And, Or, Not: The Jazz Drum

Comparing and combining

A sensor that reports a number cannot be used to make a decision on its own — 23 is neither true nor false. An operator turns that number into an answer by comparing it with something.

Blocks reference

<(x) > (50)>

<(x) < (50)>

<<> and <>>

<<> or <>>

Try it: which way round does it go?

Forget the symbols for a moment. A comparison is a question about position on a number line: is x to the left of the other number, or to the right? Left is smaller, right is bigger — and that is the whole of it.

Drag the orange x and the black marker, and change the comparison. The green stretch is every position of x that would make the answer true — so you can see where the answer flips before you get there. Turn not on and watch the green jump to the other side.

• < is true while x sits on the left. Slide x past the marker and it flips.
• > is the same question the other way round — so exactly one of the two is true, unless the markers are on the same spot.
• = is true for one single position out of twenty-one. Try landing on it. That is why a sensor is almost never compared with =: a reading passes straight through the exact number without ever being measured there.
• not flips the answer, whatever it was. not (x < 4) covers everything x < 4 does not — including landing exactly on 4.

Try it: which numbers make it true?

The lab above asks one question at a time: is this x true? A robot never has just one x, though — a sensor reading slides up and down all the time, so what really matters is which stretch of the line makes the condition true. This one draws the whole answer at once.

Drag the circle to move the number you are comparing against, and change the comparison. Everything shaded green is a value of x that would make it true.

Watch the circle, because it carries the part everyone gets wrong:

• Hollow ○ — the boundary is not included. x < 0.2 shades everything left of 0.2 but leaves 0.2 itself out, because 0.2 is not less than 0.2.
• Filled ● — the boundary is included. Choose = and nothing is shaded at all: one single number qualifies.

Now turn not on with x > 2 selected and watch two things happen together. The shading jumps to the other side, and the circle fills in — because “not greater than 2” means 2 or less, and 2 has to be part of it. That pairing is the whole reason a hollow circle is worth drawing.

Why a robot cares. Two conditions that look almost identical — light < 30 and not (light > 30) — differ by exactly one value, the reading of precisely 30. A robot sitting right on its threshold behaves differently under the two, and that is the sort of bug that only shows up occasionally and looks like a broken sensor.

Try it: and, or, not

These three join answers together rather than numbers. The trap is that English is looser than a program: “stop if it is close and the bumper is pressed” sounds like it covers both situations, when it covers neither on its own.

Flip the two conditions and watch the table. There are only four possible situations in total, and and and or differ on exactly two of them.

• and is true on one row out of four. It narrows — the robot acts less often, but more certainly.
• or is true on three rows out of four. It widens — the robot acts more readily.
• The two agree on the top and bottom rows and disagree in the middle. Whenever swapping one for the other seems to make no difference, you have only tried the rows where they agree.

Watch them decide

Two sensors are running below: an Ultrasonic reporting a number, and a Touch Sensor reporting true or false. Watch the comparison turn the number into an answer, and watch and and or disagree.

The comparison is doing one job: it takes a reading that is neither true nor false and, by holding it against a number you chose, produces something a decision can use. The moment the blue fill crosses the black marker is the moment the answer changes.

Choosing the threshold

The number you compare against is a design decision, not a fact. “Close” for a parking sensor might be 15 cm; for a robot arm it might be 3. Pick it by measuring what the sensor actually reads in the situation you care about, then leave a margin.

Combining two conditions

and narrows: both must hold, so the robot acts less often but more certainly — stop only if something is close and the bumper is pressed. or widens: either will do, so the robot acts more readily — stop if something is close or the bumper is pressed.

In the four situations above, and was true in one of them and or in three. That is the practical difference: swapping one for the other does not adjust a robot slightly, it changes how often it reacts at all.

Making a decision

Up to now a robot has been able to wait for a sensor. Deciding is different: the robot checks the sensor and does one thing or another depending on the answer — and then carries on either way.

Blocks reference

if <> then
end

if <> then
else
end

Deciding again and again

A decision made once, at the start, is almost never what you want. Here are two robots with the identical if-else, testing the identical sensor against the identical number — one inside a loop and one not.

Nothing is wrong with the right-hand program’s decision. It asked the question, got a truthful answer, and acted on it correctly. It simply never asked again, and the world moved on. Decisions belong inside a loop, so the robot keeps re-deciding as things change.

when program starts :: events hat
forever
  if <([4 v] distance in [cm v] :: sensors) < (15)> then
    stop moving :: movement
  else
    start moving [straight: 0] :: movement
  end
end

Four shapes, and how to choose

Once there is more than one question, decisions can be arranged in four ways. They look nearly identical stacked up in the editor, which is exactly why they get muddled — the thing that differs is not what the blocks say, it is which routes through them exist.

One question sorts them almost completely:

Separate ifs — independent questions

Each if is asked no matter what the others answered, so any number of them can fire on the same pass. That is the right shape when the conditions genuinely have nothing to do with each other.

forever
  if <[3 v] is ambient light intensity [< v] (20) %? :: sensors> then
    [A v] start motor [clockwise v] :: motors
  end
  if <[4 v] is distance [< v] (15) [cm v]? :: sensors> then
    [D v] start motor [clockwise v] :: motors
  end
end

if / else — one question, two answers

Exactly one branch runs, every time. Reach for this whenever the robot must do something either way — and in preference to two ifs testing opposite conditions, which is the same idea written twice and can drift apart.

Nested if — a follow-up question

Putting one if inside another means the inner question is only ever asked when the outer one is true. Use it when the second question is meaningless otherwise: there is no point asking which side an obstacle is on when there is no obstacle.

if <[4 v] is distance [< v] (15) [cm v]? :: sensors> then
  if <([2 v] angle :: sensors) < (0)> then
    start moving [right: 50] :: movement
  end
end

When not to nest. If you only want “both true” and nothing happens at the outer level, an and says it in one block and reads better:

if <<[4 v] is distance [< v] (15) [cm v]? :: sensors> and <([2 v] angle :: sensors) < (0)>> then
  start moving [right: 50] :: movement
end

Nesting earns its place when something happens at the outer level too, or when there is an else at each level and the two mean different things.

Chained if / else — one winner out of several

This is the shape for a list of cases where exactly one should win: colour bands, distance bands, speed ranges. EV3 Classroom has no else-if block, so you build a chain by putting the next if inside the else of the last one.

And here is why it matters, because this is the single commonest bug in this whole module. Three bands written as three separate ifs are each perfectly correct, and together they are wrong: a reading of 20 is under 30 and under 60 and under 90, so all three run and the last one to run is the one that sticks.

The rule to carry away: if the cases are meant to be exclusive, they must be made exclusive. Chaining does it by construction. Separate ifs only work if you are careful to write non-overlapping bands yourself — light < 30, 30 to 60, 60 and over — which is more to get right and easy to break later.

Why it matters

This is the point at which a machine stops following a script and starts responding. A thermostat, an automatic door, a robot vacuum — all of them are a decision inside a loop.

The Colour Sensor

The Colour Sensor looks down at a surface and can answer three quite different questions: what colour is this?, how bright is this? and how light is the room? Choosing the wrong one is the usual reason a line-following robot refuses to work.

front

side

Blocks reference

([3 v] color :: sensors)

([3 v] reflected light intensity :: sensors)

<[3 v] is color [red v]? :: sensors>

([3 v] ambient light intensity :: sensors)

Which colour, exactly?

The sensor does not describe a colour — it picks one from a list of eight, and that list is the whole of what it can ever say:

Anything you put under it is forced into one of those eight. There is no orange and no purple: an orange brick comes back as red or as yellow, and often as red one moment and yellow the next as the robot creeps along. Light blue and grey are the other classic pair to avoid — grey is neither black nor white, so it flips between them.

This is why colour mode is a good fit for a task you control and a bad fit for one you do not. Sorting the LEGO bricks that come in the set works, because they are made in exactly these colours. Reading a printed sheet, a coloured tile from another set, or anything pastel is asking the sensor to answer a question it does not have a word for.

Two practical points follow from how it decides. It shines its own lamp and looks at how much red, green and blue comes back, so it must be close — about half a centimetre, and no more than a centimetre. Lift it and the answer decays to 0. And because it takes those three readings before it can answer, colour mode is the slowest thing this sensor does; a robot driving quickly can pass right over a small patch without ever reporting it.

When a colour must be recognised reliably, test it. Drive the robot slowly over the real surface with color shown on the screen and watch what it actually says — including what it says at the edges between two colours, which is where the wrong answers live.

Colour, or brightness?

Both questions are asked of the same surface at the same moment. Watch the two answers travel across a strip of colours and then over the edge of a black line.

Over the patches, both read-outs are useful. Over the edge of the line they part company: the colour name has only two answers to give and jumps between them, while the number slides smoothly from 88 down to 8. Every value in that slide tells you how far onto the line the sensor is — which is information the name simply does not carry.

• Use colour when the answer really is a name — sorting red bricks from blue ones, stopping on a green square.
• Use reflected light when the answer is a matter of degree — following the edge of a black line, where the useful readings are all the greys between black and white.

A line follower built on colour names only knows “black” or “not black”, so it can only lurch. Built on reflected light it can tell how far onto the line it has drifted, which is what makes smooth following possible.

The third mode: ambient light

The first two modes both switch the sensor’s own lamp on and measure what bounces back off the surface. Ambient light intensity does the opposite: the lamp goes off, and the sensor simply reports how much light is arriving from wherever — 0 in the dark, up to 100 in bright light.

That makes it the only one of the three that is not really about the floor. A number between 0 and 100 means very little on its own, so watch the same sensor sit through five different rooms — nothing underneath it changes at any point.

Those are the shape of the scale rather than exact figures, but the shape is the useful part: a lit room is nowhere near 100, and the top of the range is reserved for a light pointed straight at the sensor. Cover it with your hand and the number drops to near zero — which is the easiest way to check the sensor is doing what you think.

Point it at the ceiling and it tells you whether the room lights are on; point it forwards and a torch will spike the reading, which is a way of signalling to a robot without touching it.

Do not reach for it as a substitute for reflected light. Room light falling on a black line and on white paper is almost the same, so ambient mode can barely tell them apart — the reason reflected light works is precisely that the sensor brings its own light and measures how much of it survives.

It is also the mode most at the mercy of the room. A reading taken by a window in the morning will not match the same spot in the afternoon, so anything built on ambient light needs measuring on the day, in the place, with the lights as they will be.

Light and height matter

Even the two lamp-on modes are affected by room lighting — a reading taken by a sunny window differs from one taken in a corner. The sensor must also sit close to the surface and at a constant height, because lifting it changes the reading even though the surface has not changed.