How sensing capabilities influence map quality

Most research on robot mapping focuses on developing algorithms for mapping with particular sensors, such as laser rangefinders, stereo cameras, or SONAR arrays. In this paper we instead take a broad approach and apply a single mapping algorithm to a large class of sensors with the goal of uncovering relationships between sensing capabilities and map quality. We describe a sensor model which encapsulates most of the interesting aspects of range-bearing sensors used for mapping, including sensing radius, beam width, range and bearing noise, and so on. We then apply the model to occupancy grid mapping and prove a bound on the expected error in the map, in terms of the sensor characteristics and trajectory length. In doing so, we also obtain a bound on the expected number of observations of each cell and conditions on the sensor for convergence to the correct map. We have implemented our model in simulation and we show that our bounds match the empirical results.