Get anim. gifs of motors & the other aminated gif I have downloaded

Controlling motors and controlling robots… PID motor control The fine art of motor arranging… getting things done even when you can’t control what you’re doing... First, to refresh your memory…

Spherical Stepper Motor complete motor statorrotor applications

Nanorover No More… JPL’s “nanorover” was to be used by ISAS to explore 1989ML Electroactive Polymer wiper

The solution to many problems! the MUSES-C project optical navigation camera LIDAR laser range finder completely map the asteroid g = m/s 2 play ball! feature extraction sample collection

(Slightly) Tamer Projects Extinguishers’ Maze

Possible designs Extinguishers Include pictures of things NOT working, if you have them There is a camera in the gray cabinet in B120 and Software on the robot croupier’s PC I also have a video camera (as do many of you) Write-up “FlameBot”

Possible architectures Doing HW Playing golf ? (Paul P.) Mazlov’s hierarchy of human needs (Will) Hockey goalie (Eric) Shopping at Lowe’s or Home Depot ! Clown balancing on stilts ?? avoid whirling work sleep seek human help check notes work Rodney Brooks: subsumption

Possible architectures Doing HW Playing golf ? (Paul P.) Mazlov’s hierarchy of human needs (Will) Hockey goalie (Eric) Shopping at Lowe’s or Home Depot ! Clown balancing on stilts ?? avoid whirling work sleep seek human help check notes work Rodney Brooks: subsumption Ron Arkin: motor schemas Trying to get around the Libra complex as a freshman Driving a car: attracted to green lights & the goal; repelled by cars & red lights Adjusting the shower water (Paul P) or seasoning spaghetti sauce (Ken) Finding avalanche survivors (Brie) or Skiing (Eric) Football players or a soccer player with the ball Mingling at a party -- drifting toward food; away from certain people (like a maze, but more embarrassing)

Possible architectures Doing HW Playing golf ? (Paul P.) Mazlov’s hierarchy of human needs (Will) Hockey goalie (Eric) Shopping at Lowe’s or Home Depot ! Clown balancing on stilts ?? avoid whirling work sleep seek human help check notes work Rodney Brooks: subsumption Ron Arkin: motor schemas Trying to get around the Libra complex as a freshman Driving a car: attracted to green lights & the goal; repelled by cars & red lights Adjusting the shower water (Paul P) or seasoning spaghetti sauce (Ken) Finding avalanche survivors (Brie) or Skiing (Eric) Football players or a soccer player with the ball Mingling at a party -- drifting toward food; away from certain people (like a maze, but more embarrassing) Erann Gat: 3-layer architecture Mudder studying for a test (Paul R)

Low-level control getting things done even when you can’t control what you’re doing... PID control

Low-level control getting things done even when you can’t control what you’re doing... PID control N S NS stator rotor commutator on shaft + - brushes DC motor We can control: the voltage applied We want to control: the rotational speed  V V

Low-level control getting things done even when you can’t control what you’re doing... PID control N S NS stator rotor commutator on shaft + - brushes DC motor We can control: the voltage applied We want to control: the rotational speed  V V Case 1: We trust equations ! Case 2: We trust data !

Motor specs Electrical Specifications For motor type S006S012S nominal supply voltage(Volts) armature resistance(Ohms) maximum power output(Watts) maximum efficiency(%) no-load speed (rpm)12,00010,60013,00014,400 no-load current(mA) friction torque(oz-in) stall torque(oz-in) velocity constant(rpm/v) back EMF constant(mV/rpm ) torque constant(oz-in/A) armature inductance (mH) k motor constant

Open-loop control desired  d V The world dd compute V from the equation controller Maybe... V = + k  d  R k Case 1: We trust equations ! voltage load torque motor resistance motor constant rotational speed 

Open-loop analysis We don’t know everything about  ! or maybe not!  = guessed torque required  a = actual torque required Guessed voltage Actual voltage needed V = + k  d  a R k V = + k  d  R k The Road Less Traveled Bang-bang control

Dynamic performance Desired speed:  d = 1 Computed voltage: V = + k  d  R k Actual torque req.:  a = 2  Results k2 dk2 d 2R with  = “motoring uphill”

Dynamic performance Desired speed:  d = 1 Computed voltage:  t V = + k  d  R k Actual torque req.:  a = 2  Results k2 dk2 d 2R with  = “motoring uphill”

Dynamic performance Desired speed:  d = 1 Computed voltage: attained speed = 0.5  t V = + k  d  R k Actual torque req.:  a = 2  Results k2 dk2 d 2R with  = “motoring uphill”

Dynamic performance Desired speed:  d = 1 Computed voltage: attained speed = 0.5  t V = + k  d  R k Actual torque req.:  a = 2  Results k2 dk2 d 2R with  = “motoring uphill” dd  d 

Closed-loop control desired  d V The world feedback the actual speed  - compute V prop. to the error e  d  Error signal e Proportional control V = K p (  d  ) V = K p e Proportional control actual  Case 2: We trust data !

The road to Hana

(k+K p ) Closed-loop analysis V = + k   a R k V = K p (  d  ) controllerthe world presuming I’ve done the algebra correctly…  = K p  d -  a R k(k+K p )

(k+K p ) Closed-loop analysis V = + k   a R k V = K p (  d  ) controllerthe world presuming I’ve done the algebra correctly…  = K p  d -  a R k(k+K p ) The actual speed lags behind the desired speed -- with both a multiplicative term and an offset.

Closed-loop analysis But the constant is under our control... not very close to the desired speed of 1 K p = 5

Closed-loop performance K p = 20 K p = 200 K p = 50 K p = 500

Evaluating the response How can we eliminate the steady-state error? steady-state error settling time rise time overshoot overshoot -- % of final value exceeded at first oscillation rise time -- time to span from 10% to 90% of the final value settling time -- time to reach within 2% of the final value ss error -- difference from the system’s desired value

Errors K p = 200K p = 50 Idea: translate error time into increased gain...   d

The Integrator... desired  d V The world actual  actual speed  - compute V using P and I feedback  d  a Error signal e Proportional & Integral control V = K p (  d  ) + K i ∫ (  d  ) dt V = K p ( e + K i ∫ e ) ( with a different K i ) Your average integral control enthusiast

Control, PI - style K p = 100 K i = 50 Magnum, PI K i = 200

You’ve been integrated... K p = 100 resistance is futile (if it’s <.001  instability & oscillation ringing What to do?

You’ve been integrated... K p = 100 resistance is futile (if it’s <.001  instability & oscillation ringing What to do? error

PID control desired  d V The world actual  a actual speed  a - compute V using PID feedback  d  a Error signal e Proportional / Integral / Derivative control V = K p (  d  ) + K i ∫ (  d  ) dt + K d V = K p ( e + K i ∫ e + K d ) d e dt d e dt ( redefining K d )

PID results K p = 100K i = 200 K d = 2 K d = 10K d = 20 K d = 5

PID final control

PID tuning: the untold story How to get the PID constants ? (1) Try out different values until some look good. Optimize performance while tuning only one variable, then repeat with another variable. 2-3 iterations should provide reasonable results. (2) Find values that produce common behavior, then adjust. Using only Proportional control, turn up the gain until the system oscillates w/o dying down, i.e., is marginally stable. Assume that K and P are the resulting gain and oscillation period, respectively. Then, use Ziegler-Nichols Tuning for P controlfor PI controlfor PID control K p = 0.6 K K i = 2.0 / P K d = P / 8.0 K p = 0.45 K K i = 1.2 / P K p = 0.5 K

Implementing PID Use discrete approximations to the I and D terms: Proportional term: e i =  desired -  actual Integral term:  e i  t i at time i i= 0 i=now Derivative term: e i - e i-1 How could the time-discretization affect performance?  t i = elapsed time titi

PID wrap-up photomultiplier temperature regulation automobile cruise control pipeline gas flow robotics (joint position and velocity) Widespread control strategy Summary of the terms’ effects reaching a desired setpoint wall-following Performance depends on tuning and delays in the feedback loop KpKp KiKi KdKd rise time overshoot settling time steady state error decreases minor effect increases decreases minor effect increases decreases eliminates

Short Assignment #3: PD control Achieving a goal position, given velocity control. goalstart

2d Motor Schema control A 2d vector field for controlling robot motion… (a motor schema with an attractor and an obstacle) How do we use those “forces” to direct the robot’s motors?

2d Motor Schemas: a thought experiment The Nomad (and most robots) are limited in their maneuverability -- they can only move forward and backward in the direction their wheels are facing. Thus, you can control 2 things: the translational velocity of the robot the rotational velocity of its wheels Task: Design several strategies for setting the translational and rotational velocities so that the Nomad can efficiently change course to a goal point in 2d. For example, suppose the Nomad is moving along the negative x-axis to the right (toward the origin) at a velocity v o. Just when the robot reaches the origin, it realizes it wants to be at the point (1000,1000). What are possible control strategies that will get it there. Consider as many as you can (but at least two). What are their (dis)advantages? goal current state

Wall/Corridor following Achieving a desired offset, given control over turning angle: L R  = K p (R-L) Absolute limits should be used on  ! How would you detect L and R ?

Fire finding Achieving a desired offset, given control over turning angle: light-balancing just one sensor? L R

Wrapping Up Examining robots’ inputs: building & using models of the world Inverse kinematics: what we would really like to know... Forward kinematics: some alternatives to the differential-drive robot Short Assignment #3 due Monday Lab Project #1 write-up due Sunday night, 2/16 (midnight) PID control: strategy for effectively controlling one system characteristic with a related (but not identical) one

this is as far as I got in Spring 2003

Perspective At least you’re not Jar Jar... pic

Robotic use of EAPs shape memory alloys “nitinol” (nickel titanium)

Perspective If your robot doesn’t do what you want... … you can always change what you’re looking for.

to intelligent robots the MUSES-C project optical navigation camera LIDAR laser range finder Fan beam sensors g = m/s 2 squishy sphere feature extraction sample collection

Possible designs Extinguishers See example write-up at the CS154 website. Use pictures to help explain approach and results. Write-up

Dynamic performance V = + k   a R k the world : kV =  a + k 2  R R torque = inertia  acceleration kV = J  +  L + k 2  R R external load torque internal to the motor There must be a transient and a steady-state response to the input, V

Motors and Encoders desired  d V The world aa actual speed  a - compute V using the error e  d  a Error signal e Basic input / output relationship: We want to control . V = + k   R k We can control V. PID control

Closed-loop control desired  d V The world aa actual speed  a - compute V using the error e  d  a Error signal e Basic input / output relationship: We want to control . V = + k   R k We can control V. PID control

Wrapping Up Examining robots’ inputs: building & using models of the world Inverse kinematics: what we would really like to know... Forward kinematics: some alternatives to the differential-drive robot Short Assignment #3 due Monday Lab Project #1 write-up due Sunday night, 2/16 (midnight) PID control: strategy for effectively controlling one system characteristic with a related (but not identical) one