Robots going round the bend - A comparative study of estimators for anticipating river meanders

Marine robots and unmanned surface vehicles will increasingly be deployed in rivers and riverine environments. The structure produced by flowing waters may be exploited for purposes of estimation, planning, and control. This paper adopts a widely acknowledged model for the geometry of watercourse channels, namely sine-generated curves, as a basis for estimators that predict the shape of the yet unseen portion of the river. Predictions of this sort help a robot anticipate the future, for example, in throttling speeds as it rounds a bend. After examining how to reparameterize standard filters to incorporate this model, we compare the performance of three Gaussian filters and show that nonideality and theoretical challenges (of non-linearity, multi-modality/periodicity) degrade the performance of standard Kalman filters severely, but can be successfully mitigated by imposing an interval constraint. Thereafter, we present results of a constrained interval Kalman filter on data from three natural rivers. The results we report show the effectiveness of our method on the estimation of meander parameters. The results we report, including data from simulation, from maps, and from GPS tracks of a boat on the Colorado river, show the effectiveness of our method on the estimation of meander parameters.