BallBot

1. BallBot Brian Kosoris Jeroen Waning BahatiGitego YuriyPsarev 10/11/2011

2. System Overview • Mechanical Structure • Base • Vertical structure • Landing gear • Electronics • Sensors • Actuators/Motors • Control System • State-space variable model • MatLab/Simulinkcode • Synthesis of 3D motion

3. Mechanical Design (CAD) • Base • Critical mechanism • Mechanical function impacts success • Aluminum vs. steel? • Feasibility • Cost • Workability • Aesthetics • Strength/rigidity vs. weight • Two perpendicular pairs of motors (@ 45’s) • Built in damper for vertical disturbances

4. Mechanical Design (CAD) Top View Bottom View

5. Mechanical Design • Vertical structure • Simple aluminum frame • Multiple modular-plateau design • Houses main CPU, IMU board, power supply, etc. • Modular/adjustable for optimization • Facilitates testing phase • Adjustable center of mass • Serves as a three-dimensional inverted pendulum • Bolt-able design for quick adjustments

6. Mechanical Design (CAD) • Landing gear • Supplemental ‘fail-safe’ design • Protects investment • Backup if minimum success criteria is not met • i.e. BallBot topples over • Simple & effective • Worm-screw actuator design • Encapsulates ball when BallBot is balanced

7. Electrical Components • New components • Micro ITX gigabyte board • High-level CPU to run MatLab • Processes integer data from IMU board • Runs control algorithm to digest sensor data • Provides output to motor controllers • 100% onboard control for self-sufficiency • A321 batteries x 30 for onboard power supply • Provides 12-16.5V (3-5A) to motors • Provides 5V for digital logic (IMU board and CPU)

8. Micro ITX onboard Computer • 1.6GHz CPU • 4GB DDR3 • Windows 7 • MatLab2010 • Rotational matrix manipulation • State-space matrix processing

9. IMU Board • Arduino ATmega2560 • Microcontroller/microprocessor • ADXL345 Accelerometer • Three-axis acceleration measurement unit • IDG500 Gyroscope • Two-axis angular velocity measurement unit • Provides real-time feedback of inertial orientation/rotation in 3D space

10. IMU Board

11. Sensor Data Processing • IMU data will be relayed to onboard computer • MatLab will process complex state-space equations and rotational matrices • Control system theory is used to model the system for analysis of stability • Robotics synthesis • Rotational matrices synthesize the robots orientation and angular velocity • MatLab will process the matrices to provide feedback to the Arduino which sends signals to the motor controllers

12. Electronics Overview

13. Controller Overview • State-space subsystem block diagram

14. Controller Simulation • Subsystem • Block-diagram representation of inside subsystem

15. Controller Simulation • State-space modeling • x’ = Ax + Bu; y = Cx + Du • MatLab A = 0 0 1.0000 0 0 0 0 1.0000 0 -198.9738 -0.0567 0.0567 0 42.8060 0.0092 -0.0092 B = 0 0 0 1 C = 1 0 0 0 D = 0

16. State-space model (cont.) controllability_matrix = 0 0.61661 -0.040635 19.844 0 -0.099717 0.0065714 -4.2689 0.61661 -0.040635 19.844 -2.6754 -0.099717 0.0065714 -4.2689 0.5025 Controllable_Rank_is = 4 observability_matrix = 1 0 0 0 0 0 1 0 0 -198.97 -0.056727 0.056727 0 13.715 0.0037383 -198.98

17. State-space model (cont.) Obsevabile_Rank_is = 4 Poles = 0 -6.5686 6.5168 -0.014085 Kd = -36.621 -1698.7 -40.986 -423.26 pole_placement = -14 -5 -240 -180 L = 438.93 -4372.5 51264 -26241 K_f = -0.14086 -886.74 -1.4844 -141.81 K_i = -0.0071253

18. State-space model (cont.) K_LQR = -0.14086 -886.74 -1.4844 -141.81 -0.0071253 new_A_by_K_gain = 0 0 1 0 0 0 0 0 1 0 0.086857 347.8 0.85855 87.502 0.0043935 -0.014046 -45.618 -0.13884 -14.151 -0.00071051 1 0 0 0 0

19. Robot Motion Synthesis • BallBot’s orientation/angular motion can be represented with rotational matrices • Euler angles indicate roll, pitch, and yaw of the BallBot due to disturbances (gravity, wind, push) • Simplifies balancing/stability algorithm

20. Robot Motion Synthesis • Frame 0 = 00X0Y0Z0 • Frame 1 = 01X1Y1Z1 • Position vector 0 = 3x1 matrix = [0 0 1] T • Position vector 1 = [ ] = 3x1 matrix • The angular velocities ωψ, ωϕ, ωθrepresent the data provided by the IMU board and are integrated to find position

21. Robot Motion Synthesis • The rotational matrix is very complex in terms of possible orientation synthesis • The axes of frame 0 and frame 1 are compared with the dot product of the components of position vector 0 and position vector 1

22. Robot Motion Synthesis • All possible orientations: • C1 = Cos(ψ), C2 = Cos(ϕ), C3 = Cos(θ) • S1 = Sin(ψ), S2 = Sin(ϕ), S3 = Sin(θ)

23. Design Requirements – Major milestones • In this phase of the design: • The mechanical structure must be completed by October 20th, 2011 • Electronics can then be integrated into assembly (October 27th) • Arduino and MatLab communication algorithm (November 2nd) • Begin preliminary testing (October 27th – November 10th) • Finalize complete algorithm (November 16th) • Optimization, aesthetics, minor revisions (November 27th)

24. Gantt Chart

25. Trade Study – IMU Board

26. Trade Study – Accelerometer Filter • ADXL345 • Capacitor bandwidth filter – band-limiting filter • Noise reduction – (dispose of anomalous data) • Anti-aliasing – (prevent data loss due to resolution change) • X & Y max bandwidth – 1650Hz • Z bandwidth – 550Hz • Minimum capacitance = 0.0047μF

27. Trade Study – Accelerometer Filter • Bandwidth filter - capacitor selection • Capacitance decides bandwidth • Bandwidth indicates data resolution Table 1 – Bandwidth vs. Capacitance • Cx, Cy, Cz pins on ADXL345 • Low-pass filtering • Noise reduction • 3-dB bandwidth equation • F−3 dB = 1/(2π(32 kΩ) × C(X, Y, Z))

28. Trade Study – Accelerometer Filter • F−3 dB = 1/(2π(32 kΩ) × C(X, Y, Z)) • Approximates to F–3 dB = 5 μF/C(X, Y, Z) • 1650 Hz = 5 μF/0.00303 μF • Cx = Cy = 0.00303 μF • 550 Hz = 5 μF/0.0091μF • Cz = 0.0091 μF • These capacitor values will provide the highest data resolution for • 1650 readings per second for X and Y acceleration • Detect smallest possible acceleration in planar motion • 550 readings for Z acceleration • The Z axis will thus represent the vertical axis of the BallBot from the center of the ball to the top of the BallBot • Then Z-axis data does not require high resolution

29. Trade Study – Accelerometer Filter • Rms noise= Noise Density x sqrt(BW) • Noise is thus a factor of bandwidth Table 2 – Noise Density

30. Trade Study – AccelerometerOperating Voltage • The ADXL345 output is ratio-metric • The output sensitivity (or scale factor) varies proportionally to the supply voltage. • VS = 3.6 V - output sensitivity = 360 mV/g • VS = 2 V - output sensitivity =195 mV/g. • Arduino’s 3v3 pin supplies 3.3V • Sensitivity thus approximates to 320 mV/g to 340 mV/g (or 330 mV/g average) • Sensitivity estimated to be adequate for BallBot • Arduino’s built-in serial monitor read consistent data • Only real-time testing will confirm

31. Trade Study – AccelerometerOperating Voltage X-Y-Z sensitivity (voltage/gravity) Data Sheet

32. References • Arduino – microcontroller (libraries/tutorials) • www.arduino.cc • SparkFun – sensors/electronics (datasheets) • www.sparkfun.com • MatLab resource (control system toolbox, etc.) • http://www.mathworks.com/matlabcentral/fileexchange/23931 • SolidWorkshelpfile • http://help.solidworks.com/2012/English/SolidWorks/sldworks/r_welcome_sw_online_help.htm • Robot Modeling and Control (textbook) • Control Systems Engineering (textbook)

33. Title • Contents