A biologically inspired controller to solve the coverage problem in robotics

The coverage problem consists on computing a path or trajectory for a robot to pass over all the points in some free area and has applications ranging from floor cleaning to demining. Coverage is solved as a planning problem -- providing theoretical validation of the solution -- or through heuristic techniques which rely on experimental validation. Through a combination of theoretical results and simulations, this paper presents a novel solution to the coverage problem that exploits the chaotic behaviour of a simple biologically inspired motion controller, the Braitenberg vehicle 2b. Although chaos has been used for coverage, our approach has much less restrictive assumptions about the environment and can be implemented using on-board sensors. First, we prove theoretically that this vehicle - a well known model of animal tropotaxis - behaves as a charge in an electro-magnetic field. The motion equations can be reduced to a Hamiltonian system, and, therefore the vehicle follows quasi-periodic or chaotic trajectories, which pass arbitrarily close to any point in the work-space, i.e. it solves the coverage problem. Secondly, through a set of extensive simulations, we show that the trajectories cover regions of bounded workspaces, and full coverage is achieved when the perceptual range of the vehicle is short. We compare the performance of this new approach with different types of random motion controllers in the same bounded environments.