Section 47.4: Coverage and inspection; multi-drone coordination

"Covering an area is mowing a lawn from the air: the hard part is missing nothing and counting it honestly."

A Careful Control Loop

This section develops coverage, inspection, and multi-drone coordination as a concrete embodied AI skill rather than a label. The core contract is: observe coverage grid, camera footprint, communication state, and battery reserve, allocate viewpoints and paths across agents, and judge the result with coverage completeness and duplicate-inspection rate.

For Coverage and inspection; multi-drone coordination, check the earlier frame, control, and model chapters against the exact interface used here: state variables, timing budget, action limits, and evaluation panel.

Figure 47.4.1 turns coverage and fleet coordination into inspectable artifacts: area decomposition, assignment policy, communication state, deconfliction rule, battery budget, and coverage certificate.

Theory

Coverage planning asks for a path that sweeps a camera footprint over every point of a target region. The classic exact method is boustrophedon decomposition (the word means "as the ox plows", back and forth). The free region is split into cells with no obstacles inside, and each cell is covered by parallel sweep lines, called boustrophedon, or lawn-mower, passes, spaced by the sensor footprint width $w$. The drone flies one lane to the far edge, steps over by $w$, reverses, and repeats. For a convex cell of width $W$ the number of lanes is $\lceil W / w \rceil$, and the turns happen only at the cell boundary, which keeps the path efficient.

The success criterion is the coverage fraction: the area actually seen divided by the area that should be seen,

$$\eta = \frac{\lvert \text{covered cells} \rvert}{\lvert \text{target cells} \rvert}.$$

A complete plan reaches $\eta = 1$. Lane spacing controls the trade between $\eta$ and flight time: spacing equal to the footprint gives full coverage with no overlap in the ideal case, while spacing wider than the footprint leaves uncovered stripes ($\eta < 1$) and tighter spacing wastes battery on redundant passes. Real footprints depend on altitude and camera field of view, so coverage planning and altitude planning are coupled; flying higher widens $w$ and reduces lanes but lowers ground resolution.

Worked Example

Simulate a boustrophedon sweep over a 10x10 grid and measure the coverage fraction. Lane spacing equal to one cell (every row swept) should give full coverage; doubling the spacing should leave half the area unseen. Running both makes the spacing-versus-coverage trade concrete.

# Boustrophedon (lawn-mower) coverage over a 10x10 grid.
def boustrophedon(N, lane_step):
    covered = [[False] * N for _ in range(N)]
    path = []
    for row in range(0, N, lane_step):          # one lane per swept row
        cols = range(N) if (row // lane_step) % 2 == 0 else range(N - 1, -1, -1)
        for col in cols:                        # serpentine direction per lane
            path.append((row, col))
            covered[row][col] = True
    seen = sum(cell for r in covered for cell in r)
    return path, seen / (N * N)

N = 10
path, eta = boustrophedon(N, lane_step=1)        # spacing = footprint
print(f"lanes touch every row : path length {len(path)}, coverage = {eta:.0%}")
print(f"first turns           : {path[8:13]}")

_, eta_wide = boustrophedon(N, lane_step=2)       # spacing = 2x footprint
print(f"spacing doubled       : coverage = {eta_wide:.0%}  (stripes missed)")

Expected output: a full-coverage path at unit spacing and a degraded coverage fraction when the lanes are spread out. The coverage fraction is the evidence field: report it alongside flight time, because a plan that finishes faster by widening lanes is only a win if $\eta$ still meets the inspection requirement.

Practical Recipe

1. Write the skill contract: observable variables, action interface, metric, allowed recovery actions, and stop conditions.
2. Build the smallest baseline that can fail in an interpretable way.
3. Run the maintained library version with the same inputs, scenarios, and metric code.
4. Add one perturbation aimed at the expected failure: two drones optimize local coverage and create unsafe convergence near the same structure.
5. Save one artifact containing config, seeds, logs, summary metrics, and two representative traces.

Coverage and inspection; multi-drone coordination becomes robust when the chapter separates three claims. The conceptual claim explains why the skill should work. The systems claim explains which interface changes. The evidence claim records which same-panel metric would convince a skeptical builder.

For Coverage and inspection; multi-drone coordination, keep flight physics, airspace constraint, battery state, timing, wind, and safety monitor inside the evidence artifact rather than in a post-run explanation.

When Coverage and inspection; multi-drone coordination fails, do not collapse the whole method into one score. Assign the failure to a subsystem, rerun one perturbation that isolates the suspected cause, and keep the trace as a reusable diagnostic case.