Transcript Behavior-Based Robotics

Lecture Outline
 DC motors
 inefficiencies, operating voltage and
current, stall voltage and current and
torque
 current and work of a motor
 Gearing gear ratios
 gearing up and down
 combining gears
 Pulse width modulation
 Servo motors
Definition of Actuator
 An actuator is the actual mechanism
that enables the effector to execute
an action.
 E.g, electric motors, hydraulic or
pneumatic cylinders, pumps…
 Actuators and effectors are not the
same thing.
 Incorrectly thought of the same;
“whatever makes the robot act”
DC Motors
 The most common actuator in mobile
robotics is the direct current (DC)
motor
 Advantages: simple, cheap, various
sizes and packages.
 DC motors convert electrical into
mechanical energy
 How?
How DC Motors Work
 DC motors consist of permanent
magnets with loops of wire inside
 When current is applied, the wire
loops generate a magnetic field, which
reacts against the outside field of the
static magnets
 The interaction of the fields produces
the movement of the shaft/armature
 => Electromagnetic energy becomes
motion
Motor Inefficiency
 As any physical system, DC motors
are not perfectly efficient.
 The energy is not converted perfectly.
Some is wasted as heat generated by
friction of mechanical parts.
 Inefficiencies are minimized in welldesigned (more expensive) motors, and
their efficiency can be high.
 How high?
Level of Efficiency
 Good DC motors can be made to be
efficient in the 90th percentile.
 Cheap DC motors can be as low as
50%.
 Other types of effectors, such as
miniature electrostatic motors, may
have much lower efficiencies still.
Operating Voltage
 A motor requires a power source
within its operating voltage, i.e., the
recommended voltage range for best
efficiency of the motor.
 Lower voltages will (usually) turn the
motor, but will provide less power.
 Higher voltages are more tricky; they
increase power output at the expense
of the operating life of the motor ( the
more you rev your car engine, the sooner it will die)
Current and Work
 When constant voltage is applied, a
DC motor draws current in the amount
proportional to the work it is doing.
 E.g., if a robot is pushing against a wall, it
is drawing more current (and draining more
of its batteries) than when it is moving freely
in open space.
 The reason is the resistance to the motor
motion introduced by the wall.
Stall Current
 If the resistance is very high (i.e., the
wall won't move no matter how hard the
robot pushes against it), the motor draws
a maximum amount of power, and
stalls.
 The stall current of the motor is the
most current it can draw at its
specified voltage.
Torque at the Motor Shaft
 Within a motor's operating current
range, the more current is used, the
more torque or rotational force is
produced at the shaft.
 The strengths of the magnetic field
generated in the wire loops is directly
proportional to the applied current and
thus the produced torque at the shaft.
Stall Torque
 Besides stall current, a motor also has
its stall torque.
 Stall torque is the amount of rotational
force produced when the motor is
stalled at its operating voltage.
Power of a Motor
 The amount of power a motor
generates is the product of the shaft's
rotational velocity and its torque.
 If there is no load on the shaft, i.e., the
motor is spinning freely, then the
rotational velocity is the highest
 but the torque is 0, since nothing is
being driven by the motor.
 The output power, then, is also 0.
Free Spinning and Stalling
 In contrast, when the motor is stalled, it
is producing maximum torque, but the
rotational velocity is 0, so the output
power is 0 again.
Between free spinning and stalling, the
motor does useful work, and the
produced power has a characteristic
parabolic relationship
 A motor produces the most power in
the middle of its performance range.
Speed and Torque
 Most DC motors have unloaded
speeds in the range of 3,000 to 9,000
RPM (revolutions per minute), or 50 to 150
RPS (revolutions per second).
 This puts DC motors in the high-speed
but low-torque category (compared to
some other actuators).
 How often do you need to drive
something very light that rotates very
fast (besides a fan)?
Motors and Robots
 DC motors are best at high speed
and low torque.
 In contrast, robots need to pull loads
(i.e., move their bodies and
manipulators, all of which have
significant mass), thus requiring more
torque and less speed.
 As a result, the performance of a DC
motor typically needs to be adjusted.
 How?
Gearing
 Gears are used to alter the output
torque of a motor.
 The force generated at the edge of a
gear is equal to the ratio the torque
and the radius of the gear (T = F r), in
the line tangential to its circumference.
 This is the underlying law behind
gearing mechanisms.
Gear Radii and Force/Torque
 By combining gears with different radii,
we can manipulate the amount of
force/torque the mechanism generates.
 The relationship between the radii and
the resulting torque is well defined
 The torque generated at the output
gear is proportional to the torque on the
input gear and the ratio of the two gear's
radii.
Example of Gearing
 Suppose Gear1 with radius r1 turns
with torque t1, generating a force of
t1/r1 perpendicular to its circumference.
 If we mesh it with Gear2, with r2, which
generates t2/r2, then t1/r1 = t2/r2
 To get the torque generated by Gear2,
we get: t2 = t1 r2/r1
 If r2 > r1, we get a bigger number, if
r1 > r2, we get a smaller number.
Gearing Law for Torque
 If the output gear is larger than the
input gear, the torque increases.
 If the output gear is smaller than the
input gear, the torque decreases.
 => Gearing up increases torque
 => Gearing down decreases torque
The Effect on Speed
 When gears are combined, there is
also an effect on the output speed.
 To measure speed we are interested in
the circumference of the gear, C= 2 pi r.
 If the circumference of Gear1 is twice
that of Gear2, then Gear2 must turn
twice for each full rotation of Gear1.
 => Gear2 must turn twice as fast to
keep up with Gear1.
Gearing Law for Speed
 If the output gear is larger than the
input gear, the speed decreases.
 If the output gear is smaller than the
input gear, the speed increases.
 => Gearing up decreases speed
 => Gearing down increases speed
Exchanging Speed for
Torque
 When a small gear drives a large one,
torque is increased and speed is
decreased. Analogously, when a large
gear drives a small one, torque is
decreased and speed is increased.
 Gears are used in DC motors (which
are fast and have low torque) to trade
off extra speed for additional torque.
 How?
Gear Teeth
The speed/torque tradeoff is achieved
through the numbers of gear teeth
 Gear teeth must mesh well.
 Any looseness produces backlash, the
ability for a mechanism to move back
& forth within the teeth, without turning
the whole gear.
 Reducing backlash requires tight
meshing between the gear teeth,
which, in turn, increases friction.
Gear Reduction Example
 To achieve “three-to-one” gear
reduction (3:1), we combine a small
gear on the input with one that has 3
times as many teeth on the output
 E.g., a small gear can have 8 teeth, and
the large one 24 teeth
 => We have slowed down the large
gear by 3 and have tripled its torque.
Gears in Series
 Gears can be organized in series, in
order to multiply their effect.
Gears in series can save space
 Multiplying gear reduction is the
underlying mechanism that makes DC
motors useful and ubiquitous.
Control of Motors
 Motors require more battery power
(i.e., more current) than electronics
 E.g., 5 milliamps for the 68HC11
processor v. 100 milliamps - 1 amp for
a small DC motor).
 Typically, specialized circuitry is
required
 H-bridges and pulse-width modulation
are used
Servo Motors
 It is sometimes necessary to move a
motor to a specific position.
 DC motors are not built for this
purpose, but servo motors are.
 Servo motors are adapted DC motors,
with the following additions:
 some gear reduction
 a position sensor for the motor shaft
 an electronic circuit that controls the
motor's operation
Uses of Servo Motors
 What is used to sense shaft position?
 Servos are used to adjust steering in
RC (radio-controlled) cars and wing
position in RC airplanes.
 The job of a servo motor is to position
the motor shaft; most have their
movement reduced to 180 degrees.
 Why? This is sufficient for a full range
of positions.
Control of Servo Motors
 The motor is driven with a waveform
that specifies the desired angular
position of the shaft within that range.
 The waveform is given as a series of
pulses, within a pulse-width modulated
signal.
 Pulse-width modulation is using the
width (i.e., length) of the pulse to specify
the control value for the motor.
Pulse-Width Modulation
 The exact width/length of the pulse is
critical, and cannot be sloppy.
 Otherwise the motor can jitter or go
beyond its mechanical limit and break.
 In contrast, the duration between the
pulses is not critical at all.
 It should be consistent, but there can
be noise on the order of milliseconds
without any problems for the motor.
 Why?
Noise in Modulation
 When no pulse arrives, the motor
does not move, it simply stops.
 As long as the pulse gives the motor
sufficient time to turn to the proper
position, additional time does not hurt
it.
 On the other hand, if the duration of
the pulse is incorrect, the motor turns
by an incorrect amount, so it reaches
the wrong position.