Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing

Table above summarizes performance over 50 laps. B-COD reaches the goal on 97.9 \% of attempts, yet spends only 42% of the energy. Collisions remain at 0.9%, essentially identical to the Always-ON baseline. Heuristic scheduling cannot match this trade-off: Greedy-OFF conserves energy (61%) but sacrifices success (47%). InfoGain-Greedy raises success to 90% yet violates risk eight times more often than B-COD. Random masks fare worse, proving that local environment context--not just a lower duty cycle--is essential for task completion. Pure-RL generates trajectories and schedules sensors from raw rasters; the high-dimensional action space makes exploration sparse, and the policy converges to risk-averse dithering--only 55% goals reached and a 22% collision rate. DESPOT-Lite, by contrast, evaluates a principled belief tree with analytic models and therefore is able to plan accurately, but it expands hundreds of nodes; the resulting 0.5s runtime renders it unusable in real-time on the vehicle.

The reliability curve shows numerical calibration (6 mean error). The reason behind the bound relaxing follows directly from what the diffusion planner is told to care about: belief shape, active sensors, and local map geometry. Call-out B (night lap, obstacle corridor): The semantic map reports obstacles--a fountain and a floating buoy. Colliding here would be mission-ending, so B-COD turns on LiDAR, night camera and IMU (high energy). The planner now expects rich pose updates and knows that centimeters of pose error matter; it shrinks the bound to 0.45 m, almost matching the 0.46 m ground truth drift. Call-out A (day lap): Tens of meters separate the ASV from any hazard. With only the IMU running (low energy), B-COD predicts pure dead-reckoning growth yet also "knows" that a meter of drift will not intersect anything. It therefore widens the bound to 1.85 m, closely tracking the ground truth 2.0 m error. These results demonstrate that u^CVaR is numerically reliable and spatially discriminative, providing the scheduler with the rich information needed to trade energy for certainty.

The table above sweeps the workspace radius from 25 m to 100 m (full lake sector). B-COD's latency is flat--10.3 +- 0.6 ms throughout—because the belief crop is always down-sampled and the UNet's receptive field is fixed; compute therefore scales with network width, not with world area. The InfoGain-Greedy baseline must update an n-cell covariance grid; its cost grows \Theta(R^{2}), reaching 23 ms at 100 m. DESPOT-Lite's branching factor of the belief tree increases with visible free space; runtime balloons to 9000 ms over the same sweep, far beyond what an embedded loop can absorb. The takeaway is practical as well as theoretical: constant-time scaling lets B-COD replan over lake-scale horizons without ever violating the real-time threshold, whereas analytic planners become the computational bottleneck well before the map reaches lake-scale.

During a daytime lap, we manually disabled the LiDAR 30 seconds before the ASV entered the narrow fountain corridor, which demands typically sub-meter localisation. B-COD's risk proxy spiked from 0.6 m to 1.8 m as soon as the loss of range data was reflected. The SA reacted on the next cycle: it re-enabled both cameras and the EXO2 sonde, accepted the high energy penalty, and drove risk down to 0.8 m. Once clear of the obstacle, the proxy dropped naturally; the scheduler shut the extra modalities off and returned to the energy-saving IMU-only sensor choice. No heuristic or fault-flag was required--the planner's calibrated variance alone drove the correct, context-specific recovery sequence.