Operating regimes of quarter-turn-aware frontier-based coverage path planning

Introduction The practical question in turn-aware coverage planning is when reduced angular travel compensates for extra distance and overlap. Methods We study that question with TURN-F, a deliberately simple deterministic frontier planner that searches cell–heading states and charges angular travel in 90 ° units. Its normalized motion-cost index is J β = L + β Q , where L is path length, Q is the number of quarter turns, and β exposes grid pitch, platform speed, and a rotation-to-translation power ratio; it is not measured battery energy. The main evaluation combines 178 public layouts, 4 distance-only baselines, and 2 heuristic turn-aware comparators re-planned at every β . Results At β = 1 , TURN-F reduces quarter turns by 21.2% relative to GREEDY but travels 6.1% farther and increases overlap from 0.154 to 0.192, yielding a small 1.25% mean advantage (108 wins in 178 grids) that the rank-based post hoc test does not separate. A β = 0 same-code control provides no detectable evidence that state representation or tie-breaking explains that advantage ( + 0.18 % in J 1 , 95% CI [ − 0.22 , 0.56 ] % , p = 0.20 ). The corpus-mean crossing is β * = 0.82 (grid-bootstrap 95% interval 0.74–0.89). For β > 0 , an exploratory geometry-conditioned model improves grouped-CV prediction over a β -only model, but leave-one-family-out validation fails on HouseExpo, and calibration varies by family. On 20 seeded-random non-overlapping windows from five real-robot laser logs, TURN-F is 3.21% lower at β = 1 (17 wins); the five-source test is statistically inconclusive