Robot Vacuum Coverage Path Planning

Coverage Algorithm

Robot speed 1.4 m/s

Furniture count 6

Live Readouts

Floor covered

0.0%

Elapsed time

0.0 s

Distance travelled

0.0 m

How it works

Coverage path planning (CPP) is the problem of choosing a route that passes over every reachable point of a floor, not just one that gets from A to B. Two classic strategies:

Boustrophedon ("ox-turning", lawnmower):
  sweep a lane in +x until wall/obstacle,
  step sideways by ~2r, flip direction, repeat.
  Coverage grows almost linearly:
    C(t) ≈ min(1, v·t / A_free) · (lane efficiency)

Random bounce:
  velocity fixed until a collision, then a new
  random heading is chosen (angle of incidence
  ≠ angle of reflection in general).
  Coverage grows like a "coupon collector":
    C(t) ≈ 1 − e^(−k·v·t / A_free)

Boustrophedon revisits almost no cell twice, so distance travelled per % covered stays low and coverage approaches 100% in finite time — this is how modern LIDAR/vSLAM-mapped robot vacuums (Roborock, Neato, newer Roombas) plan.
Random bounce is cheap to implement with no map at all (bump sensor + gyro only, classic early Roomba), but by the coupon-collector effect the last few percent of floor take disproportionately long — coverage asymptotically approaches but rarely reaches 100%.
The right stat panel plots this directly: watch distance travelled per point of coverage % — boustrophedon stays roughly flat, random bounce keeps climbing as it re-visits already-clean cells.
Furniture legs and low obstacles are excluded from the coverable area on both strategies, exactly as a real robot treats them as no-go cells.

✓ Sweep complete

Uncleaned floor Cleaned floor Furniture (no-go)

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