receive commands rom the teaching pendant (a device provided by Fanuc or manually controlling the hardware) and to move the
motors accordingly. The controller box is equipped with an on/o switch, a circuit breaker, an emergency stop that activates dynamic braking or each joint, and a light indicating whether a ault has occurred. The controller box includes an 8-axis control board, a 6 channel servo ampliier, dual check saety, and a CPU eaturing an Ethernet port and multi-processor based architecture. The teaching pendant is set up or manual control o the robot when the arm is not set to run a speciic program. A product documentation CD is also included and comes with HandlingTool sotware or robot control, instructions on setup and operations, a mechanical unit operators manual, and directions or maintenance. The goals o the project include the ollowing. First, operator training will be completed, and HandlingTool sotware will be used or simple operation o the robot and design o simple algorithms. MATLAB sotware will then be written and incorporated into a hardware in-theloop system, which will eature a MATLAB interace and will allow a user to send commands rom the interace through the controller box to the robot. A modeling component will also be incorporated in order to demonstrate the result o algorithms as the hardware itsel is responding to user-issued commands. 3. Mathematical Modeling or Model-Based Control Design 3.1 System model One objective o the project is to introduce the students to all the aspects o model based design by using a system or which the equations are simple and can be derived analytically. To achieve this we lock all but two joints o the robot to establish a two degree o reedom system with rotational joints perorming a motion in the plane. Shown in Fig. 5 is such a model o the robot. Figure 5. A -DOF model o the robotic arm The dynamic model or the above system is described as ollows [, 3]: a) Kinematics x L cos L cos e 1 1 1 y L sin L sin e 1 1 1 (1) b) Inverse kinematics
sign( ) 1 a tan D, 1 D where xe ye L1 L 1 xe ye L1 L D, a tan ( ye, xe), cos LL 1 L1 xe y e () c) Dynamics Denote h ml1 Lc sin and 1 then the equations o motion are given by M ( θ) M ( θ) H ( θ, θ) u i 1, i1 1 i i i where M ( θ) m L I m L I m L m L L cos 11 1 c1 1 c 1 1 c M ( θ) M ( θ) m L I m L L cos, M ( θ) m L I 1 1 c 1 c c H ( θθ, ) h h m L m L g cos m gl cos 1 1 1 c1 1 1 c H( θ, θ) h1 mgl c cos (3) d) Dierential kinematics The relation between joint velocities and end-eector velocity components is x L sin L sin L sin e 1 1 1 J( ), J( ) y θ θ e L 1 cos1 L cos L cos (4) The relation between joint accelerations and end-eector acceleration components is x L cos L cos L cos e 1 1 1 1 1 J( ) J(, ), J(, ) y θ θ θ θ θ (5) e 1L1 sin1 L sin L sin 3.. Description o the task perormed by the robot The irst task chosen to be perormed by the robot is to move the end-eector in the plane along a straight line rom location ( x0, y o) to location ( x, y) in prescribed timet, see Figure 6. The commanded end-eector trajectory was computed as 3( x * 3 x0) ( x x0) x ( t) x0 t t, where, 3 t t (6) y * * y0 ( x y0 x0 y ) y ( t) mx ( t) n, where m, n 3 x x t 0
The commanded velocities and accelerations in the task space are computed by successive dierentiation o Eq. (6). The commanded trajectory in joint space is computed by using the inverse kinematic equations () and the commanded joint velocities and accelerations in joint space are computed by using the equations o inverse dierential kinematics (4) and (5) or i and, i 1, i 3.3. MATLAB simulation program Figure 6: Commanded trajectory description A simulation program has been developed in MATLAB to simulate control laws in joint space. The program is modular where each unction implements a dierent part o the model and control algorithm. Because o its modular structure, we will be able to use it as a template or uture studies when the robot will have more degrees o reedom that are active and more complex control laws, both in joint space and end- eector space are implemented. The ollowing MATLAB unctions were developed: a. Function rrmain (main program) integrates equations o motion, computes nominal trajectory, plots the results. b. Function eetraj computes the commanded end-eector trajectory or a given task, see Eq. (6). c. Function Kin - computes end-eector trajectory, its velocity and acceleration given joint motion, see Eqs. (1), (4) and (5). d. Function InvKn - computes end- Computes trajectories in joint space, their velocity and acceleration given end-eector motion, see Eqs. (1), (4) and (5). e. Function accrr computes robot accelerations in joint space or a given control torques, see Eq. (3).. Function cont - implements control algorithm by computing torques given nominal and actual trajectory measurements. g. Function par inputs robot and control algorithm parameters ( inertial parameters, geometry, control gains, saturation limits, etc.)
3.4. Simulation o control In the irst stage o our project two relatively simple control laws are implemented on the robot as ollows: a. Independent joint control The eedback controller is given by * * * ui m i i k pi ( i i ) kri ( i i ) i 1, m m L I m L I m L m L L 1 1 c1 1 c 1 1 c m m L I c (7) b. Model-based control u M ( θ) M ( θ) k ( ) k ( ) H ( θ, θ ) i 1, (8) * * * * i i1 1 i pi i i ri i i i * In Eqs. (7) and (8), u i are control torques shown in Eq. (3), i are the reerence angles (desired output) o the robotic system, and k pi, k ri are control gains. Simulation results or the independent joint control design are shown in Figs. 7 and 8. An error o 10% in the mass properties was assumed and a saturation o the actuators was also implemented. Figure 7. End-eector trajectory under independent joint control design
Figure 8. Trajectory in joint space or independent joint control design Simulation results or model-based control design are shown in Figs. 9 and 10.
Figure 9. End-eector trajectory under model-based control design
4. Implementation Plan Figure 10. Trajectory in joint space or model-based control design This eort is aimed at a major modiication o the ollowing two undergraduate laboratory courses in dynamics and control: AME 441 Senior Projects Laboratory (100-110 students per year) AME 443 Control Systems Laboratory (60-70 students per year). We acquired the Fanuc robotic system at the end o 010. The setting and mathematical modeling results, as described in Sections and 3, will be demonstrated in the above two courses in Spring 011, and later on integrated in the new course materials. During the summer o 011, several selected undergraduate students will involve in developing new course materials related to the robotic platorm. In Fall 011, we expect ull implementation o the obtained new results in our curriculum that we will use the robotic platorm or teaching and projects in these two courses. The communication between host station (MATLAB/SIMULINK) and Fanuc controller (R-30iA) is perormed by TCP/IP based protocol (called socket message) through Ethernet cable. Userdeined program (using Fanuc s KAREL) will reside in Fanuc controller to allow high-level controller implemented in MATLAB/SIMULINK to send commands and retrieve inormation such as encoder value, register value, and I/O status. User-deined program perorms analyzing commands, storing data into registers and sending data back to the high level controller. According to the commands that high-level controller sends, commanded motion will be carried out by Fanuc controller, as shown in Fig. 11. The completion o the integration o the Fanuc robotic system with MATLAB/SIMULINK sotware, will enable the students o AME 443 and AME 441 to learn MBD techniques. In particular, the students in these classes will perorm new experiments and conduct new projects as outlined below.
Figure 11. A Fanuc robot platorm with integrated MathWorks sotware AME 443 Control Systems Laboratory: The ollowing experiments will be added: System Modeling via MATLAB and MSC ADAMS System Identiications and System Veriications Kinematics Simulations vs Robot Experiments Gravity Compensation Simulations vs Experiments Controller Design and Implementation
Open Loop control by Inverse Kinematics Feedback Controller Design to Meet Perormance Speciications Single DOF vs Multiple DOF Motion Trajectory Tracking Vision Based Feedback Control AME441 Senior Projects Laboratory: The ollowing projects will be added: Design, simulation, and implementation or a trajectory control o a robotic manipulator. The project will require the use o MATLAB, SIMULINK, SIMMechanics and MSC Adams Design, simulation, and implementation o energy based control o a robotic manipulator. The project will require the use o MATLAB, SIMULINK, SIMMechanics and MSC Adams Design, simulation, and implementation or robust min-max control o a robotic manipulator. The project will require the use o MATLAB, SIMULINK, SIMMechanics and MSC Adams This project will eventually achieve the ollowing speciic goals: Introduce students to state o the art techniques or development o dynamic systems needed in Mechtronics and robotics Demonstrate to the students the clear relation between analysis, design, modeling, and hardware implementation Teach the students all aspects o dynamic system development preparing them or work in this area Give students hands-on experience in designing and implementing dynamic systems thus enhancing their academic experience. Conclusions A Fanuc robotic platorm is being developed at the USC Aerospace and Mechanical Engineering Department. The platorm will be integrated with Mathworks sotware, which will allow our undergraduate students to learn state-o-the art Model-Based Design (MBD) techniques. The successul completion o this project will signiicantly modiy two existing undergraduate laboratory courses in dynamics and control. Reerences [1] FANUC Robotics America online support [http://www.anucrobotics.com/ilerepository/datasheets/robots/lr-mate-00ic-series-&-r-30ia-mate-controller.pd] [] H. Asada and J. J. E. Slotine: Robot Analysis and Control, Wiley-Interscience (1986) [3] J. Y. S. Luh, and C. S. Lin, "Automatic Generation o Dynamic Equations or Mechanical Manipulators", 1981 Joint Automatic Control Conerence, Charlottesville, VA (1981)