Brett Browningand

M. Bernardine DiasM. Bernardine Dias

Spring 2011

Lab #1 feedbackLab #1 feedbackFinal project overview

Final project teamsFinal project teamsLab #2 overview

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Cluttered racing taskProbably want to be able to accelerate fast, brake fast, turn quickly

Reduce mass (better power to weight)Lower Center of GravityReduce rotational inertia (bring mass close to CG)( g )

SensingEnsuring that your sensors can see the “interesting” bits for the task is essentialE.g. where should lasers be, where should they aim?E.g. where should lasers be, where should they aim?

ProtectionEnsuring that computers/sensors can’t be damaged is a good ideaAlways remember wires in a layout

AccessibilityAccessibilityBeing able to access all the parts is very useful

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Hopefully you learned toBe prepared and on time for the demoMake sure it all works for the demoStart early, have a plan, re-evaluate as you proceed

DrivingDrivingRamping up/down speeds is crucial to controlEncoders are good, but may have calibration issuesSensor is good, but doesn’t see everything

PlottiPlottingLearn to use Matlab (initial pain, but very useful)Save data in text files:

one sample per row, space or comma separated e.g.p p p p g1.3654 3.3 4.56781.4663 3.5 4.222

Load with matlab:data=load(‘foo.txt’);

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Introduction to controlClosed-loop controlPID controlER1 controlER1 controlDrive to a pointPath followinggNext…

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Detailed topic, but we’ll just focus on PID Detailed topic, but we ll just focus on PID controlWe won’t be concerned with detailed analysisanalysis

There are many books on the topic if you are interested!Al o a co e (e TAMUQ CMU P )Also many courses (e.g. TAMUQ, CMU-P…)

Key conceptsOpen loop vs closed (feedback) loop controlInput vs. ResponsePID controlRules of thumb for tuning PID loops

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How to correct the command to achieve How to correct the command to achieve target?E g Turn to pointE.g. Turn to point

θω

θ

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Generate a command (or sequence) to Generate a command (or sequence) to achieve the desired trajectoryNo feedback based on outcomeNo feedback based on outcome

Path planning is often done this p gway: have a model of how

system will respond, pick the best command, then execute

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What can go wrong?

Generate a command (or sequence) to Generate a command (or sequence) to achieve the desired trajectory and adjust it based on sensed feedback it based on sensed feedback

Velocity control can be done this way, same for steering or visual servoing:same for steering or visual servoing:

See where we are and adjust based on our observed “error”

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What can go wrong?

Give an input measure the outputGive an input, measure the output

Input Response

robot

vcmd Linear speed

p

robot

tStep input tUsually calledStep input tUsually called the plant

If we knew the system response we could

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y pinvert it to find the best command

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StepStepParabola

t t

RampSinusoidal

t t

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Overshoot

** Multiple ways to define rise time

Input

Overshoot

Ringing (non shown)

Steady state error

OutputRise time**

Steady State Response

Transitory Response

Settling time

tSettling time

Typical control problem: For given input design

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Typical control problem: For given input design system to achieve target response outputs

Add feedback path and use error as inputAdd feedback path and use error as input

ErrorCommand/in

Robot(or plant)

vcmd(t) Sensed output+ e(t)

oCo a d/put

-

Actualvact(t)

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Add feedback path and use error as inputAdd feedback path and use error as input

ErrorCommand/in

Robot(or plant)vcmd(t)

Sensed Output

+Controller

e(t)

ErrorCommand/input

( p )-

Actualvact(t) Actual

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Command is function of error and its Command is function of error and its integral/derivatives

Proportional, Integral, Derivative

In discrete time:

Robotvcmd(t)Sensed Output

+

-Controller

e(t)

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-vact(t)

Command is function of error and its Command is function of error and its integral/derivatives

Proportional, Integral, DerivativeI DP I D

In discrete time:

Robotvcmd(t)Sensed Output

+

-Controller

e(t)

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-vact(t)

Typical responseTypical responseSmaller Kp

Underdamped

OutputInput

L KLarger KpOverdamped

t

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PIDControl(Kp,Ki,Kd,deltat):ierr=0elast=0hil (1) {while (1) {

vdesired = get_new_command()vactual = sense_output()

err = vdesired-vactualierr += err*deltatderr = (err-elast)/deltatelast = errelast = err

vcmd = Kp*err + Ki*ierr + Kd*derr}

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1 Check open loop response1. Check open loop response2. Tune Kp to get okay performance (Ki=Kd=0)3. Tune Ki to get zero S.S. Errorg4. Tune Kd to reduce overshoot and improve

rise-time response5. Micro-tune Kp, Ki, Kd until target achieved

Tuning by hand is an art. Mathematical derivation is better for serious vehicles.

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ER1 ControllerER1 ControllerRuns PID on (scaled) robot speed and rotation, with commands (vn,van)Returns encoder counts on left and right wheels (n n )Returns encoder counts on left and right wheels (nr, nl)

Robot_server (C++)Performs translation from (v,w) to commands (vn,van)

f i ( θ)Performs dead reckoning to return (x,y,θ)

vω

Aligned with robot

(x,y)

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θ

gstart position

javaER1

LidarServer Robot*Main

javaER1

UDPShared

MemoryUDP

Netserver

RobotServer

ER1 Controller

BShell

er1_stereo

• 2xDC Motors

Run remotely via ssh

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• 2xOptical encoders, 512 CPR• Lead-acid battery

Xdriver

Goal: Goal: Given target goal point, drive to it

How do we do this?How do we do this?Driving arcsPIDPIDTrapezoidal control

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Given a path how do we stay on the Given a path, how do we stay on the path?

Carrot following and Pure pursuitCarrot following and Pure pursuitPID on headingDual controllerDual controller

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Pick a point ahead on the path and Pick a point ahead on the path and execute drive to point

How to pick the point? How far ahead? How to pick the point? How far ahead? How to drive to point? Heading error?

Closest point on path

Intersection with circle

L

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with circle radius L

Circle intersection with pathCircle intersection with pathDrive a circular arc to intersect the point

Driving Arc, radius r

Intersection with circle

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with circle

Circle intersection with pathCircle intersection with pathDrive a circular arc to intersect the point

Driving Arc, radius r

Intersection with circle L

curvature

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with circle L

Given v calculate w (some prefer Given v, calculate w (some prefer curvature so invert accordingly)

Driving Arc, radius r

Intersection with circle L

Note, sign takes care of left vs right turn

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with circle L

Variations: Variations: Run a PID loop on target vGeneralize eqn to PID loopGeneralize eqn to PID loop

Driving Arc, radius r

Intersection with circle L

Proportional control, can also add integral,

derivative…

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with circle L

May care about heading error when we May care about heading error when we reach the path

Run a PID on heading errorOr, combine with pure pursuitCan get very creative but need to tune to vehicle and environmentvehicle and environment

Heading errorPure pursuit Heading error

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errorp Heading error

Obstacle avoidance and navigationObstacle avoidance and navigationArcs and potential fields

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