Multi-fidelity machine learning guides adaptive exploration despite uncertain positioning

Lost but not clueless: Robotic fish maps underwater worlds while doubting its own sense of direction

Every robot that slips beneath the ocean surface trades certainty for endurance. GPS signals die within moments of a dive, and the underwater gliders prized for staying at sea for weeks must steer by dead reckoning, their sense of position drifting quietly with every meter traveled. That drift creates a paradox at the heart of autonomous exploration: a vehicle can measure the temperature, chemical pollution, or light in the water around it exquisitely well, yet have only a fuzzy idea of where each measurement belongs on the map. Engineers at Michigan State University, working with a colleague now at the Johns Hopkins University Applied Physics Laboratory, have turned that fuzziness from a liability into an organizing principle. In a study published in the journal Autonomous Robots, Demetris Coleman and colleagues taught a miniature gliding robotic fish to reconstruct a three-dimensional light field inside a large indoor tank while deliberately starved of accurate positioning, using a multi-fidelity statistical model that ranks the robot’s own data by how much it trusts itself. The payoff was dramatic: mapping errors fell to less than a quarter of those produced by conventional methods that ignore the problem.

The target of the critique is one of robotics’ favorite statistical tools. When a mobile robot must characterize a spatial field it cannot exhaustively sample, for missions ranging from search and rescue to multi-target search and environmental monitoring, it builds a surrogate model from sparse measurements, and the workhorse of that task is Gaussian process regression. A Gaussian process is fully specified by a mean function and a covariance kernel whose shape is governed by tunable hyperparameters; fed noisy measurements at known coordinates, Bayesian updating returns both a predicted value and a confidence level at every unvisited point. Those confidences are exactly what an adaptive planner needs to decide where to swim next, which is why Gaussian processes underpin so much robotic information gathering. But the mathematics carries a quiet assumption: inputs must be precise. When samples are tagged with estimated rather than true positions, predictions warp. Underwater vehicles suffer this in a particularly cruel form, because their localization uncertainty is not constant. It grows and shrinks depending on how long the robot has been submerged since its last surfacing fix, while feature-based alternatives such as simultaneous localization and mapping demand rich environments and computing power that small, energy-frugal vehicles simply do not carry.

Earlier remedies for uncertain inputs, including Monte Carlo approximations of the posterior, kernel-function expectations, and training schemes that treat input noise like output noise, typically assumed localization error stays constant, or were designed for stationary sensor networks rather than a lone robot whose uncertainty rises and falls through every dive. The team’s alternative is disarmingly simple. After each maneuver, the robot’s state estimator attaches a covariance to its position estimate, and the trace of that covariance, a single number summarizing total uncertainty, is compared against user-defined thresholds. Each measurement is then filed into one of several fidelity bins: the best-localized samples go to the highest-fidelity dataset, the most badly misplaced to the lowest. Each bin trains its own Gaussian process, and the models are coupled in a nested, auto-regressive cascade. The coarsest level builds an admittedly warped picture of the field; each higher level learns a correction to the level beneath it, anchored to its better-localized measurements; and the top level’s prediction is the final answer. Because every bin observes the same physical sensor, the authors set the scaling coefficients between levels to one. The splitting carries a bonus, too: evaluating several small models scales roughly with the sum of the cubes of their dataset sizes, which is cheaper in the worst case than one giant model trained on everything at once.

A better map is only half the problem; the robot still has to decide where to swim. The researchers paired their model with a sampling-based trajectory planner descended from rapidly-exploring information gathering algorithms, which grow a graph of candidate paths and optimize an information objective under resource constraints. Their variant adds two twists tailored to localization uncertainty. First, nodes are placed only in regions where position can be pinned down with minimal error, essentially at the surface for an underwater vehicle, while the edges between them are full three-dimensional excursions into the uncertain depths, built from feasible motion primitives such as steady glides at chosen path angles, helical spirals, flat dives, and horizontal swimming. Second, every candidate trajectory must keep its worst predicted localization uncertainty below a hard limit, on top of an energy or time budget, with an extended Kalman filter propagating position covariance along each edge. The planner can then maximize one of two objectives: the expected information gain over a grid of test points, or an ergodic metric that scores how well a trajectory’s time-averaged coverage matches a target distribution. That target is a softmax over a blend of the model’s predicted mean and its predicted uncertainty, a dial that tunes the mission between exploiting known hotspots and exploring the unknown; in these experiments the dial was set firmly toward exploration.

The platform anchoring all of this is the Miniglider, a miniature gliding robotic fish whose motion borrows more from buoyancy than from propellers. By adjusting its buoyancy and sliding an internal mass forward and backward, it glides through the water column in sawtooth paths at a fraction of the energy a swimming robot would burn, using its servo-driven tail only for low-speed maneuvers. The concept descends from pioneering autonomous gliders such as the Slocum concept of 1989 and the Spray glider, vehicles whose efficiency makes long-duration ocean missions possible precisely because they spend most of their time underwater, away from position fixes. The Miniglider’s dynamics are captured in a fifteen-state model spanning position, attitude, body-fixed velocities, the buoyancy actuator, the movable mass, and the tail angle, extended here with actuator dynamics, tail forces, and a corrected lift model, alongside an energy budget that charges the planner for every pump stroke, mass shift, and tail beat. That accounting is not decorative: it forces the planner to weigh the information value of a long glide against the cost of swimming, echoing the economics that make real ocean gliders attractive for months-long surveys.

The proving ground was a tank 4.6 meters long, 3.1 meters wide, and 1.2 meters deep, its floor and walls papered with fifteen-centimeter AprilTag fiducials. Three overhead cameras covering roughly 2.8 by 1.7 meters of the surface, together with a radio link, served as the stand-in GPS that the robot could use only when it came up for air; two tags mounted on its wings made those fixes possible. Two LED lights in the tank generated the artificial field, and the robot logged the blue-channel light intensity through its onboard color sensor at half a hertz, each reading paired with its position estimate and the growing uncertainty attached to it. A ground-truth model of the light field was assembled beforehand from about 1,100 teleoperated measurements, down-sampled by spatial density and smoothed with a Matérn kernel. The team then ran six trials of each of four strategies, single- or multi-fidelity models each driving either the information-gain or the ergodic objective, granting the planner about forty-five seconds per round and an energy budget of eighty units, doled out twenty at a time.

The scoreboard was lopsided. The single-fidelity planner that ignored localization error, treating every measurement as equally trustworthy, finished with an average weighted mean squared error of 3.803 when steered by information gain; its multi-fidelity counterpart scored 0.425. With the ergodic objective the pattern held: 2.862 for the oblivious model against 0.367 for the multi-fidelity one. In both pairings, sorting data by trust pushed the error below twenty-five percent of the baseline’s and shrank the variability across trials dramatically. The oblivious model’s failure mode is instructive. When two samples taken close together disagree because the robot misjudged where it was, a standard Gaussian process develops the geostatistical pathology known as the nugget effect, erupting into spuriously large, or even negative, predictions despite a sensor that only ever returns positive values. The multi-fidelity model makes some of the same early mistakes but can heal them: the moment a better-localized sample arrives nearby, the nested correction pulls the map back toward reality, and where no such sample exists the model simply withholds confidence. Curiously, the ergodic objective beat information gain under both models, suggesting that covering a field in proportion to its promise may guide exploration better than chasing individual measurements one at a time.

Simulations extended the result beyond the tank’s geometry. The team generated ninety synthetic datasets by replaying a reference trajectory through a ten-by-twenty-by-ten-meter volume while corrupting velocity measurements at three noise levels, then trained their model, a naive single-fidelity model, and a third baseline built to handle Gaussian input noise directly. Both uncertainty-aware approaches clearly beat the naive model, and the input-noise baseline edged out the multi-fidelity method on raw accuracy. The catch was time. On an ordinary laptop, training the input-noise baseline took roughly five to ten minutes per dataset of about two thousand points, while the multi-fidelity hyperparameters trained in seconds to a few minutes, a decisive margin on the modest computers that ride inside small, inexpensive robots. The authors also caution that the simulated positional errors stayed modest, and larger drifts of the kind real ocean gliders accumulate between surfacings may widen the gap in favor of the binned approach, which was designed precisely for those long, blind stretches.

What the study ultimately offers is a template for autonomy wherever the world’s positioning infrastructure runs out, whether under ice, in deep water, in disaster zones where GPS is jammed or absent, and in search, rescue, or pollution-tracking missions where the map must be built by a machine that cannot always know where it is. The framework asks for no new sensors; it requires only that a robot grade its own data by trust and let its planner respect that grading. The authors point to clear next steps: learning the model’s hyperparameters online during a mission, refining trajectory estimates with techniques such as motion tomography before feeding data to the map, finding principled ways to choose the number of fidelity levels, and scheduling the swing between exploration and exploitation over a mission’s lifetime. With the code released openly and the experimental evidence in hand, a robotic fish that answers “where am I?” and “what is out there?” together, while flagging which of its answers are shaky, marks a quietly radical step for machines that work where satellites cannot follow.