BallBot

Brian Kosoris

Jeroen Waning

Bahati Gitego

Yuriy Psarev

10/11/2011

System Overview

• Mechanical Structure• Base• Vertical structure• Landing gear

• Electronics• Sensors• Actuators/Motors

• Control System• State-space variable model• MatLab/Simulink code• Synthesis of 3D motion

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

Mechanical Design (CAD)

Bottom View

Top View

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

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

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)

Micro ITX onboard Computer

• 1.6GHz CPU• 4GB DDR3• Windows 7• MatLab 2010

• Rotational matrix manipulation

• State-space matrix processing

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

IMU Board

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

Electronics Overview

Controller Overview

• State-space subsystem block diagram

Controller Simulation

• Subsystem• Block-diagram representation of inside subsystem

Controller Simulation

• State-space modeling• x’ = Ax + Bu; y = Cx + Du

• MatLabA =

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

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

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

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

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

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, ωθ

represent the data provided by the IMU board and are integrated to find position

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

Robot Motion Synthesis

• All possible orientations:• C1 = Cos(ψ), C2 = Cos(ϕ), C3 = Cos(θ)

• S1 = Sin(ψ), S2 = Sin(ϕ), S3 = Sin(θ)

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)

Gantt Chart

Trade Study – IMU Board

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

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))

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

Trade Study – Accelerometer Filter

• Rms noise = Noise Density x sqrt(BW)• Noise is thus a factor of bandwidth

Table 2 – Noise Density

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

Trade Study – AccelerometerOperating Voltage

X-Y-Z sensitivity (voltage/gravity)

Data Sheet

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

• SolidWorks helpfile• http://

help.solidworks.com/2012/English/SolidWorks/sldworks/r_welcome_sw_online_help.htm

• Robot Modeling and Control (textbook)• Control Systems Engineering (textbook)

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