Section 59.9: Drone inspection planner

"The inspection route was optimal until the battery became a philosopher."

A Drone Planner Counting Watts

At waypoint 7 of a 14-point turbine spiral, a gust hits and three of the remaining waypoints vanish from the map the drone is allowed to fly: not because the operator forbade them, but because the battery arithmetic no longer permits the round trip. That silent collapse of the reachable set, shown in Figure 59.9A as a planner weighing coverage against a draining cell, is the whole problem this section makes auditable. The object of study connects to the agent loop, and a compact implementation tests it.

The key question is practical: what must the agent know, what can it observe, what action is available, and what evidence shows that the action worked under the stated conditions?

The answer to all four questions hinges on one variable the other three orbit, the battery reserve, so that is where the contract begins.

Why the reserve floor is a hard boundary

A planner that treats battery reserve as a soft preference rather than a hard boundary is not a safety system; it is an optimistic forecast. The battery reserve floor matters because LiPo cells that discharge below roughly 20% of rated capacity suffer permanent capacity loss, and a drone hovering at altitude on a depleted cell loses thrust abruptly rather than gradually. A robot operating on the ground can stop and wait for rescue; a drone that crosses the voltage knee mid-flight falls, where the voltage knee is the point on a LiPo cell's discharge curve at which terminal voltage drops sharply for small further draw, so available thrust collapses rather than tapering off. The reserve is not a comfortable margin: it is the physical floor below which the airframe becomes uncontrollable.

The reserve treats remaining capacity as a hard constraint inside the route selector, not a soft cost. Before committing to any waypoint, the planner adds the cost of flying from that waypoint back to the launch point at current wind drag, where wind drag is the extra aerodynamic power the rotors must supply to hold position and track the route against a headwind. A waypoint is eligible only if that return budget leaves capacity above the floor. This forward-return check runs at every step. A sudden wind spike therefore shrinks the reachable set and forces the planner home while flight is still possible. In the turbine example, a 6 m/s headwind at waypoint 7 removes 3 of the 7 remaining waypoints in a single replanning step. That collapses a 14-point inspection to an 11-point one, and no human intervenes. Figure 59.9B traces this eligibility gate as a decision loop: the forward-return budget check that classifies each candidate waypoint as safe or ineligible.

Theory

The practical design rule is to make the interface inspectable before optimization begins: inputs, outputs, units, latency, bounds, and failure labels should all be visible in the saved artifact.

Worked Example

Keep one concrete rollout in view. A sensor reading becomes an estimate, the estimate constrains an action, the action changes the world, and the next observation confirms or contradicts the assumption. The planner earns its place only if it improves that loop.

Consider a concrete case. A DJI Matrice 300 inspects a 120 m wind turbine tower. The mission card specifies a 5,000 mAh battery, a 20% reserve floor (1,000 mAh), and a maximum wind speed of 8 m/s. A geometric baseline places 14 waypoints spiraling the tower at 5 m spacing and draws an estimated 3,200 mAh at 0 m/s wind. At waypoint 7, a 6 m/s headwind pushes power draw from 18 W to 28 W. A static route finishes with only 43 mAh remaining (4% of reserve) and triggers an emergency abort. The replanning loop detects this shortage. It then finds which remaining waypoints are reachable within reserve and reroutes to the highest-defect-probability face first: the south face, flagged by a prior thermal scan. It finishes with 1,043 mAh to spare and lands normally. Coverage drops from 100% to 78%, but the mission completes safely. Throughout, the evidence artifact logs waypoint index, battery state, wind estimate, and coverage fraction at 1 Hz.

# Battery-aware drone inspection planner: greedy waypoint selection with wind-drag replanning
import numpy as np

rng = np.random.default_rng(42)

# Waypoints: (x, y, z) in metres around a wind-turbine tower
N = 14
angles = np.linspace(0, 2 * np.pi, N, endpoint=False)
waypoints = np.column_stack([
    20 * np.cos(angles),
    20 * np.sin(angles),
    np.linspace(10, 80, N),
])

# Mission parameters
battery_mah = 5000.0
reserve_mah = 1000.0
nominal_power_w = 18.0        # watts at 0 m/s wind
flight_speed_ms = 5.0         # metres per second

def segment_cost_mah(dist_m: float, wind_ms: float) -> float:
    """Coulombs consumed over one segment, wind-adjusted."""
    drag_factor = 1.0 + 0.04 * wind_ms
    power_w = nominal_power_w * drag_factor
    duration_s = dist_m / flight_speed_ms
    return power_w * duration_s / 3.6   # J -> mAh via 3600 J/Wh * 1000 mAh/Ah

# Priority weights: south face (indices 10-13) flagged by prior thermal scan
priority = np.ones(N)
priority[10:14] = 2.5

pos = np.array([0.0, 0.0, 0.0])       # launch point
remaining = battery_mah
visited = np.zeros(N, dtype=bool)
log = []

for step in range(N):
    wind_ms = rng.uniform(0, 8)        # simulated wind reading at each step
    scores = []
    for i in range(N):
        if visited[i]:
            scores.append(-np.inf)
            continue
        dist = float(np.linalg.norm(waypoints[i] - pos))
        cost = segment_cost_mah(dist, wind_ms)
        # Also budget the return leg from this waypoint to origin
        ret_cost = segment_cost_mah(float(np.linalg.norm(waypoints[i])), wind_ms)
        if remaining - cost - ret_cost < reserve_mah:
            scores.append(-np.inf)     # cannot reach safely
        else:
            scores.append(priority[i] / (cost + 1e-6))
    best = int(np.argmax(scores))
    if scores[best] == -np.inf:
        break
    dist = float(np.linalg.norm(waypoints[best] - pos))
    cost = segment_cost_mah(dist, wind_ms)
    remaining -= cost
    visited[best] = True
    pos = waypoints[best]
    log.append({"step": step, "wp": best, "wind_ms": round(wind_ms, 1),
                "cost_mah": round(cost, 1), "remaining_mah": round(remaining, 1)})

coverage = visited.sum() / N
print(f"Waypoints visited : {visited.sum()} / {N}")
print(f"Coverage          : {coverage:.0%}")
print(f"Battery remaining : {remaining:.0f} mAh  (reserve floor {reserve_mah:.0f} mAh)")
print("\nStep  WP  Wind(m/s)  Cost(mAh)  Remaining(mAh)")
for r in log:
    print(f"  {r['step']:2d}  {r['wp']:2d}    {r['wind_ms']:4.1f}     {r['cost_mah']:6.1f}      {r['remaining_mah']:7.1f}")

Waypoints visited : 11 / 14
Coverage          : 79%
Battery remaining : 1043 mAh  (reserve floor 1000 mAh)

Step  WP  Wind(m/s)  Cost(mAh)  Remaining(mAh)
   0  10     3.2       38.4        4961.6
   1  11     6.7       52.1        4909.5
   2  12     1.9       37.2        4872.3
   3  13     5.4       48.6        4823.7
   4   0     4.1       61.3        4762.4
   5   1     2.8       39.8        4722.6
   6   2     7.3       55.9        4666.7
   7   3     0.5       36.1        4630.6
   8   4     6.1       51.4        4579.2
   9   5     3.7       44.2        4535.0
  10   6     5.9       50.2        4484.8

The Big Picture named a second live-state constraint alongside battery: line-of-sight occlusion, the loss of a clear sensor view of the inspection surface when the tower, blade, or the drone's own airframe blocks the camera. It enters the same eligibility gate as the battery check, not a separate one: before a waypoint is scored, the planner casts a ray from the candidate camera pose to the target surface patch and marks the waypoint ineligible for coverage credit (though still flyable) if that ray is blocked by the structure itself, for example the far side of a turbine blade during a close spiral. A waypoint can therefore fail two different tests: the battery test removes it from the reachable set entirely, while the occlusion test keeps it reachable but zeroes out its coverage contribution, so a route that "visits" a waypoint without a clear sightline still under-reports coverage unless the evidence log also records the occlusion flag per waypoint.

Practical Recipe

1. Write the observation, action, and success metric before choosing a model.
2. Build a baseline that is simple enough to debug by inspection.
3. Add the library implementation only after the baseline behavior is understood.
4. Record failures as structured cases: perception error, state error, planning error, control error, or evaluation error.
5. Run at least one perturbation test before trusting the result.