An Uncertainty-Driven and Observability-Based State Estimator for Nonholonomic Robots

Abstract

The problem addressed in this paper is the localisation of a mobile robot using a combination of on-board sensors and Ultra-Wideband (UWB) beacons. By using a discrete-time formulation of the system's kinematics, we identify the geometric conditions that make the system globally observable and cast the state estimation problem into the framework of least-square optimisation. The observability filter thus obtained is remarkably different from classic Bayesian filters, such as the Kalman Filter, since it does not need a-priori stochastic models of process and measurement uncertainty contributions and thus proves to have better performance than the Kalman filters if such contributions are partly unknown or differ from the expected values. A second important outcome of this work is the analytical study of the uncertainty propagation. The effectiveness of the designed filter, the validity of the theoretical analysis of estimation uncertainties and the comparisons with a state-of-the-art extended Kalman filter (EKF) are corroborated by extensive simulations and are validated experimentally.

On-Line Optimal Ranging Sensor Deployment for Robotic Exploration

“…where i,k is the ranging measurement uncertainty, usually considered as a white sequence with zero mean and variance σ 2 ρ for all the anchors. Computing the difference of the squares of the distances ∆ ij,k = ρ2 i,k − ρ2 j,k from at least three anchors and using the same solution reported in [41], it is possible to derive the robot position estimates using a Weighted Least Squares (WLS) solution as…”

“…whose explicit form is reported in [41] and holds true when the anchor positions are perfectly known a-priori, i.e., a map of the anchors is available.…”

On-line Optimal Ranging Sensor Deployment for Robotic Exploration

“…where i,k is the ranging measurement uncertainty, usually considered as a white sequence with zero mean and variance σ 2 ρ for all the anchors. Computing the difference of the squares of the distances ∆ ij,k =ρ 2 i,k −ρ 2 j,k from at least three anchors and using the same solution reported in [40], it is possible to derive the robot position estimates using a Weighted Least Squares (WLS) solution aŝ…”

Forklift Tracking: Industry 4.0 Implementation in Large-Scale Warehouses through UWB Sensor Fusion

“…However, thanks to machine learning and other techniques [43][44][45][46][47], the effect of detrimental multipath or non-line-of-sight (NLOS) conditions can be mitigated. Alternatively, multi-sensor data fusion, also known as sensor fusion, can be used to help the UWB system in the localization task, as proposed in this paper [48][49][50][51][52][53][54][55][56].…”

“…However, the installation of multiple exteroceptive sensor systems can be wasteful, in terms of time, cost, and computational burden. Therefore, the fusion of proprioceptive sensors and a single exteroceptive sensor is preferable [55,56]. Most of these kinds of schemes rely on the usage of recursive dynamic state system estimators, such as the Kalman Filter (KF) and its variants [57], or Monte Carlo estimators, such as the Particle Filter (PF) and its variants [58].…”