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Week 4 · Improve: A useful open-loop model

Session 4 of 4 · Motors and motion · Phase 1

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 much can a timed motor command tell you about actual motion? This session focuses on a useful open-loop model.

Before you start

The previous week’s recorded baseline and Week 3, 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

A useful open-loop model

A simple local model is speed ≈ a × command + b within a tested range. It is not a universal motor law. Fit on part of the data and predict a new setting; that prediction checks whether the model generalizes. A left/right trim can reduce drift on one surface while failing elsewhere. Keep the untrimmed baseline so you can see the tradeoff. Longer pulses may improve timing resolution but need more space; do not increase duration just to get cleaner data if your lane cannot contain the run.

Worked example — illustrative values

For illustrative 0.5 s trials at command 300 and 600 travelling 0.04 and 0.10 m, speeds are 0.08 and 0.20 m/s. The local slope is (0.20 − 0.08)/(600 − 300) = 0.0004 m/s per command unit. It predicts 0.14 m/s at 450. These are fictional values, not a safe command recommendation.

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/w04.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.
command = [300, 600]
speed_m_s = [0.08, 0.20]  # fictional
slope = (speed_m_s[1] - speed_m_s[0]) / (command[1] - command[0])
intercept = speed_m_s[0] - slope * command[0]
print("predicted_m_s", slope * 450 + intercept)

Compare the unchanged baseline and your proposed change on the same inputs. Keep the original files so another reader can reproduce the comparison. 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

The two-point slope is rise in measured speed divided by rise in command: its units are m/s per command unit. The intercept makes the straight line pass through the first point. With the illustrative points the model predicts 0.14 m/s at command 450. This is interpolation between measured settings. Extrapolating to zero or a very large command is unjustified because friction creates a dead zone and the motor/battery imposes limits. Plot raw points beside the fitted segment. A two-point fit has no spare evidence to assess its own quality, so reserve another setting for validation.

Practical instructions

  1. Fit a local line using two settings and predict a third without fitting to it.
  2. Compare prediction with the held-out measurements.
  3. If drift is important, try one small wheel trim within the established limit and repeat three trials.
  4. Retain the model range, trim decision and untrimmed data in a baseline report.

Experiment

Test one held-out command and one trimmed/untrimmed comparison. Judge against a predeclared 20% speed-prediction tolerance, explaining if it fails.

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

A held-out model check and evidence-based trim decision; state the model validity range.

Save notebook/w04-s4.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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