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Autonomous exploration is a complex task where the robot moves through anunknown environment with the goal of mapping it. The desired output of such aprocess is a sequence of paths that efficiently and safely minimise theuncertainty of the resulting map. However, optimising over the entire space ofpossible paths is computationally intractable. Therefore, most explorationmethods relax the general problem by optimising a simpler one, for examplefinding the single next best view. In this work, we formulate exploration as avariational problem which allows us to directly optimise in the space oftrajectories using functional gradient methods, searching for the Next BestPath (NBP). We take advantage of the recently introduced Hilbert maps to devisean information-based functional that can be computed in closed-form. Theresulting trajectories are continuous and maximise safety as well as mutualinformation. In experiments we verify the ability of the proposed method tofind smooth and safe paths and compare these results with other explorationmethods.

Functional Path Optimisation for Exploration in Continuous Occupancy Maps