State estimation for robots with complementary redundant sensors

In this paper, robots equipped with two complementary typologies of redundant sensors are considered: one typology provides sharp measures of some geometrical entity related to the robot pose (e.g., distance or angle) but is not univocally associated with this quantity; the other typology is univocal but is characterized by a low level of precision. A technique is proposed to properly combine these two kinds of measurement both in a stochastic and in a deterministic context. This framework may occur in robotics, for example, when the distance from a known landmark is detected by two different sensors, one based on the signal strength or time of flight of the signal, while the other one measures the phase-shift of the signal, which has a sharp but periodical dependence on the robot-landmark distance. In the stochastic case, an effective solution is a two-stage extended Kalman filter (EKF) which exploits the precise periodic signal only when the estimate of the robot position is sufficiently precise. In the deterministic setting, an approach based on a switching hybrid observer is proposed, and results are analyzed via simulation examples.