Optimal placement of passive sensors for robot localisation

We consider the problem of self-localisation for a mobile robot in an environment with a requested level of accuracy. The robot moves in a known environment following typical trajectories, which can be characterised in statistical terms. One of the main drivers of this paper is its application to assistive robots guiding senior or impaired users in shopping centres or in other public spaces. To localise itself the robot uses onboard sensors such as encoders and inertial platforms. The level of noise in these sensors and the lack of absolute measurements determines a steady growth of the uncertainty on its position. To alleviate the problem, we assume the presence of a number of visual markers deployed in the environment. Whenever the robot comes across one of these sensors, the uncertainty on its position is reset. In the paper, we show a methodology to minimise the number of these sensors and to select their position so that the uncertainty is never worse than a given target threshold with an assigned probability.