WS7-1 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation WORKSHOP 7 DESIGN OF EXPERIMENTS

WS7-2 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation

WS7-3 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation WORKSHOP 7 - DESIGN OF EXPERIMENTS n Problem statement u In this workshop you will simulate the motion of a one-legged robot, referred to as a unipod. This unipod has a triangular truss structure that has been parameterized using points whose locations are defined by eight design variables. The unipod is able to move through a small force actuator that turns on and off repeatedly, applying 650 N of force during its extension. A spring allows the return stroke of this leg. Your goal is to make the robot walk toward the semi-circular arc located at the edge of the platform in such a way that when the simulation is complete, its base is contained within the boundary of the semicircle.

WS7-4 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation u You will learn how to run Design of Experiment (DOE) analyses to identify which design variables are significant. This screening process will result in a good starting point for an optimization study. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-5 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation n Getting started To get started: 1. Start ADAMS/View from the mod_07_unipod_DOE directory. 2. Import the baseline model, unipod_start.cmd. 3. Move the strip chart aside so you can see the unipod. 4. From the Settings menu, select Names. 5. In the Default Names dialog box, select Full names. 6. Select OK. 7. Simulate the model for 1 second using the script SIM_SHORT. 8. Animate as needed to answer the following question: Does it walk? _____ Yes _____ No WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-6 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation  w1 and w2 represent weighting factors. The smaller the value, the less “pull” the corresponding ball has at the vertex.  When w1=w2=0.333, the foot is centered in the lower triangle as shown by the solid black circle. Each ball has equal weighting.  When w1=w2=0.15, the foot is biased toward ball 3 as shown by the x. These two variables are coupled to each other. WORKSHOP 7 - DESIGN OF EXPERIMENTS Figure 1. Description of the Unipod Design

WS7-7 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation n Performing a design study u To perform a design study: 1. Review the eight design parameters by studying Figure 1 on the previous slide, and sweeping the design variables with the Sweep Variable customized menu button l From the Build menu, point to Design Variables, and then select Sweep. Tip: Use 15 frames. 2. Circle the two parameters that you think would have the biggest effect on making the unipod walk: pt4_ypt2_xpt3_xw1 pt4_zpt2_zpt3_zw2 WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-8 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation 3. Perform a five-level design study of pt4_z: l Simulation Script: SIM_SHORT l Study a: Minimum of l Measure: DM_TO_ZONE l Design Variable: pt4_z l Default Levels: 5 4. Create a tabular report of the results. Save the file as U_DS_summary.txt. 5. Which trial made it walk closer to its destination than the others? Write the trial number and the value of pt4_z here: ______, _____ 6. Save the design study multi-run results set: l Use the Save Last Results button to open the Save Design Evaluation Results dialog box. l Name the design study U_DS. 7. Set the value of pt4_z to that of trial 5: l From the Design Evaluation Tools dialog box, select the Set Variables button to open the Update Design Variables dialog box. l Set the Trial to 5. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-9 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation n Simulating the unipod u You used a short simulation to get the unipod moving. Now you will see how well it travels in a longer simulation run. To run a simulation: 1. Run a 5-second simulation using SIM_LONG. 2. Run an animation using trace markers (.model_1.PART_2.MAR_BALL_CTR_1, for example) to better see the path it has taken. 3. Describe, in general, the nature of the path that the unipod takes. _____________________________________________________ _____________________________________________________ WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-10 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation n Performing a DOE of w1 and w2 u Now you’ll study the effect variables w1 and w2 have on the measure DM_TO_ZONE. DM_TO_ZONE is the distance magnitude from the center-of-mass of PART_2 to the ground.ZONE_MARKER. Basically, it measures if the unipod is walking toward the desired zone or away from it. n To perform a DOE: 1. To improve simulation speed, turn off the execution graphics by setting Update Graphics to At Simulation End. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-11 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation 2. Set up the DOE: l Simulation Script: SIM_LONG l Study a: Minimum of l Measure: DM_TO_ZONE l Design Variables: w1, w2 l Default Levels: 4 l DOE Technique: Full Factorial (16 runs) Tip: Use the Check Variables, Guess # of Runs button to compute number of runs required. 3. Start the DOE. 4. Save the DOE multi-run results set as U_DOE_w1w2 5. Create a tabular report of results named U_DOE_w1w2.txt. 6. In which trial did the unipod walk the farthest? _______ 7. Write the corresponding values of w1 and w2.________, ________ 8. Set the w1 and w2 variables to the values from that trial. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-12 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation n Performing a DOE by direct input u Now you’ll run a DOE of design variables pt2_x and pt2_z. n To perform a DOE by direct input: 1. Generate the list of acceptable values for pt2_x. l Ignore the error that current value is not one of the allowed values. l From the Build menu, point to Design Variable, and then select Modify. l Select pt2_x from the Database Navigator. l In the Modify Design Variable dialog box: n Select List of allowed values. n Select Generate. n In the Total Number of Values text box, enter 4. n Select Generate new list. n Select Apply. n The values should be , , , and WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-13 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation 2. Repeat the procedure in Step 1 to generate the list of acceptable values for pt2_z: The values should be , , , and Perform a DOE of pt2_x and pt2_z. l Simulation Script: SIM_LONG l Study a: Minimum of l Measure: DM_TO_ZONE l Design Variables: pt2_x, pt2_z l Default levels: 4 l Trials defined by: Direct Input l Number of Trials: 8 l Trial Matrix:1, -2 1, -1 1, +1 1, +2 2, -2 2, -1 2, +1 2, +2 WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-14 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation 4. Start the DOE. 5. Save the DOE multi-run results set as U_DOE_pt2. 6. Create a tabular report of the results named U_DOE_pt2.txt. 7. In which trial did the unipod walk the farthest? _________ 8. Write the corresponding values of pt2_x and pt2_z. _______, _______ 9. Set the pt2_x and pt2_z variables to the values from that trial. 10. Set output settings to Save Files: Yes with a File Prefix: after_DOE_screen. 11. Set Update Graphics back to At Output Step. 12. Simulate the model again using SIM_LONG to review its performance after completing the DOE screening process. Use trace markers (.model_1.PART_2.MAR_BALL_CTR_1, for example) to see the path when you animate. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-15 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation 13. Describe, in general, the nature of the path that the unipod takes. _____________________________________________________ 14. Is the unipod fully contained inside the blue semi-circle arc? ____ Yes ____ No 15. Does this seem like a good starting point for an optimization? ____ Yes ____ No 16. Turn off the Saving of Solver files and set Model Display Update to At simulation end so as to maximize the speed of the optimization multi-run simulations. 17. Save the model database as after_DOE_screen.bin. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-16 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation n Optional tasks Optimization 1 1. Using the results from the DOE screen as a starting point, optimize the design using all eight design variables (pt2_x, pt2_z, pt3_x, pt3_z, pt4_y, pt4_z, w1, w2) and the optimization constraints OPT_CNSTR_1, OPT_CNSTR_2, OPT_CNSTR_3. l Simulation Script: SIM_LONG l Study a: Last Value of l Measure: DM_TO_ZONE l Goal: Minimize Des. Meas./Objective l Set Optimer Algorithm settings to: OPTDES_SQP 2. Save the optimization multi-run result set as U_OPT_all. 3. Create a tabular report of results named U_OPT_all.txt. WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-17 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation Optimization 2 u Using the best solution from the initial design study as a starting point (Trial 5), see if the solution can be found without the DOE screen, using only an unconstrained optimization: l Simulation Script: SIM_LONG l Study a: Minimum of l Measure: DM_TO_ZONE l Design Variables: pt2_x, pt2_z, pt3_x, pt3_z, pt4_y, pt4_z, w1, w2 l Goal: Minimize Des. Meas./Objective l Computing gradients/performing line search. Iteration: 8 Pass: 1 l Set Optimer Algorithm settings to: OPTDES_SQP WORKSHOP 7 - DESIGN OF EXPERIMENTS

WS7-18 ADM , Workshop 7, August 2005 Copyright  2005 MSC.Software Corporation