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Line Tracker Threshold

Where to put the threshold on a reflectance sensor, from readings you took on the real field, and how often it will get the call wrong at that setting.

Inputs

Take readings with the sensor at its real mounted height, on the real field, under the lighting you will compete in. Get several on the line and several off it, moving the robot between each so you catch the variation rather than the same spot ten times.

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Results

Use this threshold

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On the line, average

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Off the line, average

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Separation

—SD

Gap between the two, in units of their own scatter.

Expected wrong calls

—%

At the threshold above, from the spread you measured.

Is this sensor good enough?

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Readings used

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Separation, against what a threshold needs—

Filling the bar means four standard deviations of separation, which tolerates a lighting change. Under half of it, no threshold works.

Move the threshold

Move the thresholdon the lineoff the line
50% across

Your readings, with the bell curve each group's average and spread describe. The solid line is your threshold: everything on one side is called on the line, everything on the other side off it. The shaded tails are the readings that would be called wrong. Slide the threshold and watch one tail shrink as the other grows. The dashed line is where the page suggests, which keeps both tails small together.

How this is calculated

A line tracker returns a number, not a yes or no. Turning it into a yes or no needs a threshold, and where you put that threshold decides how often the sensor is wrong. Picking it by eye from two readings is how a line follower works in the pits and fails on the field.

threshold = (on × spread_off + off × spread_on) ÷ (spread_on + spread_off) separation = |on − off| ÷ pooled spread wrong calls = Φ((threshold − on) ÷ spread_on) + Φ((off − threshold) ÷ spread_off)

The threshold is not just halfway between the two averages. It is weighted by how much each group scatters, so it sits closer to whichever side is tighter. That is the placement that gets the fewest calls wrong when the two groups spread by different amounts, which they usually do: field tiles vary more than tape does.

Separation is the number that decides whether this works

The gap between the averages means nothing on its own. Divided by the scatter, it says how distinguishable the two really are. Below about two standard deviations the distributions overlap enough that no threshold saves you, and the answer is to fix the sensing rather than tune the number: lower the sensor, shield it from ambient light, or use a different surface.

Take the readings where it has to work

Reflectance sensors are sensitive to height, to ambient light, and to how dusty the tile is. A threshold found on a practice field at home under fluorescent light is not the threshold for a venue with sunlight through the roof. If you can only calibrate once, calibrate at the event.

Better still, take the readings again in the pits before elimination matches. It costs two minutes and it is the single most common reason an autonomous that worked in qualifications stops working later in the day.

Sources & assumptions

Every number here is yours. No sensor reading, threshold or tile reflectance is shipped with this page, because those depend on the sensor, the mounting height, the surface and the lighting in the room.

The threshold placement and the error estimate are derived, with the formulas above. The error estimate treats each group as normally distributed, which is a reasonable approximation for sensor noise and a poor one if something systematic is going on, such as a shadow falling across half the field.

Every source the site uses, and when it was checked

Save this run, and compare

Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.

Make a notebook page

Turns this calculation into a dated engineering notebook page: the setup, data, results, figures, working and sources, numbered and cited. You add the goal, the decision and the reflection in your own words, plus photos and sketches. Print it, paste it into Google Docs, or download a Word file or slides.

My notebook

Notebook page

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    This page

    Our own layouts

    A layout remembers how a page is set up: its type, its system, which parts print and which of your tables it uses. It never remembers a word, a number or a photo.

    Your team kept on this device
    Add someone to the team list
    Your words never written for you

    These are the parts a judge or teacher reads to see your thinking, so the page leaves them to you. Leave a box empty to get lined space for writing by hand. Start lines with "- " for a list. The notes under each box only count and point things out; they never change what you wrote.

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    The word counts can be measured against a target your team sets on My notebook. The reading level is Flesch-Kincaid grade level = 0.39 × (words ÷ sentences) + 11.8 × (syllables ÷ words) − 15.59. Syllables are counted by vowel groups, so the grade is an estimate of the school year the writing reads at. It says nothing about whether the writing is any good.

    One part at a time, with a clock. At the end of practice, while you remember it.
    How you tested your details

    Fill in what applies. These print as a small table under the method.

    Before and after

    Compare this calculation with a run you saved earlier on this tool (under “Saved runs”). The page shows what changed and by how much.

    A line through the data from your recorded table

    Pick two measured columns from the same table. The page plots them and draws the least-squares line, only across the range you measured.

    Robot log a CSV from the robot's SD card

    Load a CSV your robot saved. Pick the time column and up to three columns to plot, and type their units. Only those columns go on the page; the file stays on this device.

    Two versions' trials your data, compared

    Pick a column of recorded trials for each version, from this page or another saved page. The page shows both averages and a 95% range for the difference. The numbers are copied in when you pick them, so later changes to the other page don't change this one.

    Options compared your scores

    Score each option 1 to 5 on each criterion, and weight each criterion 1 to 5 by how much it matters. The page only multiplies and adds.

    Photos and sketches stay on this device

    Up to 4. Paste a screenshot with Ctrl+V, drop pictures here, or pick them. Photos are shrunk before they’re kept, and an unsaved page keeps them in its draft. Use Mark up to draw arrows, labels, dimensions and numbered callouts on a photo. Mark one photo Before and one After to print them side by side.

      Test plan written before testing

      Write this before you test: the question, what you expect with a number, and what result would make you drop the idea.

        Build steps our build

        One row per step, in order, so someone could rebuild from this page.

          Parts used our parts list

          Lengths in holes are also shown in inches between the end holes. Weights are only added up where you type them.

            Plan the cuts: packs every piece of one part (sizes in holes, or inches on the hole grid) onto whole sticks of the stock length you type.

            Ways it could fail our scores

            List the ways this could fail. Score how likely (1 to 5) and how bad (1 to 5); the page multiplies them and puts the biggest risks first.

              Designed against built our measurements

              What the CAD or the plan said, and what you measured on the robot. The tolerance is yours.

                Changes from the last version our changes

                What changed since the last version, why, and which result it was meant to move.

                  That page’s settings, results and first photo are copied in and set beside this page’s. The result each change should move is looked up on both pages.

                  Tasks our plan

                  What needs doing, who, and by when. Open tasks carry to the next meeting page until someone ticks them done.

                    The pages behind this idea our evidence

                    The pages in this notebook that show the idea being tried, measured or changed. A judge reading the claim can turn straight to them.

                      Time spent our hours

                      Who worked on this and for how long.

                        Session log what we did, as we did it

                        Notes taken during a session. The time comes from the clock when the note was taken; every word is yours.

                          Size limit does it fit?

                          Type the starting size limit from the current game manual, and the robot's size as designed or measured, in inches. The site doesn't store the limit, because it changes with the game.

                          What broke from your breakage log

                          The breakage log is on My notebook. Copy it onto this page as a table, as it stands now; later entries don't change this page.

                          CAD model which version this page is about

                          Paste a link to the model (Onshape, Fusion or anything else) and the name you use for this version. For Onshape, the page reads from the link whether it points at a saved version or a workspace that keeps changing. Nothing is fetched.

                          Your code
                          Comments notes for the team, not the page

                          A teammate or coach can leave a note here. Comments stay beside the page, travel with it in exports and links, and don't print unless you tick them under Include.

                            Sources you used besides this tool

                            Videos, other teams, manuals, people. The tool’s own sources are cited for you.

                              Sign-off
                              Include

                              Press a ? to see what an option is for, or read them all on How the notebook tools work.

                              What “The calculator’s figures” is for

                              The calculator’s own diagrams and charts, numbered as figures and drawn from your numbers. Judges look for pictures that explain a design.

                              What “How it was calculated” is for

                              The formulas and steps the calculator used, so a reader can check the arithmetic for themselves.

                              What “The calculator’s warnings” is for

                              Things the calculator flagged, such as a motor near stall. They’re quoted and credited to the calculator, so they never read as your conclusion.

                              What “The calculator’s notes” is for

                              The calculator’s plain-language notes on the result. Off at first, because they read like conclusions, and the conclusions on a page should be yours.

                              What “Lined space” is for

                              Ruled lines under any part you haven’t written yet, so a printed page can be finished by hand.

                              What “Writing space as” is for

                              The blank space for handwriting as ruled lines, a dot grid or quarter-inch squares. Dots and squares suit sketches and hand-drawn graphs.

                              What “A summary under recorded data” is for

                              The number of readings, the average, the spread, the lowest and the highest under each table you recorded, worked out from your numbers. It shows every run counted, not just the best one.

                              What “Words used” is for

                              A small box with the site’s one-line definitions of glossary terms the calculator used, for readers who don’t know them. It never looks at your own writing.

                              What “Robot at the time” is for

                              The Robot Profile as it was when the page was first saved, so weeks later you can tell which version of the robot a test was run on.

                              What “Long tables in full” is for

                              Long calculated tables printed complete on an extra page, instead of every few rows on the page itself.

                              What “Fit on one sheet” is for

                              Smaller type and shorter tables, aiming for one printed sheet. Use it when every entry in your notebook should be a single page.

                              What “Wider left margin” is for

                              A wider left edge, so the page can be hole-punched or bound without losing any words.

                              What “Larger type, for reading aloud” is for

                              Bigger print with more room between lines, for the team member who reads the page to a judge. It overrides Fit on one sheet.

                              What “Our rubric scores” is for

                              Your own scores against the rubric, on a sheet of their own, for checking a page before a judge does.

                              What “When this page was first saved” is for

                              The day the page was first saved, printed beside its date. It shows the notebook was kept while the work happened.

                              What “Teammates’ comments” is for

                              Prints the comments teammates left on this page at the end, marked as not part of the page. Off at first, because comments are notes for the team, not for judges.

                              What “Show every table and block” is for

                              Shows every table and block in the editor, not only the ones this type of page usually uses. It changes the editor, not the printed page.

                              Rubric check

                                This checks what is on the page, not how good it is. Clear, specific writing in your own words is what earns the top marks.

                                Preview, letter size

                                Write it now

                                Where this goes next

                                Explore further on the full map

                                Where the answers on this page can be used, and which tools could have given you the numbers it asks for.

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                                Sensor Fusion Calculator

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                                Line Tracker Threshold

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                                Compare Test Versionstest whether the new cutoff really misses the line less in real runs

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