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Week 6 · Experiment: Fit and inspect residuals

Session 3 of 4 · Wheel encoders · Phase 2

Plan about 15 minutes for explanation, 30 minutes for practical work and 10–15 minutes for documentation. A longer build may continue into the next session: stop safely, commit the current state and record the next check. Desktop simulations count as software evidence; label them clearly and record physical validation separately.

Engineering challenge

How can you turn encoder counts into distance without assuming the wrong gearbox or counting convention? This session focuses on fit and inspect residuals.

Before you start

The previous week’s recorded baseline and Week 5, Improve. For later sessions this week, retain the preceding session’s files and predictions.

Equipment: Desktop Python, editor, paper and ruler; for physical work, the configured 3pi+ 2040, clear floor mat and hardware checklist. Week 3 additionally uses the separate low-voltage LED circuit described in its procedure.

For any motion, verify the stop button, short time limit and clear floor area first. Keep the wheels raised for a new device program until its commands and stop behaviour are checked. A hazard or uncertain input is a reason to stop and document, not to force the trial to finish.

Theory and mathematics

Fit and inspect residuals

For repeated pairs (N,d), a through-origin least-squares scale is k = Σ(Nd)/Σ(N²). It gives greater influence to larger count spans and assumes distance error dominates count error and zero offsets were removed. A residual is measured d minus predicted kN. Plot residuals against N; a trend suggests a missing offset, slip or changing conditions. Calibration on the same data always looks more flattering than a prediction on new data. Use some trials for fitting and hold others back.

Worked example — illustrative values

If a marked wheel gives 900 counts per turn and circumference is measured as 0.100 m, k ≈ 0.100/900 = 0.000111 m/count. A 1800-count interval predicts 0.200 m. These are illustrative numbers; your variant must be measured.

Write the calculation in your notebook before running code. State which values you measured, which you assumed and which the program calculates. A correct numerical calculation cannot rescue an incorrect physical assumption.

Run and explain the model

The following is desktop Python, not a ready-to-run motor program. Download this week’s example, save it in your student repository and run python3 code/w06.py from the repository root. The same small model is reused across the week so you can learn it, build with it, test it and revise it.

# Desktop Python teaching example. Numerical inputs are illustrative.
pairs = [(900, 0.100), (1800, 0.201), (2700, 0.298)]  # fictional
scale = sum(n * d for n, d in pairs) / sum(n * n for n, d in pairs)
for n, d in pairs:
    print(n, "predicted_m", scale * n, "residual_m", d - scale * n)

Use your own recorded data or named test fixtures instead of the illustrative inputs. Save expected and actual values side by side. If an exception appears, read its final line, identify the input or assumption that caused it and make the smallest explained correction. Do not delete validation merely to obtain output.

Understanding the model and its limits

A through-origin least-squares fit chooses the scale that minimizes squared distance residuals when zero count change should mean zero travel. Each count-distance product contributes to the numerator, and squared counts to the denominator. At least one nonzero count is required. The printed residual is measured distance minus the prediction, retaining its sign. A consistent positive residual can reveal an underestimated scale; alternating large residuals can reveal poor repeatability or a violated model. Do not assess accuracy solely on the three fitting pairs. Predict a withheld distance and compare it with an independent ruler measurement.

Practical instructions

  1. Collect three additional count/distance pairs inside the existing safe lane.
  2. Fit the scale using only the first three trials; reserve the new trials for validation.
  3. Plot measured versus predicted distance and a separate residual plot.
  4. Flag slip or counter problems in notes rather than deleting their rows.

Experiment

Fit on three and predict three unseen trials; calculate residuals and test for a pattern versus count span.

Before testing, record your prediction, changed factor, measured response, fixed conditions and stopping rule. Save every attempted run, including failures, with a condition and source version. If hardware is unavailable, use an explicitly labelled synthetic/replay dataset and list the physical question it cannot answer. Do not invent completed trials.

Deliverable

Separate fit/validation data and residual plots; explain why counts cannot directly detect all slip.

Save notebook/w06-s3.md, the relevant code revision, raw CSV or test-case records, and one labelled diagram/plot/table. Link the files relatively from your notebook. Use the entry template and report guide.

Completion criteria

A documented failed prediction can meet the learning criteria. A missing physical trial must remain marked untested; software success alone does not validate the robot.

Reading and video

Reflection and next step

Which assumption most affected your result? Point to one observation that supports your explanation and one alternative explanation the evidence has not ruled out. Write a specific next test with a changed factor and measurable outcome, then proceed through the week’s Learn → Build → Experiment → Improve cycle.

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