Robot Actuation: Motors Stepper motors Servo motors Physics “review” DC motors Electric fields and magnetic fields are the same thing. Nature is lazy. Things seek lowest energy states. iron core vs. magnet magnetic fields tend to line up v + - v + - N S N S Torque is a good scrabble word. Author: CIS

Stepper Motors N S stator rotor electromagnets

Stepper Motors N S stator rotor S N electromagnets “variable reluctance” stepper motor How does rotor angle affect the torque?

Stepper Motors N S stator rotor S N electromagnets “variable reluctance” stepper motor angle torque

Stepper Motors N S stator rotor S N electromagnets “variable reluctance” stepper motor angle torque

Stepper Motors N S stator rotor S N S N electromagnets “variable reluctance” stepper motor on to the next teeth…

Stepper Motors N S electromagnets stator rotor S N S N “variable reluctance” stepper motor Direct control of rotor position (no sensing needed) May oscillate around a desired orientation Low resolution printers computer drives machining on to the next teeth… can we increase our resolution?

Increasing Resolution Half-stepping S S N N energizing more than one pair of stator teeth

Increasing Resolution Half-stepping S S N N angle torque energizing more than one pair of stator teeth

Increasing Resolution Half-stepping S S N N angle torque More teeth energizing more than one pair of stator teeth

Increasing Resolution Half-stepping S S N N angle torque More teeth energizing more than one pair of stator teeth on the rotor and/or stator Question 2 this week…

Motoring along... direct control of position very precise positioning What if maximum power is supplied to the motor’s circuit accidently ? Underdamping leads to oscillation at low speeds At high speeds, torque is lower than the primary alternative… Beckman 105 ?

DC motors -- exposed !

DC motor basics N S NS stator rotor permanent magnets commutator on shaft V + - brushes

DC motor basics N S NS stator rotor permanent magnets commutator on shaft V + - NS S N V + - brushes

DC motor basics N S NS stator rotor permanent magnets commutator on shaft V + - NS S N NS N S V + - V + - brushes

Who pulls more weight? N S NS stator rotor DC motor Stepper motor N S electro- magnets stator rotor

Who pulls more weight? N S NS stator rotor DC motor Stepper motor N S electro- magnets stator rotor Position control High holding torque Durability (no brushes) Energy used is prop. to speed Higher torque at faster speeds More popular, so they’re cheaper Smoother at low speeds

Open-loop control An “open-loop” strategy desired speed  Controller solving for V V Motor and world  “the plant”

Bang-bang control General idea works for any controllable system... desired speed  Controller solving for V V Motor and world  desired position  Controller solving for V(t) V(t) Motor and world  actual speed actual position

Returning to one’s sensors But the real world interferes... desired speed  d Controller solving for V V Motor and world aa desired speed  d  actual speed  a V r = + k   R k We don’t know the actual load on the motor.

Closed-loop control Compute the error and change in relation to it. desired  d V The world aa actual speed  a - compute V using the error e  d  a Error signal e how do we get the actual speed?

Proprioceptive Sensing Resolver = measures absolute shaft orientation Potentiometer = measures orientation by varying resistance, it has a range of motion < 360º Power/Contact

Servomotors Direct position control in response to the width of a regularly sent pulse. A potentiometer is used to determine the motor shaft angle. modified to run continuously potentiometer

Optical Encoders Detecting motor shaft orientation potential problems?

Gray Code #Binary

Gray Code #Binary with FPS applications !

Gray Code #Binary among others wires?

Absolute Optical Encoders Complexity of distinguishing many different states -- high resolution is expensive! something simpler ?

Relative Encoders Track position changes grating light emitter light sensor decode circuitry

Relative Encoders Relative position - calibration ? - direction ? - resolution ? grating light emitter light sensor decode circuitry

Relative Encoders Relative position - calibration ? - direction ? - resolution ? grating light emitter light sensor decode circuitry

Relative Encoders Relative position grating light emitter light sensor decode circuitry A B A B A lags B - calibration ? - direction ? - resolution ?

Relative Encoders Relative position grating light emitter light sensor decode circuitry A B A leads B - calibration ? - direction ? - resolution ? quadrature encoding 100 lines -> ?

Ideal Relative Encoders Relative position mask/diffuser grating light emitter light sensor decode circuitry Real A diffuser tends to smooth these signals With motors and sensors, all that’s left is... A B

Control

Closed-loop control Compute the error and change in relation to it. desired  d V The world aa actual speed  a - compute V using the error e  d  a Error signal e Feedback

Initial Feedback “First” feedback controller

Other Systems Biological feedback systems Chemical feedback systems intelligent hydrogels

at low pH values, the carboxylic acid groups of PMAA tend to be protonated, and hydrogen bonds form between them and the ether oxygens on the PEG chains. These interpolyer complexes lead to increased hydrophobicity, which causes the gel to collapse. At high pH values, carboxylic groups become ionized, the complexes are disrupted, and the gel expands because of increased electrostatic repulsion between the anionic chains. Additional Feedback Chemical feedback systems for insulin delivery Why I’m not a chemist: ph dependant

Robotic use of EAPs

Short Assignment #3 A second page and picture(s) for Lab Project #1. work in a citation for the paper you read! Putting the step into stepper motors… problem 1 problem 2 Implementing one-dimensional PD control (Nomad) problem 3 Remember that these may be done either individually or in your lab groups. Reading: Choose 1 of these four papers on design/locomotion: Implementing two-dimensional PD control (Nomad) Extra Credit Designing a Miniature Wearable Visual Robot An Innovative Locomotion Principle for Minirobots Moving in the Gastrointestinal Tract Get Back in Shape! A reconfigurable microrobot using Shape Memory Alloy Walk on the Wild Side: The reconfigurable PolyBot robotic system

Wednesday Coming soon! The ancient art of motor arranging... Controling motion by controlling motors: PID

Spherical Stepper Motor complete motor statorrotor applications

Returning to one’s sensors But the real world interferes... desired speed  d Controller solving for V V Motor and world aa desired speed  d  actual speed  a V r = + k   R k We don’t know the actual load on the motor.

How robotics got started...

Proportional control better, but may not reach the setpoint

PI control better, but will overshoot but I thought PI was constant...

PID control Derivative feedback helps damp the system other damping techniques?

And Beyond Why limit ourselves to motors? Nitinol -- demo stiquito robot ? Electroactive Polymers EAP demo Wiper for Nanorover dalmation

Control Knowing when to stop... DC servo motor -- what you control and what you want to control are not nec. the same thing motor model -- equivalent circuit to control velocity to control position

DC motors Basic principles N S N S NS N S S N stator rotor permanent magnets NS S NNS N S

Control What you want to control = what you can control For DC motors: speedvoltage N S NS V  V

Controlling speed with voltage DC motor model V e “back emf” R windings’ resistance e is a countervoltage generated by the rotor windings The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I

the following are the DC motor slides

Controlling speed with voltage DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I

k  k e Controlling speed with voltage DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Consider this circuit’s V: V = IR + e I stall = V/R current when motor is stalled speed = 0 torque = max How is V related to  V = + k e   R k  - or -  = -  + R  k e V Speed is proportional to voltage.

speed vs. torque torque  speed   k e V at a fixed voltage  R k  V max torque when stalled no torque at max speed

speed vs. torque torque  speed   k e V at a fixed voltage  R k  V stall torque no torque at max speed Linear mechanical power P m = F  v Rotational version of P m = 

speed vs. torque torque  speed   k e V at a fixed voltage  R k  V stall torque max speed Linear mechanical power P m = F  v Rotational version of P m =  power output speed vs. torque

torque  speed   k e V  R k  V power output speed vs. torque gasoline engine

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor V = IR + e circuit voltage V:

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m actuator’s power P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m ( ac’s ) P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor P R = I 2 R E & M lives on ! P e = VI

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m ( ac’s ) P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor VI = I 2 R + e m ( ac’s ) P R = I 2 R E & M lives on ! P e = VI

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m ( ac’s ) P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor VI = I 2 R + e m ( ac’s ) P R = I 2 R E & M lives on ! P e = VI VI > e m ( ac’s ) Finally ! Scientific proof !

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  actuator’s power P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor P R = I 2 R E & M lives on ! P e = VI

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  P R = I 2 R E & M lives on ! P e = VI VI = I 2 R +  P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  P R = I 2 R E & M lives on ! P e = VI VI = I 2 R +  P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor k e = k  VI = I 2 R + k  Ie/ k e V = IR + k  e/ k e IR + e = IR + k  e/ k e

single-parameter summary torque  speed   k V  R k  V stall torque max speed Linear mechanical power P m = F  v Rotational version of P m =  power output speed vs. torque

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

the preceding were the DC motor slides

Bang-bang control An “open-loop” strategy desired speed  Controller solving for V V Motor and world  “the plant”

gearing up... should be gearing down...

Another example of feedback control Nomad going to a designated spot

Power loss a good thing ? DC motor model V e R The back emf depends only on the motor speed. The motor’s torque depends only on the current, I. e = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor P R = I 2 R E & M lives on ! P e = VI

Back to control Basic input / output relationship: (1) Measure the system:  R, k (2) Compute the voltage needed for a desired speed  (3) Go ! We want a particular motor speed . V = + k   R k We can control the voltage applied V.

Back to control Basic input / output relationship: (1) Measure the system:  R, k (2) Compute the voltage needed for a desired speed  (3) Go ! We want a particular motor speed . V is usually controlled via PWM -- “pulse width modulation” V = + k   R k We can control the voltage applied V. V t V t (half V max ) (1/6 V max ) V V t t