August 24, 2004 Sam Siewert

CEC 450 Real-Time Systems

Lecture – Robotics Project Concepts

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Basic Requirements 5 Degree of Freedom Actuation – Base, Shoulder, Elbow, Wrist, Gripper – 5 Motors, Forward and Reverse

Target Pick and Place Within Base Reachability – 3.5 to 13.5 inches from center of base – -180 deg to +180 deg around base – At least on pick target and one place target

Soft or Hard Limit Switches on all Degrees of Freedom – 2 Switches on each rotational joint – Hard limit disables motors and requires over-ride – Soft limit safes arm at any limit

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Simple Reversible Motor with Switches

DC Motor+6V +3V

Switch A

Switch B

Switch C

SW A SW B SW C MOTOR Off X Off Off Off On On Forward On Off On Reverse

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Simple Reversible Motor with 2 Relays

DC Motor+6V +3V

Relay A

NO

NC

Relay B

NO

NO = Normally OpenNC = Normally Closed

NC

RLY A RLY B MOTOR Off Off Off Off On Forward On Off Off On On Reverse

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5-DOF Arm Relay Control

Base

+6V +3V

Base Direction

Gripper On/Off

Shoulder

Elbow

Wrist

Gripper

Base On/Off

Shoulder Direction

Shoulder On/Off

Elbow Direction

Wrist On/Off

Wrist Direction

Elbow On/Off

Gripper Direction

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Arm Rotation Hard Limit Switches

DC Motor

+ 6 V + 3 V

Relay A

NO

NC

Relay B

NO

NO = Normally Open NC = Normally Closed

NC

Pushbutton Break Limit Disable Switch

Pushbutton Make Limit Over - ride Switch

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Soft Limit Switches

A to DAnalogInputs

+5V

Referenceand Ground

Limit Switch #1Limit Switch #2

Limit Switch #3

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Relay H-Bridge Motor Control

DC MotorRelay A Relay A

Relay A Relay A

+3V

A

B D

C

A B C D MOTOR 0 0 0 0 Off 0 0 1 1 Brake 0 1 0 1 Fuse Test 0 1 1 0 Reverse 1 0 0 1 Forward 1 0 1 0 Fuse Test 1 1 0 0 Brake

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MOSFET H-Bridge Motor Control

DC Motor

+3V

A C

B D

A B C D MOTOR 0 0 0 0 Off 0 0 1 1 Brake 0 1 0 1 Fuse Test 0 1 1 0 Reverse 1 0 0 1 Forward 1 0 1 0 Fuse Test 1 1 0 0 Brake

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Arm Coordinates 5 DOF, Center at Base – Degrees of Freedom – Each Joint Rotation – Base

Rotate around Z -180 to 180 deg

– Shoulder Rotate around Y 0 to -135 deg

– Elbow Rotate around Y 0 to -135 deg

– Wrist Rotate around X -180 to 180 deg

– Gripper Fully Open Fully Closed

X

Y

Z

Home Position

X

Shoulder Segment

Elbow Segment Target Search/Carry Position

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Concentric Rings of Arm Reach Ability

Innermost Ring IntermediateRing

OuttermostRing

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Arm Surface Reach Ability Concentric Rings Around the Base Innermost Ring – Compound Rotation – Shoulder -45 deg – Elbow -135 deg

Outermost Ring – Shoulder Rotation Only – Shoulder -135 deg – Elbow 0 deg

Intermediate Ring – Raise Shoulder – Lower Elbow

X

Z 135° 45°

Compound Shoulder/Elbow Rotation

X

Z 135°

Shoulder Only Rotation

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Arm Navigation – Open Loop Dead Reckon from Home to Target – From known start position (Home position)

Home Position Known By Soft Limits Base at 0 Shoulder at 0 Elbow at 0 Wrist at 0 Gripper Fully Open

– Motors on for specific time periods to translate to target – Motors on for specific time periods to translate to release target – Motors on in specific directions to Home using Limits to Stop

Canned Set of Pick Targets Canned Set of Place Targets

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Feedback Arm Navigation - Closed Loop

Computer Vision Feedback Position Encoder Feedback – Electrical (Potentiometer) – Optical (LED, Photodiode Counter) – Mechanical (Switch Counter)

Command

Error ( Command –

Measurement ) Control Function

Actuator Output System

( Plant )

Disturbance

Output

Feedback Sensor

Measurement

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Shoulder Position Encoder Feedback Relay On/Off Motor Control (Only Gain is Mechanical Gearing)

– H-Bridge Can Provide Braking – DAC Can Provide Voltage Supply Scaling

10K Ohm Multi-Turn Potentiometer, 5 Volt Reference 8 Bit Analog to Digital Converter Position 0 to 255 => 0 deg to -135 deg, Approx ½ degree knowledge Calibrate for Home Position (0 degrees) and Full Throw (-135 degrees)

– Angle = (0.52734375 x Position) +/- Offset – Make Sure Potentiometer Zero Crossing Not in Rotational Range

Translational and Rotational Inertia (Forces/Torques), Gear Friction/Slip Error Deadbands Set at +/- 1 degree to Avoid Over-Controlling Position

Shoulder Commanded

Position

Error ( Command –

Position ) Relay Command

Logic

Relay Command Robotic Arm

( Shoulder Motor ) Shoulder Rotation

Disturbance ( Stick / Slip Friction )

Potentiometer Resistance

A to D Measurement

( Scaling to Degrees )

Shoulder Position

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Analog-Digital-Analog Control Loop Digital Command and Error Computed Digital Control Function Plant Control in Analog Domain via D/A – Digital to Analog Converter – Output Actuator Hold Properties

Measurement via A/D – Accuracy (8, 12, 16 bit) for Analog to Digital Converter – Hold Properties, Sampling Rate, Delay

Digital Domain Analog Domain

Command Error

( Command – Measurement ) D / A Converter

Actuator Output System

( Plant )

Disturbance

Output

Analog Sensor

Measurement A / D Converter

Digital Computer

Control Output

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PID Controller – Transfer Function

Two Zeros and a Pole at Origin – Root Locus Stability Boundary – Negative Roots = Stable – Positive Roots = Unstable

Integral Compensator Derivative Compensator

ssKKsK

sKs

KKsG dipd

ipc

2

)(++

=++=

R(s) G(s)Kp

Ki / s

Kds

C(s)++++

-

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PID Controllers – Process Control Function

u(t) is Output from Control Function to Actuators/Plant y(t) is Measured Error Great for Single Input, Single Output Control Problems - Processes – Proportional

y(t), Error = Command - Measurement u(t), Actuator Output = (Gain x Error) + Bias Gain = Output-Change / Input-Change Bias Adjustment is Manual

– Integral Error is Integrated over Time Automates Bias Adjustment

– Derivative Delay in Sensed System Changes with Output Changes

– Servo actuation time – Motor slow down, ramp up

Change in Error over Time Includes Changes in Command over Time Too

tyKtyKtyKtu dip ∆

∆++= ∑ )()()(

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PID Digital Implementation Digital Error Gains Applied to Digital Error Proportional, Integrated, and Differentiated Outputs Summed Output Sum is Digital Control Output Embedded in Analog-Digital-Analog Feedback Control

M(z)Kp

Kd

Ki

+

++

NumericalIntegrator

NumericalDifferentiator

E(z)

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Comparison of P, PI, and PID A Well-Tuned PID has overshoot control, good settling, and decent rise time (Kp=0.1, Ki=0.4, Kd=0.05)

Comparison of P, PI, and PID Controllers (Set Point = 100)

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time Step

Ou

tpu

t PPIPID

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PID Tuning

Parameter Rise Time Overshoot Settling Time

Kp gain increase

Decreases Increases Small Change

Ki gain increase

Decreases Increases Increases

Kd gain increase

Small Change Decreases Decreases

As a function of increasing a Parameter

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State Space Control Systems Time Domain Control – Well Suited to Digital Control – System Described by Differential Equation (Dynamics) – System of First Order Differential Equations Can Be Derived

matrixforwardfeedmatrixouputvectorinputvectoroutput

matrixinputmatrixsystemtimetrwderivativevectorstate

−−=−=−=−=

+=−=−=

−−=−=+=

DCuy

DuCxyBA

xxBuAxx

,,

,...,

u +B+

dx/dt ∫ x C y

D

A

+

+

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Fixed Camera Navigation – Closed Loop

Overhead/Front/Side View camera(s) can see gripper and targets – Entire Arm Reach Ability Space in Field of View – Will Require Multiple Camera Angles for Full Reach Ability

Image processing to find gripper base XY plane location offset from target – Command base, shoulder, and elbow within reach ability space to place

gripper over target – Wrist and gripper marked with image targets (red dots)

Target objects known color and shape – Closed Loop Control Drives gripper target to target object location in XY

plane – Requires Centroid calculation for gripper target and target object

Controlled lighting Home position at limits and so gripper markers visible

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Gripper Camera – Open + Closed Loop

Start at limits home position Camera embedded in gripper Base ring search patter to find target – Open Loop – Start at outermost ring and scan 360 degrees around base – Move in one camera field of view, scan 360 degrees – When object seen, command shoulder/elbow to lower gripper to

target

Closed Loop Process to Lower Gripper to Target – Elbow and Shoulder Rotation Commanded to Keep Target in

Center of FOV – Camera Tilt May be Required for Full Reach Ability

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Building Your Own Arm Construct from Basswood and Hobby Servos – Bass or Spruce has high strength to weight ratio – Hobby Servos Move to Commanded position – Hobby Servo Uses PWM to Set and Hold Servo Position

Motors Require Timing or Feedback – Timing-based motion will have repeatability problems – Consider Feedback with Cameras or Joint Position Encoders

Position Encoders – Simple Multi-turn Potentiometer Input to ADC – Calibrate ADC to Potentiometer Rotation – Difficult to Mount and Integrate with Joint Rotation