Transcript Servos and Control

Robot Motion
• Forward and Inverse Kinematics – Next
quarter
• PID Control
• Frame-Based Motions on the AIBO
• Modeling Effects of Motions
Automatic Control
Systems, Servos,
Automatic Tracking,
Feedback Control
VOCABULARY:
Automatic Control Systems
 Automatic: able to activate, move or regulate itself.
 Control: command, direct, rule, check, limit,
restrain, regulate or operate.
 System: a group or combination of interrelated,
independent, or interacting elements forming a
collective entity.
• Control engineering is concerned with modifying
the behavior of dynamical systems to achieve
desired goals.
Control System Terminology
• Input - Excitation applied to a control
system from an external source.
• Output - The response obtained from a
system
• Feedback - The output of a system that is
returned to modify the input.
• Error - The difference between the input
and the output.
Types of Control Systems
• Open-Loop
 Simple control system which performs its
function without concerns for initial conditions
or external inputs.
 Must be closely monitored.
• Closed-Loop (feedback)
 Uses the output of the process to modify the
process to produce the desired result.
 Continually adjusts the process.
Control Systems
Transducer or Sensor Factors
Open Loop
Controller
Open Loop Controller
1. An open-loop controller (or non-feedback
controller) is a type of controller which computes its
input into a system using only the current state and
its model of the system
2. The system does not observe the output of the
processes that it is controlling
Inpu
t
Controller
Motor
Outp
ut
Open Loop Controller (cont…)
1. Open-loop control is useful for welldefined systems where the relationship
between input and the resultant state can
be modeled by a mathematical formula
2. For example determining the voltage to be
fed to an electric motor that drives a
constant load, in order to achieve a desired
speed would be a good application of
open-loop control
Open Loop Controller (cont…)
1. An open-loop controller is often used in
simple processes because of its simplicity
and low-cost, especially in systems where
feedback is not critical
2. Generally, to obtain a more accurate or
more adaptive control, it is necessary to
feed the output of the system back to the
inputs of the controller
Open-loop control
• Advantages:
 Stability not a problem
 Cheaper than closed-loop
 Can be used even if output cannot be measured
• Disadvantages:
 Changes in system or disturbances ? errors
 Periodic calibration required
Closed Loop
Controller
Example of a simple Control
in Closed Loop
Closed Loop Controller
1. Closed-loop controllers have the following
advantages over open-loop controllers:
1. Disturbance rejection (such as unmeasured
friction in a motor)
2. Guaranteed performance even with model
uncertainties, when the model structure does not
match perfectly the real process and the model
parameters are not exact
Closed Loop Controller
1.
A closed-loop controller uses feedback to control states or outputs of a
dynamical system
Controller
Input
Motor
Output
Measurement
Output
Feedback
2.
Process inputs have an effect on the process outputs, which is measured with
sensors and processed by the controller; the result is used as input to the
process, closing the loop
The General View of a
Control Loop
e
u
Feedback or Closed Loop System
PID Control
• Proportional Integral Derivative Control
• The Basic Problem:
– We have n joints, each with a desired position which we
have specified
– Each joint has an actuator which is given a command in
units of torque
– Most common method for determining required torques is
by feedback from joint sensors
What is PID Control?
• Proportional, Integral, & Derivative Control
– Proportional: Multiply current error by constant to try to
resolve error
– Integral: Multiply sum of previous errors by constant to
resolve steady state error (error after system has come to
rest)
– Derivative: Multiply time derivative of error change by
constant to resolve error as quickly as possible
Feedback Signal is subtracted
Integrated circuit
with differential
amplifier
Motor and gears
rotate the wheel
Potentiometer
on the wheel
Feedback Signal is subtracted
Proportional
Controller
Control Law
Step response of the system
for proportional control
only
Complete PID
controller
Control Law
Step response of the system
for proportional plus
integral plus derivative
(PID) control.
Kp = 20
KI = 75
KD = 0
time
Cruise
Control
Example
V = velocity, speed
All opposing
forces
Force
created by
motor
Acceleration
is derivative of
speed
acceleration
speed
Two
terminologies
integrator
Closed-loop (feedback) control
• Advantages:
 Reduced sensitivity to:
• Disadvantages:
 disturbance inputs
 Increased complexity
and cost
 parameter changes
 Risk of instability
 Can stabilize an open- loop
unstable plant
 Can change system
dynamics:
 speed of response
 accuracy
 reduce effect of non-linearities
Advantages of a Closed-Loop Feedback System
• Increased Accuracy
 Increased ability to reproduce output with varied input.
• Reduced Sensitivity to Disturbance
 By self correcting it minimizes effects of system changes.
• Smoothing and Filtering
 System induced noise and distortion are reduced.
• Increased Bandwidth
 Produces satisfactory response to increased range of
input changes.
In general, the control system is more
complex….
Designing
control systems
is complex
Humanoid robot
can have more than
43 variables to
control
… simplified stages
of control system
design….
Major Types of Feedback Used
• Position Feedback
 Used when the output is a linear distance or
angular measurement.
• Rate & Acceleration Feedback
 Feeds back rate of motion or rate of change of
motion (acceleration)
 Motion smoothing
 Uses a electrical/mechanical device called an
accelerometer
Target
Tracking
In unstable system the periodic
component would not disappear
Target Tracking Parameters
•
•
•
•
Azimuth
Elevation
Range
Relative Target Velocity
 Target’s motion with respect to the
platform’s motion
Five Basic Functions of AngleTracking Servo Systems
• Sense position error (magnitude and
direction)
• Provide position feedback
• Provide velocity feedback
• Provide data smoothing / stabilization
• Provide a power-driving device
Uses of Angle-Tracking Servo
Systems
• Monotrack fire control radars
• Homing missiles
• Acoustic homing torpedoes
• Aviation fire control tracking
systems
Motion
Control
System
1. Scope of Study
2. Servo System
3. Mechanical
Transmission
4. Applications
Motion Control System
• The primary purpose of the
servo system is to control the
motion of the load
Motion
Requirements
Servo
System
Mechanical
transmission
Motion Control System - Principles
• The digital ac servo system is
typically available with three
modes of operation:
– Torque Control Mode
– Velocity Control Mode
• In other words, in
order to control the
position the torque and
velocity should be
controlled.
– Position Control Mode
Motion
Requirements
Servo
System
Mechanical
Transmission
Motion Control System Example
2. Speed
Regulator
1. Position
Regulator
3. AC Motor
AC supply
Electronic
commutator
Desired
output
Position feedback
Speed feedback
The ac servo system consists of
five major components.
5. Position
Sensor
4. Power
Converter
Motion Control System
• Most applications are more complicated than
directly driving load.
– Common mechanical transmissions include :
•
•
•
•
•
timing belts,
gears,
conveyors,
leadscrews, and
rack & pinion mechanism.
– Especially, the timing belt and gearbox can be utilized
as a speed reducer, and the other are to be used as
translators.
Motion Control System with linear motion
Change to linear motion…...
• For instance, if the application requires linear motion of the
load:
– a leadscrew,
– rack & pinion, or
– conveyor
is used to translate the motor’s rotary motion into linear motion.
Load
Tacle
Motor
Coefficient of friction
Optional
Timing Belt or
Gear Reducer
Ball Nut
Ball Screw
Linear Servo
Systems
Application of linear servo
system: box packing
Troubles in
Control
Systems
Actuator Hysteresis
Mechanical Hysteresis
Mechanical Hysteresis
- backlash
Friction
Electronic Hysteresis
Sony AIBO
Robot
Joint Angle Limits
Intelligent Complete Robot
Perception
Cognition
Sensors
Action
Actuators
External World
What is good about robots like AIBO?
• These concepts make up the low level
functionality of the AIBO
• Implemented once and used repeatedly
• For more information about PID Control
and Forward & Inverse Kinematics take
Matt Mason’s Robotic Manipulation course
AIBO Actuators
• 18 degrees of freedom with a continuously
controllable range of motion
–
–
–
–
3 DOF in each leg (12 total)
3 DOF in the head
2 DOF in the tail
1 DOF in the jaw
• Each joint is controlled by specifying to a desired joint
angle to OVirtualRobotComm.
• 2 binary motors for the ears
• A speaker for general sound production
Motor Control
• Each message to OVirtualRobotComm contains
a set of target angles for the joints
– Each target is used for a PID controller (part of the
OS) that controls each motor
– Each target angle is used for one 8ms motor frame
• Each message contains at least 4 motor frames
(32ms)
The Motion Interface
Dynamic Walking Motion
Static Frame-Based Motion
Walk Parameters
Motion Frames
Walk Engine
Frame Interpolator
Frame-Based Motion
• Each motion is described by a series of
“frames” which specify the position of the
robot, and a time to interpolate between
frames
• Movement between frames is calculated
through linear interpolation of each joint
Kicking
• A series of set positions for the robot
• Linear interpolation between the frames
– Kinematics and interpolation provided by
CMWalkEngine
• Set robot in desired positions and query the
values of the joints
Use of Kicks in Behaviors
• Modeling effects of kicking motions
– Ball vision analysis
– Ball trajectory angle analysis
– Kick strength analysis
• Kick selection for behaviors
– Selection algorithm
– Performance comparison
Kick Selection
• Incorporate the kick models into the selection
algorithm
– The robot knows its position on the field relative to the
goal and the desired ball trajectory
– The robot selects appropriate kick by referencing the
kick model
– If no kick fits desired criteria, robot selects closest
matching kick and turns/dribbles ball to appropriate
position
Frame-Based Motion
Frame-Based Motion
• Each motion is described by a series of
“frames” which specify the position of the
robot, and a time to interpolate between
frames
• Movement between frames is calculated
through linear interpolation of each joint
Examples: Valid Motion Frames
BodyPos(b,98,RAD(16));
HeadAng(b, 0.5, 1.5, 0.0);
LegPos(b,0, 123, 85, 0);
LegPos(b,1, 123,-85, 0);
LegAng(b,2, 0.1, 0.0, 0.2);
LegAng(b,3, 0.1, 0.0, 0.2);
m[n].body = b;
m[n].time = 100;
n++;
LegAng(b,0, 0.0, 1.5, 0.0);
LegAng(b,1, 0.0, 1.5, 0.0);
LegAng(b,2, 0.1, 0.0, 0.2);
LegAng(b,3, 0.1, 0.0, 0.2);
m[n].body = b;
m[n].time = 100;
n++;
BodyPos(b,98,RAD(16));
HeadAng(b, 0.5, 1.5, 0.0);
MouthAng(b,-.7);
LegPos(b,0, 123, 85,0);
LegPos(b,1, 123,-85,0);
LegPos(b,2, -80 , 75,0);
LegPos(b,3, -80 ,-75,0);
m[n].body = b;
m[n].time = 100;
n++;
m[n].body = b;
m[n].time = 100;
n++;
Defining a Frame
• The position of the robot in each frame can
be described using any of the following:
– Position of the legs - in terms of angles of each
joint or position of the foot in motion coordinates
– Angle of the head (tilt, pan, roll)
– Body height and angle
struct BodyState{
BodyPosition pos;
– Angle of the mouth
LegState leg[4];
HeadState head;
MouthState mouth;
};
Questions and
Problems to
Solve
What did we learn?
Problem 1
• Feedback control is a fundament of robot control
• Various kits (Lego Dacta Control Lab) have several
demonstrations and project to explain the principles of
feedback:
– Line following
– Speed control
– Temperature control (fan, lamp, sensor)
• Find on internet some of these kits and explanations of
projects for high school.
What did we learn?
Problem 2
• Control of Many DOF robots is tough
• In addition to classical and modern control theory we use:
–
–
–
–
fuzzy control
genetic algorithms
neural control
bio-mimetic systems
• Review your control knowledge (for next quarter), but remember
that in this class all knowledge is through programming.
• Describe a simple robot arm which uses fuzzy logic and a motor.
• Describe a mobile robot that uses a genetic algorithm and a motor.
How FGA is used in relation to a motor?
Your task
Problem 3
• Learn about the particular servo that you plan to use. If the
servo was not suggested by the professor, learn about servos
that are available, calculate your project requirements for a
servo and pick one. The more servos we order, the cheaper
the price of one.
• If you do not want to use one of standard servos, your
choices are:
– build your own servo from a DC motor. This is a big project by
itself and you must have clear reasons to do so
– Use stepper motor. Remember that they are slow and weak, why
you want to use them? You must be sure of your reasons
Problem 4
Your task
• Use hydraulic control. Why? You need to purchase or build
your own actuator. Think about redesigning our horse leg
with better syringes and oil instead of water. How can you
connect the syringe to a stepper motor?
Problem 5
Use pneumatic control. Read first the documentation of
pneumatic hand or old Electric Horse. Talk to designers.
– Find pistons in Mondo-Tronics or other robot store. They are good.
Problem 6
• Use Nintinol or other similar actutors. They are good for face muscles
or similar small and weak movements.
– Can they be used for a hexapod? I doubt, but try to convince me
– Before you do this, read the two-volume book of Conrad and Mills
Formulas & Units useful to solve
practical problems with motors and
gears
• Unit conversions of interest
–
–
–
–
–
1lbs = 4.45 N
1 inch = 0.0254 meters
1 in-lbs = 0.11 N-m
1 RPM = 60 Rev / Hour = 0.105 Rad / Sec
1 mile = 5280 X 12 inches = 63,000 inches
• Power = Force (N) X Velocity (m/s)
• Power = Torque (N-m) X Angular Velocity (Rad/Sec)
• Electrical Power = Voltage X Current
Problems with Motor Characteristics
Problem 7
• Torque v Speed Curves
–
–
–
–
Stall Torque (T0)
Stall Current (A0)
Free Speed (Wf)
Free Current (Af)
1. Find these data for the motors
that you use.
2. Calculate the torque of your
robot arm or mobile robot to
solve problems that you want.
3. Draw the Torque vs Speed
Curve for your motor and
check if this is what you
expect.
Stall Current
T0
K (slope)
A0
Af
Speed
Wf
Free Current
Slope-Intercept (Y=mX + b)
•
•
•
•
Y=Motor Torque
m=K (discuss later)
X=Motor Speed
b=Stall Torque (T0)
T0
K (slope)
A0
Af
Speed
Wf
What is K? … It is the slope of the line.
Slope = change in Y / change in X = (0 - T0)/(Wf-0) = -T0/Wf
K = Slope = -T0/Wf
How to calculate slope when the characteristic is not linear?
(Y=mX + b) Continued ...
•
•
•
•
Y=Motor Torque
m=K = -T0/Wf
X=Motor Speed
b=Stall Torque = T0
T0 (b)
K (-T0/Wf)
A0
Af
Speed
Equation for a motor:
Torque = (-T0/Wf) * Speed + T0
How to calculate torque in any point of the
characteristic curve?
Wf
Current (Amps) and FIRST
• What are cutoff Amps?
– Max useable amps
– Limited by breakers
– Need to make assumptions
T0
A0
Cutoff
Amps
Af
Speed
Can our Motors operate above 30 amps?
Wf
- Absolutely, but not continuous.
When designing, you want to be able to perform continuously;
so finding motor info at 30 amps could prove to be useful.
Torque at Amp Limit
• T30 = Torque at 30 Amps
• W30 = Speed at 30 Amps
Current Equation:
T0
A0
Cutoff
Amps
Current = (Af-A0)/Wf * Speed + A0
Af
Motor Equation:
Torque = (-T0/Wf) * Speed + T0
S @ 30A (W30) = (30 - A0) * Wf / (Af-A0)
T @ 30A (T30) = (-T0/Wf) * W30 + T0
Speed
Wf
Power - Max vs. 30 Amps
Power = Torque * Speed
Must give up torque for speed
Power
T0
Max Power occurs when:
T = T0/2 & W=Wf/2
What if max power occurs at
a current higher than 30A?
A0
Af
Speed
Wf
Paul’s Tip #1: Design drive motor max power for 30A!
Power is Absolute - It determines the Torque - Speed tradeoff!
Motor Comparisons
Let’s Look at Some FIRST Motors
1. Chiaphua Motor
2. Drill Motor
3. Johnson Electric Fisher-Price Motor
We will compare T0, Wf, A0, Af, T30, W30, max
power (Pmax), amps @ max power (Apmax), and
power at 30 amps (P30).
We will be using Dr. Joe’s motor spreadsheet updated
to handle the new motors.
Motor Comparisons
T0
Wf
A0
Af
Pmax
T30
W30
P30
N-m
RPM
Amps
Amps
Watts
N-m
RPM
Watts
Chiaphua
2.2
5,500
107
2.3
321
0.58
4045
245.7
Johnson F-P
0.51
20,000
109
1.84
273
0.14
15000
219.9
Bosch Drill
0.65
20,000
117
2.5
340
0.15
15333
240.9
Motor
We will be using Dr. Joe’s motor spreadsheet updated
to handle the new motors.
Motor Equations:
1. Fisher-Price: T = (-0.51/20,000) * W + 0.51
2. Bosch Drill:
T = (-0.65/20,000) * W + 0.65
3. Chiaphua:
T = (-2.2/5,500) * W + 2.2
Combining Motors
Using multiple motors is common for drive trains. We
will look at matching the big 3 motors.
I try to match at free speed, but you can match at any
speed you like!!
FP and drill will match 1:1
Wf FP(drill) / Wf Chiaphua = 20000/5500 = 40/11
Gear ratio to match Chip & FP(drill) is 40/11.
We will use an efficiency of 95% for the match gear.
More to come on Gear Ratio & Efficiency in the
Second Half!
Combined Motor Data
T0
Wf
Pmax
T30
W30
P30
N-m
RPM
Watts
N-m
RPM
Watts
F-P & Drill
1.16
20,000
607
0.29
15,000
456
F-P & Chip
3.96
5,500
570
1.09
4,045
462
Drill & Chip
4.45
5,500
641
1.13
4,045
479
F-P, Drill, & Chip
6.21
5,500
894
1.63
4,045
690
Motor
Motor Equations:
1. F-P & Drill:
T = (-1.16/20,000) * W + 1.16
2. F-P & Chip:
T = (-3.96/5,500) * W + 3.96
3. Drill & Chip:
T = (-4.45/5,500) * W + 4.45
4. F-P, Drill, & Chip: T = (-6.21/5,500) * W + 6.21
NXT® motor internals for calculations
Center of Mass of
Lego Motors
NXT motor characteristics
• The following charts show the characteristics of the NXT motor versus applied
load.
• For the dark blue curves, the NXT was powered at 9V (voltage of alkaline
batteries), the magenta ones were obtained at 7.2V (voltage of NiMH
batteries).
• Power level is 100% for all charts.
•
•
•
•
This curve shows that the maximum mechanical power is obtained at a torque load of about
15 N.cm.
If you compare to the curves obtained for the RCX with 71427 motor, you see that the
available mechanical power is much higher, almost 4 times!
Even powered with 7.2V NiMH batteries, the NXT can deliver more power than a RCX
output with 2 paralleled motors and 9V supply.
This comes with a price of course, the current drained at that power level is much higher you better have good batteries...
• The current vs. torque shows a linear increase with the
load.
• Because of power limitations in NXT driver, and
thermistor trip current in NXT motor, I suggest that
you don't exceed a 15 N.cm torque for extended time
periods.
• Higher loads (thus current drains) are possible for
short periods, but the protections will soon reduce
current and available power
Sources
Manuela Veloso
Paul E. Rybski