1. DOUBLE ARM JUGGLING SYSTEM
Final Presentation
ECSE-4962 Control Systems Design
Group Members:
John Kua
Trinell Ball
Linda Rivera

2. Presentation Outline Introduction Objectives System Specifications
Plan of Action
System Integration
Physical Design
Modeling
Control System
Camera Development
Results
Future Improvements

3. Introduction Goal: To design and develop a juggling system mechanism
Pivoted double-ended arm
Able to handle two or more ping pong balls

4. Introduction Motivation Previous Project  CSD Team 7 of 2004
Single arm
Open loop
Research Project by Dr. D. E. Koditschek – University of Michigan
Tossed pucks vertically with single padded arm
Uses camera for feedback

5. Objectives
Develop mechanism to simultaneously juggle two or more balls
Execute toss and catch operations quickly
Provide feedback on arm’s state
Provide feedback on balls’ state
Predict trajectory of the ball
Design control system
Learn from toss/catch errors
Compensate for disturbances in flight path of the balls

6. Specifications Flight Profile: x: 0.75m, t: 1s
Pan: Range of Motion – ±10°
Max Accel: 34.9 rad/s2
Overshoot: <5% (pos)
Settling Time: <0.1 sec
Steady State Error: ±1° (±6.5mm)
Tilt: Range of Motion – ±30°
Max Accel: rad/s2
Launch (Max) Velocity: 5.4 m/s
Overshoot: <5% (pos), <1% (vel)
Can track 2Hz sinusoidal input
Pan 20 degrees in 0.2 seconds
Reach 5.4m/s at tip in 30 degree displacement (assuming radius arm)

7. Plan of Action Model Development Model Verification Parameter Analysis
Build System
Develop Camera Subsystem
X-Y Tracking
Z Tracking
Trajectory Prediction
Pan/Tilt Control Systems Design
Open Loop 1-D
Testing
Open Loop 2-D
Open Loop
Two Ball Juggle
Closed Loop 2-D
Closed Loop
Vision Feedback Controller Design
Plan of
Action

8. Vision Processing Laptop
System Integration
Vision Processing Laptop
Parallel
Port
NI cRIO Controller

9. Code Structure (Vision)
Video Stream In
Frame Grab
Image Processing
Data Processing
Pan Correction Calculation
Tilt Correction Calculation

10. Code Structure (cRIO) FPGA Host Encoder Input User Interface
Velocity Estimation
Controller
Parallel Port Input

11. Physical Design - Additions
Camera Mounting Overall System Mounting

12. Other Physical Modifications
Shaft Mounting Cable Extension Parallel Port

13. Challenges - Net Design Process
Fabric Foil Cones

14. Final Net Design
Tossing Catching

15. Modeling & Simulation System: Trajectory: Projectile Motion, Drag
Treat as Decoupled Links
Parameters: Motor Torque, Gear Ratios, Inertial Loads, Shaft Oscillations
Nonlinearities: Friction, Backlash, Noise
Linearize Model for Control Design
Trajectory: Projectile Motion, Drag

16. Model Development
Lagrange-Euler Model
Single Joint

17. Simulink Model - Nonlinear

18. Friction Identification
Identify Viscous and Coulomb Friction
Apply constant torque and measure steady state velocity
Automate with LabVIEW
Process data with MATLAB

19. Other Parameters Inertia/Mass Shaft Spring Constant
Calculated with SolidWorks
Shaft Spring Constant
Possible cause of oscillations
Experimentally measured
Found to be very stiff - k=4600N/m

20. Trajectory Calculation
Drag force on the ball
Trajectory deviates from standard projectile motion equation
Differential Equation
Simulink ODE Solver

21. Control System Tilt and Pan Axis: PID controller θt θt θp θp
Controller Tilt
Plant Tilt θt
Shaft Dynamics θp
Controller Pan
Plant Pan θp
Vision p,t
Ball Dynamics

22. Control Systems Development
Two methods for designing controllers used
MATLAB rltool (Pole Placement method)
1. Obtain transfer function (System Parameters)
2. Define design constraints, such as rise time and settling time
3. Run simulation to test
PID block MATLAB (simulink)
Kp = Proportional
Ki = Integral
Kd = Derivative

23. Non-Linear Simulation Step Response
rltool controller PID controller
Overshoot: 28.7% Overshoot: 0%

25. Camera Development Image Processing Data Verification
Trajectory Prediction
Pan
Tilt

26. Image Processing Challenges Overcome
Script
Original Image Threshold Circle Detection
Challenges Overcome
Blur  Change shutter speed 1/100 sec
Extra circles  Set black background
Circle #
Center X
Center Y
Radius 1
231 98 9

27. Data Verification Rolling down the ramp experiment Actual Height(cm)
Vision Height(cm)
Error
49.993
1.4753
0.0407
1.3968
2.8498
4.084
4.9749
9.2457

28. Trajectory Prediction
Pan
Linear Curve Fit

29. Trajectory Prediction
Tilt
X Data Averaging
Radius > 7 pixels Y x

30. Parallel Port Standard networking VIs slow
FPGA can read digital inputs quickly
Write to Parallel Port to communicate with NI 9401 Digital I/O
Lines
Packet Start (1)
Data Ready (1)
Data (4)

31. Parallel Port Protocol
Toggle Packet Start
Write Data Type (Pan, Tilt) to Bus
Toggle Data Ready
Write Data to Bus
Packet Start
Data Ready
Data
Type
Data
Type
Data
Type
Data

32. Results Catching Accuracy Tossing Accuracy
30 tosses: catches made 83.3%
Can not catch overshoot, or undershoot beyond constraints
Tossing Accuracy
While setting ball on tossing ring, too much force can not be exerted otherwise launch initial conditions change
Belts are too tight  Non-linear friction
Loosening belts can lead to slipping (trade off)

33. Controller Response - Pan
Overshoot 0% (5%)
Settling Time 0.07s (0.1s)
Steady State Error 0.29° (±1°)
Rise Time 0.1s

34. Controller Response - Tilt
Overshoot 16% (5%)
Settling Time 0.3s (0.1s)
Steady State Error 0.34° (±1°)
Rise Time 0.08s

35. Video
Play Video Here

36. Future Improvements Implement Trajectory Generation
Better Controller (LQR)
Improve Height Estimation
Add second camera
Increase camera resolution (processing power)
Better way to transfer torque from motor to pan tilt joints other than existing belts
Juggling
System response not fast enough
Nets need dual-use optimization