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Lesson / authored

Week 20 · Learn: A waypoint is a target, not a command

Session 1 of 4 · Follow waypoints · Phase 5

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 a planned position become reliable, bounded physical motion? This session focuses on a waypoint is a target, not a command.

Before you start

The previous week’s recorded baseline and Week 19, 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 waypoint is a target, not a command

For a current pose (x,y,θ) and waypoint (gx,gy), position error is dx = gx−x, dy = gy−y. Target bearing is atan2(dy,dx). Heading error must wrap to the shortest signed angle: atan2(sin(target−θ), cos(target−θ)). Ordinary subtraction near ±π can request an almost-full turn. Separate a turn phase from a short forward phase at first. Declare arrival using a distance tolerance and independently inspect the stopping position; odometry reaching a target does not prove the real robot did.

Worked example — illustrative values

For pose (0,0,170°) and a target bearing −170°, the shortest heading error is +20°, not −340°. With b = 0.10 m, v = 0.10 m/s and ω = 0.50 rad/s, vL = 0.075 m/s and vR = 0.125 m/s. These are wheel-speed targets requiring calibrated device conversion.

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/w20.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.
from math import atan2, sin, cos, hypot, radians

def waypoint_action(pose, target, tolerance_m=0.03):
    x, y, theta = pose
    dx, dy = target[0] - x, target[1] - y
    if hypot(dx, dy) <= tolerance_m:
        return "arrived", 0.0, 0.0
    error = atan2(sin(atan2(dy, dx) - theta), cos(atan2(dy, dx) - theta))
    if abs(error) > radians(8):
        return "turn", 0.0, max(-0.5, min(0.5, 2 * error))
    return "advance", min(0.1, hypot(dx, dy)), max(-0.3, min(0.3, error))

print(waypoint_action((0, 0, radians(170)), (-1, -0.1763)))
print(waypoint_action((0, 0, 0), (0.02, 0)))

Predict the example’s output by hand. Mark the inputs, units and assumptions; explain where this model could fail. 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 function first checks arrival distance, then computes a wrapped heading error. Large error selects a turn with zero forward target; a small error permits a slow advance with bounded correction. The returned values are desired centre speed and turn rate, not raw motor commands. The integration layer must apply validity/hazard priority before translating them to calibrated wheel control. Test a target behind the robot and targets across the ±π seam. An odometry arrival can disagree with measured endpoint, so retain independent truth and examine tolerance-related corner cutting on the mapped route.

Practical instructions

  1. Calculate range and bearing for three paper targets.
  2. Test angle wrapping across ±180° and draw the requested turn direction.
  3. Choose arrival/heading tolerances consistent with your measured error and map clearance.
  4. Draw the turn/advance/arrive states with hazard and timeout transitions to stop.

Experiment

Test 179° to −179°, −179° to 179° and equal headings; shortest turn errors should be +2°, −2° and 0°.

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

Correct bearing/wrapping arithmetic and a bounded controller-state design.

Save notebook/w20-s1.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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