# Forklift Tracking: Industry 4.0 Implementation in Large-Scale Warehouses through UWB Sensor Fusion
## 2 UWB Forklift Localization Method  
### Forklift Motion Model  
In this section, we present the forklift 2D tracking method based on the integration of IMU, OFS, and UWB sensors in a sensor-fusion algorithm. The tracking method is based on the dynamic system state estimation theory and relies on an UKF estimator. A forklift is usually a heavy vehicle with relatively high inertia, and can be modeled as a rigid body with size \(L\times W\times H\), being \(L\), \(W\), \(H\) the length, width, and height of the vehicle, respectively. In this analysis, we suppose that the IMU and OFS are located at the same location, whereas the onboard UWB tag is in another location. This configuration will also be adopted in the experimental analysis in Section 4. First, we define a right-handed local reference frame \(\langle N\rangle=\{O_{n},X_{n},Y_{n},Z_{n}\}\) as the reference frame of the target area, which could be a plant or a warehouse (we will refer to \(\langle N\rangle\) as the plant/warehouse reference frame). \(O_{n}\) indicates the origin of the reference frame and \(X_{n}\), \(Y_{n}\), and \(Z_{n}\) are the \(x\)-, \(y\)- and \(z\)-axes, respectively. We define at each timestep \(k\) a body reference frame \(\langle B^{(k)}\rangle=\{O_{b}^{(k)},X_{b}^{(k)},Y_{b}^{(k)},Z_{b}^{(k)}\}\) where \(O_{b}^{(k)}\) is the origin of the reference frame, which is centered on the IMU/OFS location, whereas \(X_{b}^{(k)}\), \(Y_{b}^{(k)}\), and \(Z_{b}^{(k)}\) are the local \(x\)-, \(y\)- and \(z\)-axes at timestep \(k\), respectively. The IMU and the OFS sensor reference frames are considered oriented as the forklift body frame. The local forklift reference frame and the plant/warehouse reference frame are then linked by a rigid roto-translational transformation, which depends on the location \([x_{k},y_{k}]^{T}\) and orientation \(\theta_{k}\) of the forklift at each timestep \(k\), as described in Figure 1, where \([x_{k},y_{k}]^{T}\) corresponds with \(O_{b}^{(k)}\), and \(\theta_{k}\) is the angle between \(X_{b}^{(k)}\) and \(X_{n}\). The UWB tag has a constant displacement in the body frame, with respect to \(O_{b}^{(k)}\), which can be defined as \(\Delta\mathbf{p_{UWB}}=[\Delta x_{UIWB},\Delta y_{UIWB},\Delta z_{UIWB}]^{T}\). This offset must be translated in the plant/warehouse frame according to the estimated orientation \(\theta_{k}\). The UWB tag location is estimated through a multilateration algorithm, which is supposed to involve a maximum of four UWB anchors at once, as the case of the experimental analysis. Without loss of generality, we suppose that the UWB system measures each UWB tag coordinate with an additive white Gaussian error with zero-mean value and standard deviation \(\sigma_{UIWB}\), namely \(v_{x_{k}}\sim\mathcal{N}(0,\,\sigma_{UIWB}^{2})\), and \(v_{y_{k}}\sim\mathcal{N}(0,\,\sigma_{UIWB}^{2})\) for the \(x\)- and \(y\)-coordinates, respectively. The noise standard deviation \(\sigma_{UIWB}\) increases when the tag anchor distance increases due to a lower signal quality. However, as it will be shown in the experimental-analysis section, the anchors are attached at the ceiling, and the forklift is  
Figure 1: Schematic representation of the RFID Smart Forklift equipped with IMU, OFS, and UWB tag along with the plant/warehouse reference frame and the local body frame. constrained to travel in such a way that the distances of the four closest UWB anchors are always similar; consequently, the noise parameters can be considered as constant. The onboard sensors measure kinematic quantities with respect to the body frame. In particular, since the forklift is constrained to move on the ground, we consider the 2D acceleration \(\mathbf{a_{k}}=[a_{x_{k}},a_{y_{k}}]^{T}\), the angular speed \(\omega_{k}\), and the 2D forklift velocity \(\mathbf{v_{k}}=[v_{x_{k}},v_{y_{k}}]^{T}\).